These include a standard vdW cavity construction, as in the original PEqS approach, which simply means smoothing the sharp dielectric boundary according to eq. 21. (For the present calculations, that boundary surface consists of a single sphere.) In addition, we consider pointwise construction of ε(r) according to the Voronoi scheme in eq. 28. These calculations use large atomic radii (R = 3.12R vdW ) to ensure that there is no escaped charge, since the analytic Born model is only exact under that assump- tion. A 21 Å × 21 Å × 21 Å grid is employed, with ∆x = ∆y = ∆z = 0.29 Å, which is typical of earlier PEqS calculations. For the PEqS calculations using the standard vdW cavity construction, the discretized Poisson model solvates the ions slightly more strongly than the exact analytic solution to Poisson's equation, although the discretization errors are smaller than 0.3 kcal/mol or about 1% of ∆G elst . For the Voronoi construction of ε(r), the errors are in the other direction but also about 1% of ∆G elst .