A model for ultrafast vibrational cooling in molecular crystals

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Abstract
A model is presented to describe vibrational cooling (VC) in crystals of large molecules. Vibrational cooling is the process by which a vibrationally excited crystal returns to the ground state. This process may consist of many sequential and parallel vibrational relaxation (VR) steps. The model describes a highly excited, vibrationally dense molecular crystal at zero and finite temperatures. An initially excited vibration relaxes via anharmonic coupling by sequential emission of many lattice phonons until all vibrational energy is destroyed. The time evolution of vibrational excitation probability is described with a Master equation. Various models for the phonon density of states, which exerts primary control over the VR process, are considered. It is found that VC occurs on a much slower time scale than VR, and that the rate of VC is only weakly dependent on temperature, even in systems where VR is highly temperature dependent. An important conclusion of this work is that vibrational cooling is described by an ensemble averaged vibrational population distribution function which moves to lower energy states and broadens as time increases. The motion to lower energy is described by a ‘‘vibrational velocity’’ (emitted energy per unit time) which is independent of temperature, while the width of the distribution increases with increasing temperature. The model is then used to calculate experimental observables including time resolved absorbance, emission, and Raman scattering following excitation of a high frequency vibration.