Two-phonon infrared absorption spectra in crystalline carbon dioxide

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 ${\nu }_3{\mathrm{+\nu }}_1{\mathrm{,\nu }}_3{\text{+2ν}}_2\text{\hspace{0.17em}(3600\hspace{0.17em}}{\mathrm{cm}}^{\text{−1}})$ and ${\nu }_2{\mathrm{+\nu }}_1{\mathrm{,\nu }}_2{\text{+2ν}}_2\text{\hspace{0.17em}(2000\hspace{0.17em}}{\mathrm{cm}}^{\text{−1}})$ regions are calculated and are in reasonable agreement with experiment.