Grid positioning independence and the reduction of self‐energy in the solution of the Poisson—Boltzmann equation

A common problem in the solution of the Poisson–Boltzmann equation using finite difference methods is the self‐energy of the system, also known as the grid energy. Because atoms are typically modeled as a point charge, the infinite self‐energy of a point charge is likewise modeled. In this article, a simple, alternate treatment of atomic charge is described where each atom is represented as a sphere of uniform charge. Unlike the point charge model, this method converges as the grid spacing is reduced. The uniform charge model generates the same electrostatic field outside the atoms. In addition, the use of fine grids reduces the variations in the potential due to variations in the position of atoms relative to the grid. Calculations of Born ion solvation energies, small‐molecule solvation energies, and the electrostatic field of superoxide dismutase are used to demonstrate that this method yields the same results as the point charge model. © John Wiley & Sons, Inc.