Density functional theory of solvation in a polar solvent: extracting the functional from homogeneous solvent simulations.

In the density functional theory formulation of molecular solvents, the solvation free energy of a solute can be obtained directly by minimization of a functional, instead of the thermodynamic integration scheme necessary when using atomistic simulations. In the homogeneous reference fluid approximation, the expression of the free-energy functional relies on the direct correlation function of the pure solvent. To obtain that function as exactly as possible for a given atomistic solvent model, we propose the following approach: first to perform molecular simulations of the homogeneous solvent and compute the position and angle-dependent two-body distribution functions, and then to invert the Ornstein-Zernike relation using a finite rotational invariant basis set to get the corresponding direct correlation function. This rather natural scheme is proved, for the first time to our knowledge, to be valuable for a dipolar solvent involving long range interactions. The resulting solvent free-energy functional can then be minimized on a three-dimensional grid around a solute to get the solvent particle and polarization density profiles and solvation free energies. The viability of this approach is proven in a comparison with "exact" molecular dynamics calculations for the simple test case of spherical ions in a dipolar solvent.