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Continuum solvation models enable efficient first principles calculations ofchemical reactions in solution, but require extensive parametrization andfitting for each solvent and class of solute systems. Here, we examine theassumptions of continuum solvation models in detail and replace empirical termswith physical models in order to construct a minimally-empirical solvationmodel. Specifically, we derive solvent radii from the nonlocal dielectricresponse of the solvent from ab initio calculations, construct a closed-formand parameter-free weighted-density approximation for the free energy of thecavity formation, and employ a pair-potential approximation for the dispersionenergy. We show that the resulting model with a single solvent-independentparameter: the electron density threshold ($n_c$), and a singlesolvent-dependent parameter: the dispersion scale factor ($s_6$), reproducessolvation energies of organic molecules in water, chloroform and carbontetrachloride with RMS errors of 1.1, 0.6 and 0.5 kcal/mol respectively. Weadditionally show that fitting the solvent-dependent $s_6$ parameter to thesolvation energy of a single non-polar molecule does not substantially increasethese errors. Parametrization of this model for other solvents, therefore,requires minimal effort and is possible without extensive databases ofexperimental solvation free energies.

Weighted-density functionals for cavity formation and dispersion energies in continuum solvation models