Collision Frequency for Energy Transfer in Unimolecular Reactions

Pressure dependence of unimolecular reaction rates is governed by the energy transfer in collisions of reactants with bath gas molecules. Pressure-dependent rate constants can be theoretically determined by solving master equations for unimolecular reactions. In general, master equation formulations describe energy transfer processes using a collision frequency and a probability distribution model of the energy transferred per collision. The present study proposes a novel method for determining the collision frequency from the results of classical trajectory calculations. Classical trajectories for collisions of several polyatomic molecules (ethane, methane, tetrafluoromethane, and cyclohexane) with monatomic colliders (Ar, Kr, and Xe) were calculated on potential energy surfaces described by the third-order density-functional tight-binding method in combination with simple pairwise interaction potentials. Low-order (including non-integer-order) moments of the energy transferred in deactivating collisions were extracted from the trajectories and compared with those derived using some probability distribution models. The comparison demonstrates the inadequacy of the conventional Lennard-Jones collision model for representing the collision frequency and suggests a robust method for evaluating the collision frequency that is consistent with a given probability distribution model, such as the exponential-down model. The resulting collision frequencies for the exponential-down model are substantially higher than the Lennard-Jones collision frequencies and are close to the (hypothetical) capture rate constants for dispersion interactions. The practical adequacy of the exponential-down model is also briefly discussed.