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

计算化学反应速率是一项困难的任务，特别是在复杂的化学系统，如燃烧。几何技术是一种很有前途的技术，它利用系统的低维切片来估计化学反应速率。在这个项目中，研究人员将比较计算化学反应速率的两种几何技术，即叶状动力学和过渡态理论。PI将与北海道大学教授小松崎Tamiki Komatsuzaki合作，他是使用过渡态理论计算化学反应速率的知名专家。通过比较这两种技术，PI希望能够帮助缩小每种技术在获得精确化学反应速率时的应用范围。氢在外场中的电离类似于化学反应。原子被注入一些能量，如果它超过一定的阈值，它就会被电离。电离率可以通过对一组有代表性的轨迹进行积分来计算。对于具有多种反应物和生成物的反应系统，混沌使得相空间的充分采样和反应速率的精确计算变得困难。过渡态理论和同伦叶动力学都是计算混沌系统反应速率的有前途的方法，但两种方法都有各自的优点和局限性。过渡态理论通过低维表面的通量来计算反应速率，需要更少的轨迹。然而，它假设系统中存在非交叉的过渡状态，这通常是不成立的。同伦叶瓣动力学利用相空间结构的拓扑结构来表征和计算周期轨道，然后利用周期轨道理论计算反应速率。本研究的目的是比较两种方法的有效性范围和计算可行性，并计算在宽场强范围内平行场中氢原子的电离反应速率。该奖项隶属于东亚和太平洋暑期研究所项目，由美国国家科学基金会和日本科学促进会共同资助，支持一名美国研究生进行暑期研究。

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.