Molecular Dynamics Study of the Dependence of Water Solvation Free Energy on Solute Curvature and Surface Area

We have investigated changes in water properties when deforming an initially spherical cavity into an oblate ellipsoid of equal volume in liquid water. The purely hydrophobic cavity has an initial thermal radius of 6.45 A and is flattened out to an oblate ellipse with a thickness corresponding to one layer of methane molecules. The water-solute interactions are modeled by a repulsive, single-site Gay-Beme potential that preserves the volume of the solute; water-water interactions are modeled using a pairwise additive potential. The Gibbs free energy change, AG, of the aqueous solution was calculated using thermodynamic perturbation theory. Comparison with the process of radially expanding a sphere shows that the free energy change cannot consistently be interpreted as being solely proportional to an exposed solute area but contains terms involving the curvature of the solute. As the meanings of exposed surface area and molecular curvature are not welldefined concepts on the microscopic length scale, these terms have to be defined to yield a consistent interpretation of the free energy data. The microscopic origin of the curvature dependence of the free energy is traced back to changes in water-water interactions in the region immediately surrounding the solute. The process of deforming the liquid around the hydrophobic pocket was found to be dominated by entropic contributions. The free energy values do not contain any contributions arising from the deformation of the hydrophobic solute itself nor any attractive solute-solvent term and thus cannot be compared directly with hydrocarbon-water surface tension data.