Charge penetration in dielectric models of solvation

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Abstract
Dielectric continuum models are widely used for treating solvent effects in quantum chemical calculations of solute electronic structure. These invoke a reaction field wherein solute-solvent electrostatic interactions are explicitly or implicitly described by means of certain apparent polarization charges. Most implementations represent this polarization through an apparent surface charge distribution spread on the boundary of the cavity that nominally encloses the solute. However, quantum chemical calculations usually lead to a tail of the wave function penetrating outside the cavity, thereby causing an additional volume polarization contribution to the reaction field that is rarely recognized or treated. In principle the volume polarization should be represented by a certain apparent volume charge distribution spread throughout the entire dielectric medium. It is shown here that this effect can be closely simulated by means of a certain additional apparent surface charge distribution. This provides a convenient and efficient route to treat volume polarization in practice. A very simple approximation to this correction can be obtained from knowledge only of the amount of penetrating solute charge. This supplies a theoretical context as well as justification for the concept of surface charge renormalization that some workers have advocated. The analysis also points to a new prescription for properly making this renormalization in practice, improving on various ad hoc procedures that have been previously suggested for this purpose.