Harmonic averaging of smooth permittivity functions in finite-difference Poisson–Boltzmann Electrostatics

Finite-difference Poisson–Boltzmann calculations offer an efficient and accurate means for electrostatic characterization of solvated molecules. However, discretization of charge and permittivity results in sensitive dependence on molecular position and orientation relative to the finite-difference grid. In this article, an improved method for limiting the error associated with discretization of the molecular volume, combining harmonic averaging between grid vertices and Gaussian-based smooth permittivity functions, is presented. While both these methods have the broader result of a smoothly varying permittivity, the Gaussian model represents a fundamental description of the dielectric boundary while harmonic averaging serves to provide information about the permittivity between grid points. Grid positional error is reduced by an order of magnitude in calculations of Born ion solvation energies, small molecule and protein solvation energies, and the solvation energy contribution to a protein-inhibitor complex.