Application of the level-set method to the implicit solvation of nonpolar molecules

TL;DR

This paper develops a level-set numerical method to determine the equilibrium solute-solvent interface in implicit solvation models, accurately capturing phenomena like dewetting and matching molecular dynamics results.

Contribution

It introduces a novel level-set approach for implicit solvation, coupling interfacial and van der Waals energies, and applies it to nonpolar molecules with successful validation.

Findings

Accurately predicts solvation energies for nonpolar molecules.

Captures solvent dewetting and nanobubble formation.

Shows good agreement with molecular dynamics simulations.

Abstract

A level-set method is developed for numerically capturing the equilibrium solute-solvent interface that is defined by the recently proposed variational implicit solvent model (Dzubiella, Swanson, and McCammon, Phys. Rev. Lett. {\bf 104}, 527 (2006) and J. Chem.\Phys. {\bf 124}, 084905 (2006)). In the level-set method, a possible solute-solvent interface is represented by the zero level-set (i.e., the zero level surface) of a level-set function and is eventually evolved into the equilibrium solute-solvent interface. The evolution law is determined by minimization of a solvation free energy {\it functional} that couples both the interfacial energy and the van der Waals type solute-solvent interaction energy. The surface evolution is thus an energy minimizing process, and the equilibrium solute-solvent interface is an output of this process. The method is implemented and applied to the solvation of nonpolar molecules such as two xenon atoms, two parallel paraffin plates, helical alkane chains, and a single fullerene $C_{60}$. The level-set solutions show good agreement for the solvation energies when compared to available molecular dynamics simulations. In particular, the method captures solvent dewetting (nanobubble formation) and quantitatively describes the interaction in the strongly hydrophobic plate system.