Effect of the geometric phase on nuclear dynamics at a conical intersection: Extension of a recent topological approach from one to two coupled surfaces
Effect of the geometric phase on nuclear dynamics at a conical intersection: Extension of a recent topological approach from one to two coupled surfaces
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DOI：
10.1063/1.3031215
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发表时间：
2008-12-07
影响因子：
4.4
通讯作者：
Bouakline, Foudhil
中科院分区：
文献类型：
--
作者：
Althorpe, Stuart C.;Stecher, Thomas;Bouakline, Foudhil
最近的方法[S]。C. Althorpe， J. Chem。物理学报，124,084105(2006)]用于解释局限于两个锥形相交势能面下部的核波函数中的几何相位（GP）效应，扩展到处理两个表面上的耦合动力学。这种方法是精确的，并且使用简单的拓扑结构将波函数从费曼路径中分离出来，这些路径绕着锥形交叉点旋转了不同的次数，在不同的意义上。我们首先通过将描述耦合动力学的时间相关波包映射到双空间来推导该方法，然后通过在路径积分的时间有序展开中对费曼路径进行分类来推导该方法。对一个简单的Exe Jahn-Teller系统和一个B-1(1)-S-0交叉的pyrorole模型进行了数值验证。该方法允许人们研究和解释GP对表面之间人口转移的影响，并且还可以从不同的反应路径中提取对耦合核波函数的贡献。
A recent approach [S. C. Althorpe, J. Chem. Phys. 124, 084105 (2006)] for interpreting geometric phase (GP) effects in a nuclear wave function confined to the lower of two conically intersecting potential energy surfaces is extended to treat coupled dynamics on both surfaces. The approach is exact, and uses simple topology to separate the wave function into contributions from Feynman paths that wind different numbers of times, and in different senses, around the conical intersection. We derive the approach first, by mapping the time-dependent wave packet describing the coupled dynamics onto a double space, and second, by classifying the Feynman paths within a time-ordered expansion of the path integral. The approach is demonstrated numerically for a simple Exe Jahn-Teller system and for a model of the B-1(1)-S-0 intersection in pyrrole. The approach allows one to investigate and interpret the effect of the GP on population transfer between the surfaces, and also to extract contributions to the coupled nuclear wave function from different reaction paths.