On the relation between collinear and three dimensional collision rates with applications to vibrational energy transfer

A simplistic procedure for the generation of three dimensional rate constants is introduced and applied to vibrational energy transfer. The method is based on correcting for the different volumes in phase spaceavailable to the products of a collinear and a 3-D collision. Explicit expressions are derived for the 3-D distribution of final vibrational states and the effect of reagent vibrational excitation on the rate for collisions where the initial translational (and rotational) energy is thermally distributed. The procedure is applied to an exactly soluble collinear model of vibrational excitation. The resulting 3-D detailed rate constants are shown to correspond to an exponential decay of the bulk mean vibrational energy. The temperature dependence of the rates is compared to experimental results for the He-CO, Ar-HCl, He-HCl, and He-H₂ systems. A surprisal analysis of the rates conforms to an "exponential gap" representation.