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arXiv 2003.14163physics.chem-phcond-mat.stat-mechmath.DSnlin.CD
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化学反应动力学中势能面的深度和平坦度的作用

The role of depth and flatness of a potential energy surface in chemical reaction dynamics

Wenyang Lyu, Shibabrat Naik, Stephen Wiggins

摘要:

在这项研究中,我们分析了如何在势能面的深度和平坦度方面的几何形状的变化可以影响反应动力学。我们制定的深度和平坦度的上下文中的一个和两个自由度(DOF)的哈密顿范式的鞍结分岔和量化它们对化学反应动力学的影响。在最近的一项工作中,García-Garrido、Naik和Wiggins说明了改变势能面(PES)的阱深如何导致鞍结分叉。他们已经展示了与秩1鞍点相关的圆柱形流形的几何形状如何在通向鞍结分岔的途中发生变化。使用这里提出的配方,我们展示了如何在势能的参数的变化控制的深度和平坦度,并显示它们的作用,在定量测量的化学反应。我们量化的深度和平坦度的作用,通过计算的比的宽度和井的宽度,反应概率(也被称为过渡分数或人口分数),间隙时间(或第一次通过时间)分布,和定向通量通过分割表面(DS)的小到高的总能量值。这些定量措施所获得的结果与反应动力学的定性理解一致。

英文摘要:

In this study, we analyze how changes in the geometry of a potential energy surface in terms of depth and flatness can affect the reaction dynamics. We formulate depth and flatness in the context of one and two degree-of-freedom (DOF) Hamiltonian normal form for the saddle-node bifurcation and quantify their influence on chemical reaction dynamics. In a recent work, García-Garrido, Naik, and Wiggins illustrated how changing the well-depth of a potential energy surface (PES) can lead to a saddle-node bifurcation. They have shown how the geometry of cylindrical manifolds associated with the rank-1 saddle changes en route to the saddle-node bifurcation. Using the formulation presented here, we show how changes in the parameters of the potential energy control the depth and flatness and show their role in the quantitative measures of a chemical reaction. We quantify this role of the depth and flatness by calculating the ratio of the bottleneck-width and well-width, reaction probability (also known as transition fraction or population fraction), gap time (or first passage time) distribution, and directional flux through the dividing surface (DS) for small to high values of total energy. The results obtained for these quantitative measures are in agreement with the qualitative understanding of the reaction dynamics.

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