Nagahata Yutaka, Hernandez Rigoberto, Komatsuzaki Tamiki
Department of Chemistry, Johns Hopkins University, Baltimore, Maryland 21218, USA.
Research Center of Mathematics for Social Creativity, Research Institute for Electronic Science, Hokkaido University, Kita 20 Nishi 10, Kita-ku, Sapporo 001-0 020, Japan.
J Chem Phys. 2021 Dec 7;155(21):210901. doi: 10.1063/5.0059618.
The complexity of gas and condensed phase chemical reactions has generally been uncovered either approximately through transition state theories or exactly through (analytic or computational) integration of trajectories. These approaches can be improved by recognizing that the dynamics and associated geometric structures exist in phase space, ensuring that the propagator is symplectic as in velocity-Verlet integrators and by extending the space of dividing surfaces to optimize the rate variationally, respectively. The dividing surface can be analytically or variationally optimized in phase space, not just over configuration space, to obtain more accurate rates. Thus, a phase space perspective is of primary importance in creating a deeper understanding of the geometric structure of chemical reactions. A key contribution from dynamical systems theory is the generalization of the transition state (TS) in terms of the normally hyperbolic invariant manifold (NHIM) whose geometric phase-space structure persists under perturbation. The NHIM can be regarded as an anchor of a dividing surface in phase space and it gives rise to an exact non-recrossing TS theory rate in reactions that are dominated by a single bottleneck. Here, we review recent advances of phase space geometrical structures of particular relevance to chemical reactions in the condensed phase. We also provide conjectures on the promise of these techniques toward the design and control of chemical reactions.
气相和凝聚相化学反应的复杂性通常是通过过渡态理论近似揭示的，或者通过轨迹的（解析或计算）积分精确揭示的。通过认识到动力学和相关几何结构存在于相空间中，可以改进这些方法，确保传播子像在速度-Verlet积分器中那样是辛的，并分别扩展分隔面的空间以变分方式优化速率。分隔面可以在相空间中进行解析或变分优化，而不仅仅是在构型空间上，以获得更准确的速率。因此，相空间视角对于更深入理解化学反应的几何结构至关重要。动力系统理论的一个关键贡献是根据正常双曲不变流形（NHIM）对过渡态（TS）进行推广，其几何相空间结构在微扰下持续存在。NHIM可以被视为相空间中分隔面的一个锚点，并且在由单个瓶颈主导的反应中，它会产生精确的非再穿越TS理论速率。在这里，我们回顾与凝聚相化学反应特别相关的相空间几何结构的最新进展。我们还对这些技术在化学反应设计和控制方面的前景提出了猜想。
