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

TL;DR

This paper extends a molecular density functional theory of water to better describe hydrophobic solvation across different length scales, incorporating corrections for accurate free energy predictions and solvation structure.

Contribution

It introduces a corrected functional combining quadratic and hard-sphere terms, enabling accurate modeling of hydrophobic solvation from small molecules to nanometer-sized particles.

Findings

Accurately reproduces water structure around small hydrophobic molecules.

Overestimates solvation free energies initially, but corrections improve predictions.

Captures the transition from volume-driven to surface-driven solvation regimes at nanoscales.

Abstract

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.