Molecular Density Functional Theory of Water describing Hydrophobicity at Short and Long Length Scales

We present an extension of our recently introduced molecular density functional the-ory of water [G. Jeanmairet et al., J. Phys. Chem. Lett. 4, 619, 2013] to the solvation of hydrophobic solutes of various sizes, going from ångströms to nanome-ters. The theory is based on the quadratic expansion of the excess free energy in terms of two classical density fields, the particle density and the multipolar polariza-tion density. Its implementation requires as input a molecular model of water and three measurable bulk properties, namely the structure factor and the k-dependent longitudinal and transverse dielectric susceptibilities. The fine three-dimensional wa-ter structure around small hydrophobic molecules is found to be well reproduced. In contrast the computed solvation free-energies appear overestimated and do not exhibit the correct qualitative behavior when the hydrophobic solute is grown in size. These shortcomings are corrected, in the spirit of the Lum-Chandler-Weeks theory, by complementing the functional with a truncated hard-sphere functional acting be-yond quadratic order in density, and making the resulting functional compatible with the Van-der-Waals theory of liquid-vapor coexistence at long range. Compared to available molecular simulations, the approach yields reasonable solvation structure and free energy of hard or soft spheres of increasing size, with a correct qualitative transition from a volume-driven to a surface-driven regime at the nanometer scale