浅谈化学反应动力学相空间结构的实现
Elementary exposition of realizing phase space structures relevant to chemical reaction dynamics
摘要：
在这篇文章中，我们审查的分析和数值方法计算的相空间结构的两个自由度的哈密顿系统中出现的化学反应。特别地，这些相空间结构是与指数-1鞍相关联的不稳定周期轨道、周期轨道分割面以及不稳定周期轨道的稳定不变流形和不稳定不变流形。我们审查的背景下，一个两个自由度的哈密顿与一个四次潜在的二次潜在的方法。我们推导出了可积情形下相空间结构的解析形式，并将其在三维能量面上的几何形状可视化。然后，我们调查的分歧的分割面由于势能的参数的变化。我们还回顾了\emph{turning point}的数值方法，并提出了它的新的修改称为\emph{turning point based on configuration difference}计算两个自由度系统的不稳定周期轨道。这些方法在开源python包UPOsHam~ \cite{Lyu2020}中实现。
英文摘要：
In this article, we review the analytical and numerical approaches for computing the phase space structures in two degrees-of-freedom Hamiltonian systems that arise in chemical reactions. In particular, these phase space structures are the unstable periodic orbit associated with an index-1 saddle, the periodic orbit dividing surface, and the stable and unstable invariant manifolds of the unstable periodic orbit. We review the approaches in the context of a two degrees-of-freedom Hamiltonian with a quartic potential coupled with a quadratic potential. We derive the analytical form of the phase space structures for the integrable case and visualize their geometry on the three dimensional energy surface. We then investigate the bifurcation of the dividing surface due to the changes in the parameters of the potential energy. We also review the numerical method of \emph{turning point} and present its new modification called the \emph{turning point based on configuration difference} for computing the unstable periodic orbit in two degrees-of-freedom systems. These methods are implemented in the open-source python package, UPOsHam~\cite{Lyu2020}.
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