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A theory of two-phonon states appropriate to vibrational excitations in molecular crystals is presented. ``Phonon'' is taken to mean any vibrational excitation, external or internal to the molecules of the crystal. The theory includes general values of the wave vector. Possible mechanisms for the interaction of the two-phonon states with radiation are considered and expressions for the intensity of infrared absorption developed. Experimental results are presented for infrared absorption measurements on thin and thick films of polycrystalline carbon dioxide at low temperature. Transitions involving molecular fundamentals of the major constituent (12CO2) and of isotopic impurities and involving two- or multiphonon absorption are observed. The latter include transitions to states involving simultaneous excitation of two internal vibrations as well as excitation of one internal and one lattice vibration. Dispersion curves and densities of states are obtained for two internal molecular fundamentals coupled by dipole-dipole interactions, and comparison with one-phonon transition regions is made. Two-phonon densities of states and intensities of absorption to continua in the ν3+ν1,ν3+2ν2 (3600 cm−1) and ν2+ν1,ν2+2ν2 (2000 cm−1) regions are calculated and are in reasonable agreement with experiment.

Articles you may be interested inTemperature dependence of the vibrational relaxation processes in natural and isotopically pure 32S8: Effect of the isotopic impurities on infrared phonon lifetimes

Infrared studies of HN3 and DN3 in the gas and solid phases and of HN3 in CCl4 solutions are presented. The two low-frequency skeletal bending modes are identified, permitting calculation of the thermodynamic properties of hydrazoic acid. Hydrogen bonding of HN3 and DN3 in the solid state is indicated by frequency shifts of the NH and ND stretching motions (216 and 151 cm—1, respectively). No evidence of hydrogen bonding was observed in solutions of HN3 in CCl4 at concentrations up to 0.3 M. An irreversible phase transition is observed on warming solid hydrazoic acid above about 120°K.