Vibrational relaxation and vibrational cooling in low temperature molecular crystals

The processes of vibrational relaxation (VR) and vibrational cooling (VC) are investigated in low temperature crystals of complex molecules, specifically benzene, naphthalene, anthracene, and durene. In the VR process, a vibration is deexcited, while VC consists of many sequential and parallel VR steps which return the crystal to thermal equilibrium. A theoretical model is developed which relates the VR rate to the excess vibrational energy, the molecular structure, and the crystal structure. Specific relations are derived for the vibrational lifetime T₁ in each of three regimes of excess vibrational energy. The regimes are the following: Low frequency regime I where VR occurs by emission of two phonons, intermediate frequency regime II where VR occurs by emission of one phonon and one vibration, and high frequency regime III where VR occurs by evolution into a dense bath of vibrational combinations. The VR rate in each regime depends on a particular multiphonon density of states and a few averaged anharmonic coefficients. The appropriate densities of states are calculated from spectroscopic data, and together with available VR data and new infrared and ps Raman data, the values of the anharmonic coefficients are determined for each material. The relationship between these parameters and the material properties is discussed. We then describe VC in a master equation formalism. The transition rate matrix for naphthalene is found using the empirically determined parameters of the above model, and the time dependent redistribution in each mode is calculated.