The derivation of this results within Ewald formalism is provided in the Appendix A. When the macroscopic crystal is "wrapped" in a tin foil, the induced image charge will kill off the surface contribution to the electrostatic potential. In general, it is known that for liquid state systems, calculations based on Ewald summation with tin foil boundary condition tend to be more accurate than the ones based on "vacuum" boundary conditions. However, in order to implement the Widom particle insertion method the system must be "unwrapped" from the tin foil, so that a proton can be brought from outside into the simulation cell. As the proton enters the crystal it will experience a jump in the electrostatic potential given by qϕ B . Note, that the Bethe potential is not constant -it depends on the instantaneous positions of all the charges inside the simulation cells.