Free energy and entropy for inserting cavities in water: Comparison of Monte Carlo simulation and scaled particle theory results

The process of inserting cavities in water is studied with the aim of a better description of some of the terms necessary in continuum quantum mechanical models. Free-energy changes for the formation of soft and hard spherical cavities in TIP4P water have been computed by Monte Carlo (MC) simulation with statistical perturbation theory, up to a radius of 6 Å. The free-energy change for the formation of a hard sphere, ${\mathrm{\Delta G}}_{\mathrm{cav}},$ is obtained combining the ${\mathrm{\Delta G}}_{\mathrm{sol}}$ of a soft repulsive sphere with the $\mathrm{\Delta G}$ corresponding to the process of transforming the soft sphere into a hard one. Two definitions of hard-sphere repulsive potentials have been considered, one only based on the distance of oxygens from the center of the cavity, while the other also excludes hydrogens from the same region. Differences in free energies are significant. The cubic polynomial expression ${\mathrm{\Delta G}}_{\mathrm{cav}},$ obtained by extrapolating the exact scaled particle theory (SPT) expression for very small excluding cavities, gives results in agreement with MC, with effective “hard-sphere” diameter for water larger than 2.77 Å. The SPT prediction is compared with other treatments based on surface tension. It is shown that a properly chosen surface and an “effective” surface tension of water lead to a good agreement with MC ${\mathrm{\Delta G}}_{\mathrm{cav}}$ without curvature or microscopic corrections. The “effective” surface tension of water turns out to be very close to the experimental value. Some different simple ways to extend SPT expression to nonspherical cavities have been compared, for a limited number of nonspherical convex cavities modeled as $n$ interlocking spheres, meant to mimic $n$ -alkanes in the all-staggered conformation. Entropy changes for soft cavities have been computed with two methods, i.e., combining free energy and enthalpy computations and by finite difference methods. Discrepancies between SPT predictions and MC results are significant. The calculated probability distributions of relevant angles of first hydration shell waters are consistent with orientations where no O–H or O–lone pair vector points towards the cavity. Their variation when the cavity size increases is mostly quantitative and only the broadening of the bands observed for the largest cavities might indicate the early stage of the transition to hydration patterns peculiar to an infinite hydrophobic surface.