(432f) Finite-Size Corrections to Electrolyte Chemical Potentials Calculated from Molecular Simulations

Recent studies [1 , 2 ] have shown increased interest in calculating the concentration
dependence of salt chemical potentials (or mean ionic activity coefficients) in electrolyte solutions
from molecular simulations, yet a careful analysis of potential errors in the requisite salt solvation
free energies due to finite-size effects is necessary to establish the reliability of results.
Mean ionic electrolyte chemical potentials computed from free energies of coupling a
neutral pair/set of ions to a solution are subject to finite-size errors arising from two
major sources: 1) the altered polarization of the solvating medium (pure solvent or
electrolyte solution) around an ion in a finite system relative to that in a macroscopic
system; and 2) the (macroscopically vanishing) average effective interaction between the
distinguished ions whose coupling work is taken as an estimate of the salt excess chemical
potential
. The former (undersolvation) effect has been discussed extensively in the context of
computing single-ion solvation free energies in systems under periodic boundary conditions
[3–5]; the effect due to the interaction between distinguished ions has been discussed
in the context of the solvation free energy of an ion pair at fixed interion separation
[6, 7].

Building on these theoretical investigations, we use continuum electrostatics to estimate the
finite-size correction to the solvation free energy of a mobile cation–anion pair in a system with
electrostatic interactions treated by Ewald summation. In solutions of high dielectric
permittivity, the correction is small relative to the typical magnitude of the salt solvation
free energy (at least when, as is often the case, the lattice self-energies of the ions are
included in the solvation free energy). Nevertheless, the finite-size error depends on the
(thermodynamic state-dependent) permittivity of the solution and may induce non-negligible
systematic errors in precise calculations of the concentration dependence of the salt chemical
potential. References

[1] Mester, Z.; Panagiotopoulos, A. Z. J. Chem. Phys. 2015, 142, 044507.
[2] Moučka, F.; Nezbeda, I.; Smith, W. R. J. Chem. Theory Comput. 2015, 11, 1756–1764.
[3] Figueirido, F.; Buono, G. S. D.; Levy, R. M. J. Phys. Chem. B 1997, 101, 5622–5623.
[4] Hummer, G.; Pratt, L. R.; García, A. E. J. Chem. Phys. 1997, 107, 9275–9277.
[5] Hünenberger, P. H.; McCammon, J. A. J. Chem. Phys. 1999, 110, 1856.
[6] Figueirido, F.; Del Buono, G. S.; Levy, R. M. J. Chem. Phys. 1995, 103, 6133.
[7] Sakane, S.; Ashbaugh, H. S.; Wood, R. H. J. Phys. Chem. B 1998, 102, 5673–5682.