Figure 2.
Free energy profiles of the ion permeation and the water occupancy in different simulation systems. (a) Free energy profiles from the permeations of different cations. The free energy of H+ (the hydrated excess proton) has much lower energy barrier than the others, displaying the unique features of the excess H+. (b) Free energy profiles of the water occupancy with the H+ charge defect (green), K+ (red), or classical H3O+ (yellow) fixed at Z = 12.0 Å (2–3 Å inside the mouth of the nanotube), compared to the result without the ions present (blue). The induced wetting process is only seen in the system with H+. The average errors are (a) ±0.45 kcal/mol and (b) ±0.30 kcal/mol calculated from 500 ps block averages.