Free-Energy Calculations of Ionic Hydration Consistent with the Experimental Hydration Free Energy of the Proton

Computational free-energy correction strategies and the choice of experimental proton hydration free energy, ΔG_s^*(H⁺), are analyzed to investigate the apparent controversy in experimental thermodynamics of ionic hydration. Without corrections, the hydration free-energy (ΔG_hyd) calculations match experiments with ΔG_s^*(H⁺) = -1064 kJ/mol as reference. Using the Galvani surface potential the resulting (real) ΔG_hyd are consistent with ΔG_s^*(H⁺) = -1098 kJ/mol. When applying, in an ad hoc manner, the discrete solvent correction, ΔG_hyd matching the "consensus" ΔG_s^*(H⁺) of -1112 kJ/mol are obtained. This analysis rationalizes reports on ΔG_hyd calculations for ions using different experimental references. For neutral amino acid side chains ΔG_hyd are independent of the water model, whereas there are large differences in ΔG_hyd due to the water model for charged species, suggesting that long-range ordering of water around ions yields an important contribution to the ΔG_hyd. These differences are reduced significantly when applying consistent corrections, but to obtain the most accurate results it is recommended to use the water model belonging to the force field.