  Continuum solvation models enable efficient first principles calculations of
chemical reactions in solution, but require extensive parametrization and
fitting for each solvent and class of solute systems. Here, we examine the
assumptions of continuum solvation models in detail and replace empirical terms
with physical models in order to construct a minimally-empirical solvation
model. Specifically, we derive solvent radii from the nonlocal dielectric
response of the solvent from ab initio calculations, construct a closed-form
and parameter-free weighted-density approximation for the free energy of the
cavity formation, and employ a pair-potential approximation for the dispersion
energy. We show that the resulting model with a single solvent-independent
parameter: the electron density threshold ($n_c$), and a single
solvent-dependent parameter: the dispersion scale factor ($s_6$), reproduces
solvation energies of organic molecules in water, chloroform and carbon
tetrachloride with RMS errors of 1.1, 0.6 and 0.5 kcal/mol respectively. We
additionally show that fitting the solvent-dependent $s_6$ parameter to the
solvation energy of a single non-polar molecule does not substantially increase
these errors. Parametrization of this model for other solvents, therefore,
requires minimal effort and is possible without extensive databases of
experimental solvation free energies.
