Modeling Collisional Transitions in Thermal Unimolecular Reactions: Successive Trajectories and Two-Dimensional Master Equation for Trifluoromethane Decomposition in an Argon Bath

Abstract

Collisional transition processes in thermal unimolecular reactions are modeled by collision frequency, Z, and probability distribution function, P(E, J; E′, J′), which describes the probabilities of collisional transitions from the initial state specified by the total energy and angular momentum, (E′, J′), to the final states, (E, J). The validity of the collisional transition model, consisting of Z and P(E, J; E′, J′), is assessed here for the title reaction. The present model and its parameters are derived from the moments of transition probabilities calculated by classical trajectory simulations. The model explicitly accounts for coupling between the energy and angular momentum transfer and the dependence of transition probability on the initial state. The performance of the model is evaluated by comparing the rate constants calculated by solving the two-dimensional master equation with those obtained from the classical trajectory calculations of the sequence of successive collisions. The rate constants are also compared with available experimental data. The present collisional transition model is found to perform fairly well for predicting the pressure-dependent rate constants. The uncertainty in the prediction and sensitivities of the rate constants to the model parameters are discussed. A simplified version of the model is proposed, which performs as well as the full model. The simplifications and robust procedures for calculating the model parameters are described.

Two-Dimensional Master Equation Modeling of Some Multichannel Unimolecular Reactions

“…where x is a column vector representing the molecular population and A is a transition matrix whose elements contain the collisional transition and reaction rates. 14 The solution can be obtained by solving the following steady-state problem where k is the total thermal decomposition rate constant and g represents the normalized steady-state population distribution, g(E,J). This problem can be solved by, for example, the inverse iteration method.…”

“…This problem can be solved by, for example, the inverse iteration method. 14 The channel-specific thermal rate constant for the ith channel, k i , is obtained as…”

“…Batches of 10000 collisional trajectories were run for each molecule at each temperature. Because the unimolecular kinetics is expected to be sensitive only to collisional transition rates near the reaction threshold, 14 the initial total energies were set to be close to the threshold energies: E′ = 120 kJ mol −1 for the n-propyl, 1-pentyl, and 2-pentyl radicals and E′ = 400 kJ mol −1 for toluene.…”

“…The collisional transition model for the two-dimensional master equation used in this study has the following form 14,54…”

“…In a recent study by the present author, a method for deriving a plausible collisional transition model from trajectory calculations was developed. 14 This method utilizes the energy and angular-momentum transfer moments calculated from collisional trajectories to obtain the collision frequency and parameters of the probability function, incorporating all of the angular-momentum effects mentioned above. In this study, this method is applied to the collisional transition processes of npropyl radicals, 1-and 2-pentyl radicals, and toluene in an argon bath.…”