  Many important applications of electronic structure methods involve molecules
or solid surfaces in a solvent medium. Since explicit treatment of the solvent
in such methods is usually not practical, calculations often employ continuum
solvation models to approximate the effect of the solvent. Previous solvation
models either involve a parametrization based on atomic radii, which limits the
class of applicable solutes, or based on solute electron density, which is more
general but less accurate, especially for charged systems. We develop an
accurate and general solvation model that includes a cavity that is a nonlocal
functional of both solute electron density and potential, local dielectric
response on this nonlocally-determined cavity, and nonlocal approximations to
the cavity-formation and dispersion energies. The dependence of the cavity on
the solute potential enables an explicit treatment of the solvent charge
asymmetry. With only three parameters per solvent, this `CANDLE' model
simultaneously reproduces solvation energies of large datasets of neutral
molecules, cations and anions with a mean absolute error of 1.8 kcal/mol in
water and 3.0 kcal/mol in acetonitrile.
