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

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. (C) 2003 American Institute of Physics.