The hydration free energy (HFE) is a critical property for predicting and understanding chemical and biological processes in aqueous solution. There are a number of computational methods to derive HFE, generally classified into the equilibrium or non-equilibrium methods, based on the type of calculations used. In the present study, we compute the hydration free energies of 34 small, neutral, organic molecules with experimental HFE between +2 and −16 kcal/mol. The one-sided non-equilibrium methods Jarzynski Forward (JF) and Backward (JB), the two-sided non-equilibrium methods Jarzynski mean based on the average of JF and JB, Crooks Gaussian Intersection (CGI), and the Bennett Acceptance Ratio (BAR) are compared to the estimates from the two-sided equilibrium method Multistate Bennett Acceptance Ratio (MBAR), which is considered as the reference method for HFE calculations, and experimental data from the literature. Our results show that the estimated hydration free energies from all the methods are consistent with MBAR results, and all methods provide a mean absolute error of ∼0.8 kcal/mol and root mean square error of ∼1 kcal for the 34 organic molecules studied. In addition, the results show that one-sided methods JF and JB result in systematic deviations that cannot be corrected entirely. The statistical efficiency ε of the different methods can be expressed as the one over the simulation time times the average variance in the HFE. From such an analysis, we conclude that ε(MBAR) > ε(BAR) ≈ ε(CGI) > ε(JX), where JX is any of the Jarzynski methods. In other words, the non-equilibrium methods tested here for the prediction of HFE have lower computational efficiency than the MBAR method.

中文翻译：

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统计水合自由能的方法的统计效率

水合自由能（HFE）是预测和理解水溶液中化学和生物过程的关键属性。根据所使用的计算类型，有多种计算方法可以得出HFE，通常将其分为平衡法或非平衡法。在本研究中，我们计算了实验HFE在+2至-16 kcal / mol之间的34个中性有机小分子的水合自由能。单向非平衡方法Jarzynski正向（JF）和向后（JB），双向非平衡方法Jarzynski均基于JF和JB的平均值，Crooks高斯相交（CGI）和贝内特接受率（BAR）与双向均衡方法多状态贝内特验收率（MBAR）的估算值进行比较，这被认为是HFE计算的参考方法以及来自文献的实验数据。我们的结果表明，所有方法估计的水合自由能均与MBAR结果一致，并且所有方法均对所研究的34种有机分子提供了约0.8 kcal / mol的平均绝对误差和约1 kcal的均方根误差。此外，结果表明，单面方法JF和JB导致无法完全纠正的系统偏差。可以将不同方法的统计效率ε表示为仿真时间乘以HFE中的平均方差。通过这样的分析，我们得出结论：ε（MBAR）>ε（BAR）≈ε（CGI）>ε（JX），其中JX是Jarzynski方法中的任何一种。换句话说，