Song XiaoGeng, Van Voorhis Troy
Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139-4307, USA.
J Chem Phys. 2006 Apr 7;124(13):134104. doi: 10.1063/1.2183307.
A semiclassical (SC) approximation to the quantum mechanical propagator for nonadiabatic systems is derived. Our derivation starts with an exact path integral expression that uses canonical coherent states for the nuclear degrees of freedom and spin coherent states for the electronic degrees of freedom. A stationary path approximation (SPA) is then applied to the path integral to obtain the SC approximation. The SPA results in complex classical trajectories of both nuclear and electronic degrees of freedom and a double ended boundary condition. The root search problem is solved using the previously proposed "real trajectory local search" algorithm. The SC approximation is tested on three simple one dimensional two-state systems proposed by Tully [J. Chem. Phys. 93, 1061 (1990)], and the SC results are compared to Ehrenfest and surface hopping predictions. Excellent agreement with quantum results is reached when the SC trajectory is far away from caustics. We discuss the origin of caustics in this SC formalism and the strengths and weaknesses of this approach.
推导了非绝热体系量子力学传播子的一种半经典（SC）近似。我们的推导始于一个精确的路径积分表达式，该表达式对核自由度使用正则相干态，对电子自由度使用自旋相干态。然后将驻定路径近似（SPA）应用于路径积分以获得SC近似。SPA导致核自由度和电子自由度的复经典轨迹以及一个双端边界条件。使用先前提出的“实轨迹局部搜索”算法解决根搜索问题。在Tully提出的三个简单一维二态体系上测试了SC近似[《化学物理杂志》93, 1061 (1990)]，并将SC结果与埃伦费斯特和表面跳跃预测进行了比较。当SC轨迹远离焦散时，与量子结果达成了极好的一致性。我们讨论了这种SC形式主义中焦散的起源以及这种方法的优缺点。
