Computing the electrostatic free-energy of complex molecules: The variational Coulomb field approximation

Abstract

We introduce a novel approximate electrostatic method yielding the electrostatic fields around a molecule of complex shape embedded in a continuum dielectric solvent and the electrostatic solvation free-energies. This method extends the widely used Coulomb field approximation by supposing that the dielectric displacement can be written as the Coulomb field created by a set of fictitious “image” charges placed on the solute atomic sites. The electrostatic problem is solved by minimizing a polarization density functional with respect to the image charges. The method presents computational advantages which are reminiscent to those of the Coulomb field approximation; in particular, the solvation free-energy can be cast into a form which requires only the evaluation of space integrals limited to the interior of the solute. Its accuracy is demonstrated for simple solutes in water, ion pairs, the Tanford–Kirkwood globular protein model, and small polypeptides. It is shown also that our approach provides a systematic correction beyond the Coulomb field approximation which is able to improve the estimation of the atomic self-energies and associated Born radii in the generalized Born method.