Temperature dependence of a vibrational exciton: Some methyl motions of durene

An intramolecular vibrational frequency in a molecular crystal has been found to show a significant temperature dependence. The low lying intramolecular mode at 272 cm^-1 (room temperature value) of durene-h₁₄ (and the corresponding durene-d₁₄ frequency at 242 cm^-1) shows an increase of ∼9 cm^-1 in frequency in going from room temperature to 100°K. A theoretical discussion is presented on the role of various interactions that may give rise to the temperature dependence of the intramolecular mode. The theoretical considerations suggest that, although the thermal expansion of the lattice may be contributing to this temperature dependence, the dominant contribution is due to the cubic anharmonic interactions involving methyl torsions. It is suggested that in complex molecular crystals, where there are some very low lying intramolecular modes, the distinction between lattice modes and intramolecular modes based on the criterion that only lattice modes show frequency shift with temperature may be misleading. In such cases our mixed crystal criterion that the phonons obey the amalgamation limit in isotopic (H-D) mixed crystals, whereas intramolecular vibrations are in the separated band limit, should be more reliable. This is clearly demonstrated in the case of durene.