When evaluating energies and forces, each cell interacts with its nearest neighbors using pairwise Coulomb interactions. Outside of this shell of short-range neighbors, the target cell interacts with all other cells using Eq. 2. To determine the number of α groups, we must consider shells of cells starting from two cells away, up to the total number of cells along one axis minus two. The first α group contains the shell of cells outside of the short-range neighbors. After, this initial group, the width of the shell for each α group is approximately doubled until all cells are accounted for. The minimum and maximum distances of each group are used to determine the corresponding α value, integration cutoff z, and the associated cubature.