Department of Biology, Chemistry, Pharmacy, Freie Universität Berlin, Arnimallee 22, D-14195 Berlin, Germany.
J Chem Phys. 2021 Mar 7;154(9):094102. doi: 10.1063/5.0038408.
Path reweighting is a principally exact method to estimate dynamic properties from biased simulations-provided that the path probability ratio matches the stochastic integrator used in the simulation. Previously reported path probability ratios match the Euler-Maruyama scheme for overdamped Langevin dynamics. Since molecular dynamics simulations use Langevin dynamics rather than overdamped Langevin dynamics, this severely impedes the application of path reweighting methods. Here, we derive the path probability ratio M for Langevin dynamics propagated by a variant of the Langevin Leapfrog integrator. This new path probability ratio allows for exact reweighting of Langevin dynamics propagated by this integrator. We also show that a previously derived approximate path probability ratio M differs from the exact M only by O(ξΔt) and thus yields highly accurate dynamic reweighting results. (Δt is the integration time step, and ξ is the collision rate.) The results are tested, and the efficiency of path reweighting is explored using butane as an example.
路径重加权是一种从有偏模拟中估计动态特性的主要精确方法——只要路径概率比与模拟中使用的随机积分器匹配。先前报道的路径概率比与过阻尼朗之万动力学的欧拉-马尤马方案匹配。由于分子动力学模拟使用朗之万动力学而不是过阻尼朗之万动力学，这严重阻碍了路径重加权方法的应用。在这里，我们推导出由朗之万跃阶积分器的变体传播的朗之万动力学的路径概率比 M。这个新的路径概率比允许对这个积分器传播的朗之万动力学进行精确的重新加权。我们还表明，先前推导的近似路径概率比 M 与精确的 M 仅相差 O(ξΔt)，因此可以得到非常精确的动态重加权结果。（Δt 是积分时间步长，ξ 是碰撞速率。）结果进行了测试，并使用丁烷作为示例探索了路径重加权的效率。
