Solution of Poisson's equation requires discretization of three-dimensional space, to a distance sufficiently far from the molecule such that ϕ tot (r) ≈ 0. In PEqS, this discretization is performed on a dense Cartesian grid in order to facilitate finite-difference evaluation of the requisite Laplacian, ∇2 ϕ tot (r), and to make use of a Cartesian multigrid algorithm. In Sections 4 .1 and 4 .2, where the solute cavities are spherical, we use a relatively coarse grid spacing ∆x = ∆y = ∆z = 0.2877 Å, which is comparable to the spacing used in previous work on excitation and ionization energies. The latter quantities are relatively insensitive to the grid spacing as compared to ∆G elst , which is sensitive to how quickly ε(r) changes at the boundaries of the molecular cavity. As such, in the present work we use a very fine grid spacing of ∆x = ∆y = ∆z = 0.05 Å when the cavity is constructed from atomic radii, as in Section 4 .3. (See Table for tests of how ∆G elst converges as a function of the grid spacing.) The coordinate origin is placed at the centroid of the atomic coordinates and the grid extends to a total length of 8 Å in each direction. In most cases, this means that all nuclei are at least 2 Å away from the edges of the grid. The multigrid PEqS algorithm described in Ref. 21 is used to solve Poisson's equation at each SCF iteration.