Wang Xiaohui, Tu Xingzhao, Zhang John Z H, Sun Zhaoxi
State Key Laboratory of Precision Spectroscopy, School of Chemistry and Molecular Engineering, East China Normal University, Shanghai 200062, China.
Phys Chem Chem Phys. 2018 Jan 17;20(3):2009-2021. doi: 10.1039/c7cp07573a.
Following the previously proposed equilibrate-state sampling based adaptive sampling regime Optimum Bennett Acceptance Ratio (OBAR), we introduce its nonequilibrium extension, the Optimum Crooks' Equation (OCE) in the current work. The efficiency of the NonEquilibrium Work (NEW) stratification is improved by adaptively manipulating the significance of each nonequilibrium realization followed by importance sampling. As is exhibited in the equilibrium case, the nonequilibrium extension outperforms the simple equal time rule used in nonequilibrium stratification in the sense of minimizing the total variance of the free energy estimate. The speedup of this non-equal time rule is more than 1-fold. The Time Derivative of total Variance (TDV) proposed for the OBAR criterion is extended to determine the importance of each nonequilibrium transformation, which is linearly dependent on the variance. The TDV in the nonequilibrium case gives a totally different importance rank from the standard errors of the free energy differences and OBAR TDV due to the duration of nonequilibrium pulling being added into the OCE equation. The performance of the OCE workflow is demonstrated in the solvation of several small molecules with a series of lambda increments and relaxation times between successive perturbations. To the best of our knowledge, such a nonequilibrium adaptive sampling regime in alchemical transformation is unprecedented.
遵循先前提出的基于平衡态采样的自适应采样机制——最优贝内特接受率（OBAR），我们在当前工作中引入其非平衡扩展形式，即最优克鲁克斯方程（OCE）。通过自适应地操纵每个非平衡实现的重要性，随后进行重要性采样，非平衡功（NEW）分层的效率得以提高。正如在平衡情况下所展示的那样，在最小化自由能估计的总方差的意义上，非平衡扩展优于非平衡分层中使用的简单等时规则。这种非等时规则的加速比超过1倍。为OBAR准则提出的总方差时间导数（TDV）被扩展，以确定每个非平衡变换的重要性，其与方差呈线性相关。由于非平衡拉伸的持续时间被纳入OCE方程，非平衡情况下的TDV给出的重要性排名与自由能差的标准误差和OBAR TDV完全不同。OCE工作流程的性能在几个小分子的溶剂化过程中得到了证明，这些小分子具有一系列的λ增量和连续扰动之间的弛豫时间。据我们所知，在炼金术变换中这种非平衡自适应采样机制是前所未有的。
