Collisional energy transfer in highly excited molecules: Calculations of the dependence on temperature and internal, rotational, and translational energy

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Classical trajectory calculations of the rate of collisional energy transfer between a bath gas and a highly excited polyatomic method, and the average energy transferred per collision, as functions of the bath gas translational energy and temperature, are reported. The method used is that of Lim and Gilbert [J. Phys. Chem. 94, 72 (1990)], which requires only about 500 trajectories for convergence, and generates extensive data on the collisional energy transfer between Xe and azulene, as a function of temperature, initial relative translational energy (E′T), and azulene initial internal energy (E′). The observed behavior can be explained qualitatively in terms of the Xe interacting in a chattering collision with a few substrate atoms, with the collision duration being much too brief to permit ergodicity but with a general tendency to transfer energy from hotter to colder modes (both internal and translational). At thermal energies, trajectory and experimental data show that the root-mean-squared energy transfer per collision, 〈ΔE2〉1/2, is relatively less dependent on E′ than the mean energy transfer 〈ΔE〉. The calculated temperature dependence is weak: 〈ΔE2〉1/2∝T0.3, corresponding to 〈ΔEdown〉∝T0.23. Values for the calculated average rotational energy transferred per collision (data currently only available from trajectories, and required for falloff calculations for radical–radical and ion-molecule reactions) are of the order of kBT, and similar to those for the internal energy; there is extensive collision-induced internal-rotational energy transfer. The biased random walk ‘‘model B,’’ as discussed in text, is found to be in accord with much of the trajectory data and with experiment. This suggests that energy transfer is through pseudorandom multiple interactions between the bath gas and a few reactant atoms; the ‘‘kick’’ given by the force at the turning point of each atom–atom encounter governs the amount of energy transferred. Moreover, a highly simplified version of this model explains why average energies transferred per collision for simple bath gases have the order-of-magnitude values seen experimentally, an explanation which has not been provided hitherto.