Finite-Size Corrections to Electrolyte Chemical Potentials Calculated from Molecular Simulations

Finite-size corrections to electrolyte chemical potentials calculated from molecular simulations

Jeff P. Thompson and Isaac C. Sanchez*

McKetta Department of Chemical Engineering, The University of Texas at Austin

*Email: sanchez@che.utexas.edu

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

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