Collision Frequency for Energy Transfer in Unimolecular Reactions

Abstract

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.

“Third‐body” collision parameters for hydrocarbons, alcohols, and hydroperoxides and an effective internal rotor approach for estimating them

“…The computation of = ⟨ΔE d ⟩ using our classical trajectory code DiNT 76 involves several steps, and our approach 22,55,67 is similar to approaches used by other groups. [38][39][40][41]77 Briefly, the unimolecular reactant A is prepared with a fixed class-dependent initial total energy E' representative of typical dissociation energies (here, 95 kcal/mol for alkanes, 90 kcal/mol for alcohols, and 45 kcal/mol for hydroperoxides) and an initial rotational state J' selected from an independent thermal distribution at the temperature T of interest. As in Ref.…”

“…23–32 and the recent review from Lendvay 33 ) as well as quantum mechanical scattering predictions of transport properties, 34–37 and it is similar to ongoing work from several groups (eg, Refs. 38–41).…”

Quantum chemical and master equation study of OH + CH2O → H2O + CHO reaction rates in supercritical CO2 environment

“…The energy grain size used was set to default value of 100 cm −1 , which typically gives converged results for combustion reactions . Collisional energy transfer probability was estimated using exponential‐down model . Collision frequency was estimated by assuming the Lennard–Jones (LJ) potential.…”

“…44 Collisional energy transfer probability was estimated using exponential-down model. 45 Collision frequency was estimated by assuming the Lennard-Jones (LJ) potential. The LJ parameters for the R1 reactive system were taken to be identical to those of CO 2 ( = 3.94Å and /k B = 201 K).…”

Identification of molecular cluster evaporation rates, cluster formation enthalpies and entropies by Monte Carlo method

“…Even when the atmospheric cluster distribution can be accurately deduced from experimental data, this does not quantify the individual kinetic parameters, such as the cluster collision and evaporation rates (Kupiainen-Määttä (2016)). Collision rates may be computed from kinetic gas theory or classical trajectory simulations with reasonable accuracy (Matsugi (2018)), although recent research has shown that long-range attractive interactions may enhance collision rates (Yang et al (2018)), for example by around a factor of 2-3 for H2SO4-H2SO4 collisions (Halonen et al (2019)). These relatively minor uncertainties in the collision rates are dwarfed by the error margins of cluster evaporation rates.…”