CONTINUUM CORRECTIONS TO THE POLARIZATION AND THERMODYNAMIC PROPERTIES OF EWALD SUM SIMULATIONS FOR IONS AND ION-PAIRS AT INFINITE DILUTION

Ewald sum simulations of the solvation thermodynamics of charged solut es employ an unphysical uniform neutralizing background charge to ensu re convergence of the periodic lattice sum. Continuum corrections to t he solvation free energy, entropy, and volume of single ions and ion p airs for the effect of the neutralizing background and periodic bounda ry conditions at finite cell size are derived in order to allow effici ent calculations of the ionic properties at infinite dilution. The der ivation presented in this paper shows the physical origin of the effec ts and can be easily extended to multiple charge sites. Corrections ar e small for high dielectric constant solvents but become increasingly important as the ion size is increased, the dielectric constant is dec reased, or the unit cell size is decreased. An alternative way of calc ulating the thermodynamic properties from Ewald sum simulations is pro posed for which the corrections are small for low dielectric constant solvents. Tests for low and high dielectric constant water show that, after the appropriate continuum corrections are applied, the free ener gy of charging an ion using Ewald sum simulations agrees with the resu lts for potential truncation simulations and spherical boundary simula tions (when corrected for truncation effects). The corrected free ener gy of hydration is not sensitive to the system size even for low diele ctric constants. The continuum model correctly predicts that Ewald sum simulations yield a solvent polarization at large distance from an io n that is smaller than the polarization of a truly infinite system.