Collision Efficiency of Water in the Unimolecular Reaction CH₄ (+H₂O) ⇆ CH₃ + H (+H₂O): One-Dimensional and Two-Dimensional Solutions of the Low-Pressure-Limit Master Equation

The low-pressure-limit unimolecular decomposition of methane, CH₄ (+M) ⇆ CH₃ + H (+M), is characterized via low-order moments of the total energy, E, and angular momentum, J, transferred due to collisions. The low-order moments are calculated using ensembles of classical trajectories, with new direct dynamics results for M = H₂O and new results for M = O₂ compared with previous results for several typical atomic (M = He, Ne, Ar, Kr) and diatomic (M = H₂ and N₂) bath gases and one polyatomic bath gas, M = CH₄. The calculated moments are used to parametrize three different models of the energy transfer function, from which low-pressure-limit rate coefficients for dissociation, k₀, are calculated. Both one-dimensional and two-dimensional collisional energy transfer models are considered. The collision efficiency for M = H₂O relative to the other bath gases (defined as the ratio of low-pressure limit rate coefficients) is found to depend on temperature, with, e.g., k₀(H₂O)/k₀(Ar) = 7 at 2000 K but only 3 at 300 K. We also consider the rotational collision efficiency of the various baths. Water is the only bath gas found to fully equilibrate rotations, and only at temperatures below 1000 K. At elevated temperatures, the kinetic effect of “weak-collider-in-J” collisions is found to be small. At room temperature, however, the use of an explicitly two-dimensional master equation model that includes weak-collider-in-J effects predicts smaller rate coefficients by 50% relative to the use of a statistical model for rotations. The accuracies of several methods for predicting relative collision efficiencies that do not require solving the master equation and that are based on the calculated low-order moments are tested. Troe’s weak collider efficiency, β_c, includes the effect of saturation of collision outcomes above threshold and accurately predicts the relative collision efficiencies of the nine baths. Finally, a brief discussion is presented of mechanistic details of the energy transfer process, as inferred from the trajectories.