Calculation and use of total collision rates in thermal systems

Durant, J. L.; Kaufman, F.

doi:10.1016/0009-2614(87)80931-4

Cited by 21 publications

(27 citation statements)

References 20 publications

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“…Because of concern about the proper choice of k coll and normalization of the stepsize distribution (see later), MultiWell provides an option for utilizing the total collision rate constant, which can be estimated from Lennard-Jones parameters [46]. Since it is expected that the fraction of inelastic collisions is small at low energy (see earlier) and cannot exceed unity at high energies, the following heuristic function has been included as an option in MultiWell:…”

Section: Collisionsmentioning

confidence: 99%

Multiple‐Well, multiple‐path unimolecular reaction systems. I. MultiWell computer program suite

Barker

2001

Int J of Chemical Kinetics

558

579

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Unimolecular reaction systems in which multiple isomers undergo simultaneous reactions via multiple decomposition reactions and multiple isomerization reactions are of fundamental interest in chemical kinetics. The computer program suite described here can be used to treat such coupled systems, including the effects of collisional energy transfer (weak collisions). The program suite consists of MultiWell, which solves the internal energy master equation for complex unimolecular reactions systems; DenSum, which calculates sums and densities of states by an exact-count method; MomInert, which calculates external principal moments of inertia and internal rotation reduced moments of inertia; and Thermo, which calculates equilibrium constants and other thermodynamics quantities. MultiWell utilizes a hybrid master equation approach, which performs like an energy-grained master equation at low energies and a continuum master equation in the vibrational quasicontinuum. An adaptation of Gillespie's exact stochastic method is used for the solution. The codes are designed for ease of use. Details are presented of various methods for treating weak collisions with virtually any desired collision step-size distribution and for utilizing RRKM theory for specific unimolecular rate constants.

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Section: Collisionsmentioning

confidence: 99%

Multiple‐Well, multiple‐path unimolecular reaction systems. I. MultiWell computer program suite

Barker

2001

Int J of Chemical Kinetics

558

579

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“…The present study deals with an issue that relates to collision frequencies (or total collision rate constants). ,− This issue has been discussed several times in the literature but seems to have long been postponed as the empirical approaches adopted so far to address the energy transfer process have obscured its physical importance. The energy transfer kernel appears in the two-dimensional master equation as R ( E , J ; E ′, J ′), which is the bimolecular rate coefficient for collisional transitions from the initial (pre-collision) energy and angular momentum ( E ′, J ′) to the final (post-collision) energy and angular momentum ( E , J ).…”

Section: Introductionmentioning

confidence: 99%

Collision Frequency for Energy Transfer in Unimolecular Reactions

Matsugi

2018

J. Phys. Chem. A

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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.

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“…Because the normalization constant does not exist if there are no states, empty energy grains are omitted when evaluating Eq. (18). Thus, ρ(j ) is always >0, no singularities are possible, and the normalization constant N (y) = N d (y) + N u (y) is greater than zero and absolutely stable.…”

Section: Revisions To the Normalization Algorithmmentioning

confidence: 88%

“…Since the same density of states is used in the detailed balance expression for inelastic collisions, the energy transfer parameters refer to the active energy and not to pure vibrational or rotational transitions. In most cases, the collision frequency for changing the active energy has been estimated by assuming Lennard–Jones forces between the collision partners, but it is well known that the total collision frequency is much larger 18,19. In fact, even the collision frequency for pure rotationally inelastic collisions is much larger 20.…”

Section: Introductionmentioning

confidence: 99%

Energy transfer in master equation simulations: A new approach

Barker

2009

Int J of Chemical Kinetics

247

203

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Collisional energy transfer plays a key role in recombination, unimolecular, and chemical activation reactions. For master equation simulations of such reaction systems, it is conventionally assumed that the rate constant for inelastic energy transfer collisions is independent of the excitation energy. However, numerical instabilities and nonphysical results are encountered when normalizing the collision step-size distribution in the sparse density of states regime at low energies. It is argued here that the conventional assumption is not correct, and it is shown that the numerical problems and nonphysical results are eliminated by making a plausible assumption about the energy dependence of the rate coefficient for inelastic collisions. The new assumption produces a model that is more physically realistic for any reasonable choice of collision step-size distribution, but more work remains to be done. The resulting numerical algorithm is stable and noniterative. Testing shows that overall accuracy in master equation simulations is better with this new approach than with the conventional one. This new approach is appropriate for all energy-grained master equation formulations.

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Calculation and use of total collision rates in thermal systems

Cited by 21 publications

References 20 publications

Multiple‐Well, multiple‐path unimolecular reaction systems. I. MultiWell computer program suite

Multiple‐Well, multiple‐path unimolecular reaction systems. I. MultiWell computer program suite

Collision Frequency for Energy Transfer in Unimolecular Reactions

Energy transfer in master equation simulations: A new approach

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