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

Abstract

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