论文标题
实现与化学反应动力学相关的相空间结构的基本阐释
Elementary exposition of realizing phase space structures relevant to chemical reaction dynamics
论文作者
论文摘要
在本文中，我们回顾了用于计算化学反应中出现的两个自由度的哈密顿系统的分析和数值方法。特别是，这些相空间结构是与索引-1鞍座，周期轨道划分表面以及不稳定周期轨道的稳定且不稳定的歧管相关的不稳定的周期轨道。我们在两个自由度的哈密顿量的背景下回顾了这些方法，其四分之一的电势和二次潜力。我们得出了可集成情况的相空间结构的分析形式，并在三维能量表面上可视化它们的几何形状。然后，由于势能参数的变化，我们研究了分裂表面的分叉。我们还审查了\ emph {turning Point}的数值方法，并介绍其新修饰，称为\ emph {基于配置差异}的转弯点，用于计算两个自由度系统中的不稳定周期轨道。这些方法是在开源Python软件包中实现的，uposham〜 \ cite {lyu2020}。
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}.
