EAPSI: Comparison of Two Different Geometric Techniques for Computing Chemical Reaction Rates

Sattari Sulimon, Merced CA

Investigators

Abstract

Computing chemical reaction rates is a difficult task, especially in complex chemical systems such as combustion. Geometric techniques are promising techniques which use a lower-dimensional slice of the system to estimate the chemical reaction rate. For this project, the researcher will compare two geometric techniques for computing chemical reaction rates called lobe dynamics and transition state theory. The PI will collaborate with Hokkaido University professor Tamiki Komatsuzaki, who is a noted expert on using transition state theory to compute chemical reaction rates. In comparing the two techniques, the PI hopes to help narrow down when each technique should be used to obtain accurate chemical reaction rates. The ionization of hydrogen in external fields resembles a chemical reaction. The atom is injected with some energy, and, if it overcomes a certain threshold, it becomes ionized. The ionization rate can be computed by integrating a representative set of trajectories. For reaction systems with multiple reactants and products, chaos makes it difficult to adequately sample the phase space and accurately compute the reaction rate. Transition state theory and homotopic lobe dynamics are both promising methods for computing reaction rates in chaotic systems, but both methods have their benefits and limitations. Transition state theory computes the reaction rate using a flux across a lower-dimensional surface, requiring fewer trajectories. It assumes, however, that a non-recrossing transition state exists in the system, which does not hold in general. Homotopic lobe dynamics uses the topology of phase space structures to characterize and compute periodic orbits, and then periodic orbit theory is used to compute the reaction rate as a sum over their contributions. The goals of this research are to compare the ranges of validity and computational feasibility of the two methods, and to compute the ionization reaction rate of the hydrogen atom in parallel fields over a wide range of field strengths. This award under the East Asia and Pacific Summer Institutes program supports summer research by a U.S. graduate student and is jointly funded by NSF and the Japan Society for the Promotion of Science.