The Ewald potential was applied for the electrostatic interactions under periodic boundary conditions (PBC), and a Nos é-Hoover thermostat chain of length 3 was coupled to each ion to maintain a temperature of 1150 K for all the NVT ensemble simulations. Due to the requirement of many simulations along the thermodynamic integration paths to grow the nano-scale cavities, we were not able to employ the path integral formalism for incorporating quantum effects. These corrections are expected to be small at such a high temperature, however.