A Simple Electrostatic Model for the Hard-Sphere Solute Component of Nonpolar Solvation

We propose a new model for estimating the free energy of forming a molecular cavity in a solvent, by assuming this energy is dominated by the electrostatic energy associated with creating the static (interface) potential inside the cavity. The new model approximates the cavity-formation energy as that of a shell capacitor: the inner, solute-shaped conductor is held at the static potential, and the outer conductor (at the first solvation shell) is held at zero potential. Compared to cavity energies computed using free-energy pertubation with explicit-solvent molecular dynamics, the new model exhibits surprising accuracy (Mobley test set, RMSE 0.45 kcal/mol). Combined with a modified continuum model for solute-solvent van der Waals interactions, the total nonpolar model has RMSE of 0.55 kcal/mol on this test set, which is remarkable because the two terms largely cancel. The overall nonpolar model has a small number of physically meaningful parameters and compares favorably to other published models of nonpolar solvation. Finally, when the proposed nonpolar model is combined with our solvation-layer interface condition (SLIC) continuum electrostatic model, which includes asymmetric solvation-shell response, we predict solvation free energies with an RMS error of 1.35 kcal/mol relative to experiment, comparable to the RMS error of explicit-solvent FEP (1.26 kcal/mol). Moreover, all parameters in our model have a clear physical meaning, and employing reasonable temperature dependencies yields remarkable correlation with solvation entropies.

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