This review focuses on a recent class of path-integral-based methods for the simulation of nonadiabatic dynamics in the condensed phase using only classical molecular dynamics trajectories in an extended phase space. Specifically, a semiclassical mapping protocol is used to derive an exact, continuous, Cartesian variable path-integral representation for the canonical partition function of a system in which multiple electronic states are coupled to nuclear degrees of freedom. Building on this exact statistical foundation, multistate ring polymer molecular dynamics methods are developed for the approximate calculation of real-time thermal correlation functions. The remarkable promise of these multistate ring polymer methods, their successful applications, and their limitations are discussed in detail.

中文翻译：

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非绝热动力学的路径积分：多态环聚合物分子动力学

本综述重点介绍了最近一类基于路径积分的方法，仅使用扩展相空间中的经典分子动力学轨迹来模拟凝聚相中的非绝热动力学。具体来说，半经典映射协议用于导出系统规范配分函数的精确、连续、笛卡尔变量路径积分表示，其中多个电子态与核自由度耦合。在此精确的统计基础上，开发了多态环聚合物分子动力学方法，用于实时热相关函数的近似计算。详细讨论了这些多态环聚合物方法的卓越前景、它们的成功应用以及它们的局限性。