Theory of ultrahot molecular solids: Vibrational cooling and shock-induced multiphonon up pumping in crystalline naphthalene

A new method is presented for calculating ultrafast vibrational energy redistribution in anharmonic solids composed of large molecules. It is an improvement over the previous weak coupling model of Hill and Dlott [J. Chem. Phys. 89, 842 (1988)] because the emitted phonons are now allowed to act back on the excited vibrations. The model is used to investigate the dynamics of ‘‘ultrahot’’ molecular solids, materials with enormous levels of vibrational or phonon excitation. Ultrahot solids are produced in laser ablation and shock-induced detonation. Using model parameters for crystalline naphthalene, we investigate multiphonon up pumping after a 40 kbar shock and vibrational cooling after strong excitation of a high frequency vibrational fundamental. In both processes, the phonons attain a state of internal equilibrium characterized by a time-dependent phonon quasitemperature θp(t) within a few ps. Energy redistribution among the phonons is efficient because phonons are more anharmonic than molecular vibrations. In up pumping, there is a large excess of phonons at t=0, which decreases as vibrations are pumped by phonons. Under these conditions, the rates of anharmonic scattering processes are maximum at t=0 and the lower levels of the ladder of molecular vibrations are pumped before the higher levels. The vibrational population distribution then rapidly attains an approximate state of quasiequilibrium, characterized by a vibrational quasitemperature θv(t). Thermal equilibrium where θp(t) = θv(t) is achieved in ∼100 ps. In vibrational cooling, there is initially a large excess of high frequency vibrations and few phonons. Because phonons accumulate as the vibrations cool, the rates of anharmonic scattering processes are a minimum at t=0. Under these conditions, the vibrations are far from a state of quasiequilibrium until thermal equilibrium is attained at ∼1 ns.