Energy transfer in master equation simulations: A new approach

TLDR

Collisional energy transfer is crucial in recombination, unimolecular, and activation reactions, yet master equation simulations conventionally assume the inelastic collision rate constant is independent of excitation energy, a simplification that limits applicability across all energy‑grained formulations. The study proposes that the inelastic collision rate constant depends on excitation energy, demonstrating that this assumption removes numerical instabilities and nonphysical results in master equation simulations. The resulting model yields a physically realistic, stable, noniterative algorithm that improves overall accuracy compared to the conventional approach, though further work is needed. © 2009 Wiley Periodicals, Inc., Int J Chem Kinet 41:748–763, 2009.

Abstract

Abstract 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. © 2009 Wiley Periodicals, Inc. Int J Chem Kinet 41: 748–763, 2009