  We address the problem of predicting the solvation free energy and
equilibrium solvent density profile in fews minutes from the molecular density
functional theory beyond the usual hypernetted-chain approximation. We
introduce a bridge functional of a coarse-grained, weighted solvent density. In
few minutes at most, for solutes of sizes ranging from small compounds to large
proteins, we produce (i) an estimation of the free energy of solvation within 1
kcal/mol of the experimental data for the hydrophobic solutes presented here,
and (ii) the solvent distribution around the solute. Contrary to previous
propositions, this bridge functional is thermodynamically consistent in that it
produces the correct liquid-vapor coexistence and the experimental surface
tension. We show this consistency to be of crucial importance for water at room
temperature and pressure. This bridge functional is designed to be simple,
local, and thus numerically efficient. Finally, we illustrate this new level of
molecular theory of solutions with the study of the hydration shell of a
protein.
