In this paper, we analyze the detailed quantum-classical behavior of two alternative approaches to simulating molecular dynamics with electronic transitions: the popular fewest switches surface hopping (FSSH) method, introduced by Tully in 1990 [Tully, J. Chem. Phys., 1990, 93, 1061] and our recently developed quantum trajectory surface hopping (QTSH) method [Martens, J. Phys. Chem. A, 2019, 123, 1110]. Both approaches employ an independent ensemble of trajectories that undergo stochastic transitions between electronic surfaces. The methods differ in their treatment of energy conservation, with FSSH imposing conservation of the classical kinetic plus potential energy by rescaling the classical momentum when a surface hop occurs while QTSH incorporates a quantum force throughout the dynamics which leads naturally to the conservation of the full quantum-classical energy. We investigate the population transfer and energy budget of the surface hopping methods for several simple model systems and compare with exact quantum results. In addition, the detailed dynamics of the trajectory ensembles in phase space are compared with the quantum evolution in the Wigner representation. Conclusions are drawn.

中文翻译：

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表面跳变方法中的经典和非经典效应，用于模拟耦合的电子核动力学。

在本文中，我们分析了两种模拟电子跃迁的分子动力学方法的详细的量子经典行为：Tully在1990年提出的最流行的最小开关表面跳频（FSSH）方法[Tully，J. Chem。Phys。，1990，93，1061]和我们最近开发的量子轨迹表面跳变（QTSH）方法[Martens，J. Phys。Phys。，1990，93，1061]。化学 A，2019，123，1110]。两种方法都采用独立的轨迹集合，这些轨迹在电子表面之间经历随机过渡。这些方法在节能方面有所不同，FSSH通过在出现表面跳变时重新调整经典动量来强加经典动能和势能的守恒，而QTSH在整个动力学过程中都吸收了量子力，这自然导致了完整的经典量子能的守恒。我们研究了几种简单模型系统的表面跳变方法的人口转移和能量收支，并与精确的量子结果进行了比较。另外，在维纳表示中将轨迹合奏在相空间中的详细动力学与量子演化进行了比较。得出结论。比较了相空间中轨迹合奏的详细动力学与维格纳表示中的量子演化。得出结论。比较了相空间中轨迹合奏的详细动力学与维格纳表示中的量子演化。得出结论。