A. Geometry-independent initialization 1. Determining α groups One of the main differences between the GLST and SGT algorithms is using multiple cubatures. This is done to minimize the total number of cubature nodes that are needed to evaluate the long-range energies and forces. Each cubature can guarantee accuracy up to a given input tolerance for a specific range of distances and corresponding Ewald convergence parameter (α). To that end, based on the size of the unit cell and the desired cutoff value, we can determine the number of α groups (or cubatures) and the corresponding distance ranges and α parameters for each group.