  We present an extension of our recently introduced molecular density
functional theory of water [G. Jeanmairet et al., J. Phys. Chem. Lett. 4, 619,
2013] to the solvation of hydrophobic solutes of various sizes, going from
angstroms to nanometers. 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 polarization 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 water 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
beyond quadratic order in density. It makes 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.
