Index k saddles and dividing surfaces in phase space with applications to isomerization dynamics
Index k saddles and dividing surfaces in phase space with applications to isomerization dynamics
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DOI：
10.1063/1.3602465
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发表时间：
2011-06-28
影响因子：
4.4
通讯作者：
Wiggins, Stephen
中科院分区：
文献类型：
--
作者：
Collins, Peter;Ezra, Gregory S.;Wiggins, Stephen
在本文中，我们继续我们的研究相空间的几何和动力学与指数k鞍（k > 1）的势能面。利用Poincare-Birkhoff规范形（NF）理论，我们给出了相空间中“分界面”的一个显式公式，一个余维1的表面（在能量壳层内），所有“穿过”指数k鞍区域的轨迹都必须通过它。在一般的非共振假设下，规范形式提供了描述指数k鞍附近的鞍动力学的k（近似）积分。这些积分提供了通过鞍点邻域的所有轨迹的符号描述。我们给出了一个参数化的分割表面，这是用来作为基础的数值方法来采样分割表面。我们的技术被应用到异构化动力学的势能面上有四个极小值;两个对称相关的极小值对连接的低能量指数1鞍，与对本身连接通过较高的能量指数1鞍和指数2鞍在原点。我们计算和采样的分割面，并表明我们的方法使我们能够区分协调交叉（“山顶交叉”）异构化轨迹和那些轨迹，不协调交叉（潜在的顺序异构化轨迹）。然后，我们考虑额外的“浴模式”的动态效果，通过研究一个四度的自由度系统。对于这个系统，我们表明，正常的形式和划分表面可以实现和采样，并使用近似积分的运动和我们的符号描述的轨迹，我们能够选择相应的初始条件协调交叉异构化轨迹和（潜在的）顺序异构化轨迹。(C)2011年美国物理学会。[doi：10.1063/1.3602465]
In this paper, we continue our studies of the phase space geometry and dynamics associated with index k saddles (k > 1) of the potential energy surface. Using Poincare-Birkhoff normal form (NF) theory, we give an explicit formula for a "dividing surface" in phase space, i.e., a codimension one surface (within the energy shell) through which all trajectories that "cross" the region of the index k saddle must pass. With a generic non-resonance assumption, the normal form provides k (approximate) integrals that describe the saddle dynamics in a neighborhood of the index k saddle. These integrals provide a symbolic description of all trajectories that pass through a neighborhood of the saddle. We give a parametrization of the dividing surface which is used as the basis for a numerical method to sample the dividing surface. Our techniques are applied to isomerization dynamics on a potential energy surface having four minima; two symmetry related pairs of minima are connected by low energy index 1 saddles, with the pairs themselves connected via higher energy index 1 saddles and an index 2 saddle at the origin. We compute and sample the dividing surface and show that our approach enables us to distinguish between concerted crossing ("hilltop crossing") isomerizing trajectories and those trajectories that are not concerted crossing (potentially sequentially isomerizing trajectories). We then consider the effect of additional "bath modes" on the dynamics, by a study of a four degree-of-freedom system. For this system we show that the normal form and dividing surface can be realized and sampled and that, using the approximate integrals of motion and our symbolic description of trajectories, we are able to choose initial conditions corresponding to concerted crossing isomerizing trajectories and (potentially) sequentially isomerizing trajectories. (C) 2011 American Institute of Physics. [doi: 10.1063/1.3602465]