Computation of methodology-independent ionic solvation free energies from molecular simulations. II. The hydration free energy of the sodium cation.

The raw ionic solvation free energies computed from atomistic (explicit-solvent) simulations are extremely sensitive to the boundary conditions (finite or periodic system, system shape, and size) and treatment of electrostatic interactions (Coulombic, lattice sum, or cutoff based) used during these simulations. In the present article, it is shown that correction terms can be derived for the effect of (A) an incorrect solvent polarization around the ion due to the use of an approximate (not strictly Coulombic) electrostatic scheme; (B) the finite size or artificial periodicity of the simulated system; (C) an improper summation scheme to evaluate the potential at the ion site and the possible presence of a liquid-vacuum interface in the simulated system. Taking the hydration free energy of the sodium cation as a test case, it is shown that the raw solvation free energies obtained using seven different types of boundary conditions and electrostatic schemes commonly used in explicit-solvent simulations (for a total of 72 simulations differing in the corresponding simulation parameters) can be corrected so as to obtain a consistent value for this quantity.