Ionic charging free energies: Spherical versus periodic boundary conditions

Ionic charging free energies calculated by Ewald summation differ substantially from those calculated in spherical cluster calculations, with or without the inclusion of a Born correction in the latter. Using Gauss’ law, we derive an electrostatic potential for ions in spherical clusters that involves contributions only from the interior solvent. This “interior” potential agrees with the “P-summation” approach proposed by Hummer et al. [J. Phys. Chem. B 101, 3017 (1997)], and leads to charging free energies which agree, within simulation error, with those given by Ewald summation with finite-size corrections. The difference in charging free energies between this approach and the conventional cluster free energies including the Born correction is traced to the surface potential of water.