Charge optimization leads to favorable electrostatic binding free energy

Variational optimization of molecular electrostatic charge distributions is a tool for the study of association reactions of molecules in solution. In principle, this method can be used in drug design and protein folding to analyze and improve molecular interactions and to provide electrostatic templates for molecular design. This optimization problem reduces to an inverse source problem in classical electrostatics, where the sources are determined by a combination of external and self-polarization potentials. In this paper, we show that the electrostatic portion of the free energy of association for electrostatically optimized molecules has an upper bound of zero in many situations of physical interest. That is, variational optimization provides a ligand-charge distribution that contributes favorably to the energetics of binding, even in a strongly polar medium. This stabilizing effect on association reactions is contrary to the usual role of electrostatics in aqueous complexes, in which desolvation effects generally dominate. We also show the existence and nonuniqueness of the variational solution and make a connection to the electrostatic image charge problem.