Efficient and accurate solvation energy calculation from polarizable continuum models.

A new approach is proposed to enhance the efficiency and accuracy for calculation of the long-range electrostatic interaction from implicit solvation models, i.e., the polarizable continuum model (PCM) and its variants, conductorlike PCM/conductorlike screening model and integral equation formalism PCM. In these methods the solvent electrostatics effects are represented by a set of discrete apparent charges distributed on tesserae of the molecular cavity surface embedding the solute. In principle, the accuracy of these methods is improved if the cavity surface is tessellated to finer tesserae; however, the computational time is increased rapidly. We show that such undesired dependency between accuracy and efficiency is a result of the inaccurate treatment of the apparent charge self-contribution to the potential and/or electric field. By taking into account the full effects due to the size and curvature of the segment occupied by each apparent charge, the error in calculated electrostatic solvation free energy is essentially zero for ions (point charge at the center of a sphere) regardless of the degree of tessellation used. For molecules where gradient of apparent charge density is nonzero at the cavity surface, we propose a multiple-sampling technique which significantly lowers the calculated error compared to the original PCM methods, especially when very few numbers of tesserae are used.