Ion hydration free energies and water surface potential in water nano drops: The cluster pair approximation and the proton hydration Gibbs free energy in solution.

We estimate both single ion hydration Gibbs free energies in water droplets, comprising from 50 to 1000 molecules, and water/vacuum surface potentials in pure water droplets comprising up to 10 000 molecules. We consider four ions, namely, Li, NH , F, and Cl, and we model their hydration process and water/water interactions using polarizable force fields based on an induced point dipole approach. We show both ion hydration Gibbs free energies and water surface potentials to obey linear functions of the droplet radius as soon as droplets comprising a few hundred water molecules. Moreover, we also show that the differences in anion/cation hydration Gibbs free energies in droplets obey a different regime in large droplets than in small clusters comprising no more than six water molecules, in line with the earlier results computed from standard additive point charge force fields. Hence, both point charge and more sophisticated induced point dipole molecular modeling approaches suggest that methods considering only the thermodynamical properties of small ion/water clusters to estimate the absolute proton hydration Gibbs free energy in solution are questionable. In particular, taking into account the data of large ion/water droplets may yield a proton hydration Gibbs free energy in solution value to be shifted by several kT units compared to small clusters-based approaches.