利用基于直接动力学的轨线面跳跃方法处理非绝热过程

Treatment of Nonadiabatic Dynamics by On-The-Fly Trajectory Surface Hopping Dynamics

势能面交叉引起的非绝热过程广泛存在于光化学和光物理中。对这一过程进行描述是理论化学的重要挑战之一。非绝热过程涉及原子核与电子之间的耦合运动,因此量子化学的基本假设之一"玻恩-奥本海默"近似被打破,所以对其进行描述需要发展新的动力学理论方法。在这些方法中,Tully发展的最少轨线面跳跃方法凭借易于程序化、便于计算等优点已经发展成为处理非绝热问题的主要动力学方法之一。其中原子核以经典的方式在单一势能面上进行演化,电子以量子的方式沿着同一轨线进行演化。在整个演化过程中,非绝热跃迁通过轨线在不同势能面间的跃迁来描述,其中跳跃发生的几率与电子的演化有关。如果将该方法与从头算直接动力学相结合,可以在全原子水平上研究实际分子体系的非绝热动力学,给出其激发态寿命、非绝热动力学中分子的主要运动方式、反应通道以及分支比等重要信息。本文旨在讨论最少面跳跃直接动力学方法研究非绝热问题的一些进展,包括动力学基本理论,特别关注将最少面跳跃方法和直接动力学结合的数值实现细节,同时讨论该方法在研究实际体系当中的一些应用,并对轨线面跳跃方法下一步发展的一些方向进行合理的展望。

Nonadiabatic processes widely exist in photochemistry and photophysics. The theoretical treatment of nonadiabatic processes is an important challenge in theoretical chemistry. In nonadiabatic dynamics, the well-known "Born-Oppenheimer approximation" breaks down due to the involvement of strong nuclear-electronic coupled motions. Hence, the development of a theoretical framework is required for the proper treatment of nonadiabatic dynamics. The fewest-switches trajectory surface-hopping method developed by Tully is one of the most widely used methods in thetreatment of nonadiabatic processes because of its rather simple numerical implementation. In this approach, the nuclear degrees of freedom are propagated on the potential energy surface of an electronic state using the classical equations of motion, while the electronic degrees of freedom are propagated along the same trajectory according to the time-dependent Schr?dinger equation. Nonadiabatic effects are included by allowing sudden hops between different potential energy surfaces. After averaging over many trajectories, a reasonable description of nonadiabatic dynamics is achieved at low computational cost. Particularly, when we combine the trajectory surface-hopping dynamics with on-the-fly molecular dynamics, it is possible to describe the nonadiabatic dynamics of realistic polyatomic molecular systems at a fully atomic level with all degrees of freedom included. After the introduction of hybrid multiscale methods, the simulation of photochemistry in solutions and in biological systems becomes possible. The simulation results provide important information concerning the nonadiabatic dynamics of realistic polyatomic systems, such as excited-state lifetime, major active molecular motions, reaction channels, and branching ratio. This review article summarizes some progresses in this field. After briefly introducing the basic theory of widely used fewest switches surface-hopping dynamics methods, we mainly focus on several numerical details in the implementation of on-the-fly fewest switches surface-hopping dynamics. The seamless combination of surface-hopping dynamics and electronic-structure calculations is emphasized in this review, rather than an exhaustive discussion of rigorous nonadiabatic dynamics theories. Numerical methods to estimate nonadiabatic coupling terms are discussed, which allow us to perform the trajectory surface-hopping calculations when the nonadiabatic coupling vectors are not available in the electronic structure calculations. Several important issues, such as decoherence corrections, diabatic or adiabatic representations, and initial sampling methods are discussed in detail. We also summarize the theoretical treatment of the nonadiabatic dynamics of some interesting molecular systems, which include the photostability of DNA, photo-isomerization of organic systems, photochemistry of transition metal complexes, and photovoltaics. Finally, we discuss the theoretical challenges of this direct dynamics approach and provide an outlook of this field from our personal perspective.