Vibrational energy transfer in molecular collisions: An information theoretic analysis and synthesis

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Abstract
State‐to‐state rate constants for vibrational energy transfer (both V–V and V–T) are characterized using an ’’exponential gap’’ representation. The collisions analyzed include experimental results for both V–T and V–V transfer rates, trajectory computations for V–T transfer rates (via both inelastic and reactive, atom exchange, collisions) and quantal computations for V–V transfer rates. The results are analyzed in terms of the surprisal, a measure of deviation of the actual rate from the prior (or reference) rate. The prior rates are computed on the basis of the assumption that (at a given collision energy) all final states are equally probable. For almost all cases the surprisal could be characterized by a single parameter. The magnitude of this parameter (and its temperature dependence) could be predicted using bulk averages only. Such predictions are demonstrated for both experimental and trajectory computed rates. The link between the microscopic dynamics and macroscopic kinetics is forged by the use of sum rules (which provide constraints on the rates) and of the principle of maximal entropy (which is used to determine the least biased set of rate constants subject to the constraints).