We present a continuum solvent model (CSM) with a smooth cavity for the application in grid-based electronic structure methods. The cavity is identified with the inherently smooth distribution function of a binary mixture at infinite dilution. We obtain a cavity model based on atomic van der Waals radii and one free parameter controlling the overall size. This single parameter is sufficient to adequately reproduce experimental partial molar volumes. The CSM based on this cavity is of similar accuracy in the prediction of aqueous solvation Gibbs energies of small neutral molecules and ions as other CSMs with a smooth cavity. We apply the model to systems in non-aqueous solution, i.e., spiropyran/merocyanin energetics, a proton transfer reaction in dimethyl sulfoxide, and the electrostatic screening of charged gold clusters in an ionic liquid.

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