Molecular density functional theory: application to solvation and electron-transfer thermodynamics in polar solvents

A molecular density functional theory of solvation is presented. The solvation properties of an arbitrary solute in a given solvent, both described by a molecular force field, can be obtained by minimization of a position- and orientation-dependent free-energy density functional. In the homogeneous reference fluid approximation, the unknown excess term of the functional can be approximated by the angular-dependent direct correlation function of the pure solvent. This function can be extracted from a preliminary MD simulation of the pure solvent by computing the angular-dependent pair distribution function and solving subsequently the molecular Ornstein-Zernike equation. The corresponding functional can then be minimized on a three-dimensional cubic grid for positions and a Gauss-Legendre angular grid for orientations to provide the solvation free energy of embedded molecules at the same time as the solvent three-dimensional microscopic structure. This functional minimization procedure is much more efficient than direct molecular dynamics simulations combined with thermodynamic integration schemes. The approach is shown to be also pertinent to the molecular-level determination of electron-transfer properties such as reaction free energy and reorganization energy. It is illustrated for molecular solvation and photochemical electron-transfer reactions in acetonitrile, a prototypical polar aprotic solvent.