Comparative Assessment of Computational Methods for Free Energy Calculations of Ionic Hydration

Experimental observations for ionic hydration free energies are highly debated mainly due to the ambiguous absolute hydration free energy of proton, ΔG_hyd^*(H⁺). Hydration free energies (HFEs) of the 112 singly charged ions in the Minnesota solvation database were predicted by six methods with explicit and implicit solvent models, namely, thermodynamic integration (TI), energy representation module (ERmod), three-dimensional reference interaction site model (3D-RISM), and continuum solvation models based on the quantum mechanical charge density (SMD) and on the Poisson-Boltzmann (PB) and generalized Born (GB) theories. Taking the solvent Galvani potential of water into account, the resulting real HFEs from TI calculations for the generalized Amber force field (GAFF) modeled ions best match the experiments based on ΔG_hyd^*(H⁺) = -262.4 kcal/mol (Randles Trans. Faraday Soc . 1956 , 52 , 1573 - 1581 ), in agreement with our previous work on charged amino acids (Zhang et al. J. Phys. Chem. Lett. 2017 , 8 , 2705 - 2712 ). The examined computational methods show an accuracy of ∼7 kcal/mol for the GAFF-modeled ions, except for SMD with a higher accuracy of ∼4 kcal/mol. A biased deficiency in modeling anionic compounds by GAFF is observed with a larger standard deviation (SD) of 9 kcal/mol than that for cations (SD ∼ 4 kcal/mol). The relatively cheap ERmod and 3D-RISM methods reproduce TI results with good accuracy, although ERmod yields a systematic underestimation for cations by 9 kcal/mol; PB and GB generate relative (but not absolute) HFEs comparable to the TI predictions. Computational accuracy is found to be more limited by the accuracy of force fields rather than the models themselves.