重探用于过渡路径采样的射击点蒙特卡罗方法
Revisiting Shooting Point Monte Carlo Methods for Transition Path Sampling
AI总结：
针对过渡路径采样中射击点演变的记忆效应问题，提出含路径与射击索引的扩展系综理论框架，推导对应接受规则，并指出两类射击方法需修正接受准则。
摘要：
稀有事件采样算法对于理解分子尺度上不常发生、但对复杂分子系统的长时间动力学至关重要的过程而言不可或缺。其中一种算法——过渡路径采样（TPS），因无需预先掌握过渡区域的相关知识，已成为研究这类稀有过程的标准技术。大多数TPS方法通过以下步骤从旧轨迹生成新轨迹：沿旧轨迹选取一个点，以某种方式修改其动量，随后通过时间正向和反向积分“射出”一条新轨迹。在部分流程中，每次试验移动的射击点都是独立选取的；但在另一些流程中，射击点会从一条路径演变到下一条路径，因此连续的射击点彼此相关。为解释这种记忆效应，我们提出了一个基于扩展系综的理论框架，该系综同时包含路径和射击索引。我们在这一扩展形式体系下推导了适用于多种路径采样算法的合理接受规则，可确保对过渡路径系综的正确采样。我们的框架表明，柔性长度无规射击（flexible-length aimless shooting）和弹簧射击（spring shooting）方法需要修正接受准则。
英文摘要：
Rare event sampling algorithms are essential for understanding processes that occur infrequently on the molecular scale, yet they are important for the long-time dynamics of complex molecular systems. One of these algorithms, transition path sampling (TPS), has become a standard technique to study such rare processes since no prior knowledge on the transition region is required. Most TPS methods generate new trajectories from old trajectories by selecting a point along the old trajectory, modifying its momentum in some way, and then ``shooting'' a new trajectory by integrating forward and backward in time. In some procedures, the shooting point is selected independently for each trial move, but in others, the shooting point evolves from one path to the next so that successive shooting points are related to each other. To account for this memory effect, we introduce a theoretical framework based on an extended ensemble that includes both paths and shooting indices. We derive appropriate acceptance rules for various path sampling algorithms in this extended formalism, ensuring the correct sampling of the transition path ensemble. Our framework reveals the need for amended acceptance criteria in the flexible-length aimless shooting and spring shooting methods.
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