Bound Charge Layering Near a Spherical Ion: Moving Beyond Born Theory

The response of aqueous solvent to a dissolved ion is analyzed in terms of the bound charge, the net charge of the solvent in the vicinity of the solute. The total amount of bound charge is <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mo>-</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mn>1</mml:mn><mml:mo>-</mml:mo><mml:mfrac><mml:mn>1</mml:mn><mml:mi>ϵ</mml:mi></mml:mfrac></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mi>ion</mml:mi></mml:msub></mml:math>, where <i>Q</i>_ion is the charge of the ion and ϵ is the solvent dielectric constant, in both continuum and molecular theory. Aqueous solvation involves an inner layer of bound charge way over this value, followed by another layer that almost or over compensates the first layer, and so on. We demonstrate how layering of charge explains the strong solvation response of aqueous solvent. Born theory, in which the ion resides in a cavity within a dielectric continuum, places all the bound charge on the cavity surface. Without accounting for bound charge layering, it cannot describe the strong aqueous solvation response. The only adjustable parameter in Born theory is the cavity radius, and unphysically small values of the radius are required to match the Born prediction to the actual solvation free energy. We propose a simple analytical model for aqueous solvation of a spherical ion that incorporates bound charge layering. We point out which parameters are expected to be solvent-specific and transferable between different solutes, while other parameters should depend upon ion and solvent size. The solvation energy from finite, periodically replicated simulations must be corrected to describe an ion at infinitely dilution. We present a very simple correction, and demonstrate its accuracy.