To apply Eqs. 19 and 20 to the entire simulation box, we group cells based on the distance from the current cell where the atom a belongs (colored yellow in Fig. ). For the nearest neighbor cells (cyan in Fig. ), pairwise 1/r interactions are directly calculated. Long-range interaction starts from the next nearest neighbor. The shortest distance from the current cell to the next nearest neighbor, i.e. the cell size R cell , is used as r c in Eq. 2 to determine α 1 and also ζ 1 via Eq. 8 (subscript 1 denotes the first α-group). With the chosen α 1 and ζ 1 for distance r ≥ r c , the difference between 1/r and erf(α 1 r)/r is less than ε. Next, to determine the GLST cubature, a "far cutoff" r f is used so that Eq. 12 holds for r < r f . For the α 1 group in 1D, we thus choose r f to be the largest distance from the current cell (yellow) and the next nearest neighbor cell (Fig. ). Then the resulting GLST approximation holds for r c < r < r f . The yellow cell is the cell where energy and force from other cells are to be calculated. It is located on the corner of the simulation box for illustration, but a similar grouping should be made in all other directions. The cyan region is the nearest neighbor where pairwise short-range interaction is used. The green region represents the group of cells where the same GLST cubature is used. The shortest distance r c between the yellow cell and the green region is used to find α and ζ , and the farthest distance r f is used to find the corresponding GLST cubature.