Statistical efficiency of methods for computing free energy of hydration

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.