4.1. Evaluating Discretization Errors. As a test of the PEqS setup, including the use of smooth Voronoi cells to construct ε(r), we first consider solvation energies for monatomic ions in spherical cavities, where the Born ion model affords an analytic result for ∆G elst , 3 assuming a sharp dielectric interface and an isotropic medium, as in eq. 1. As such, comparison to PEqS results is an assessment of discretization errors in the latter. This comparison is presented in Table . Isotropic PCM results are included for completeness, and this method exactly reproduces the analytic Born model, whereas PEqS errors average about 1% of ∆G elst .