the long-ranged cutoff is required when determining the appropriate cubature parameters. Fig. shows the same system, but also depicts the optimal choice of levels for this interaction (in a strictly additive scheme). The vectors on each level are defined as the sum of their children's vectors so, e.g. the large swath of blue on that interacts in α 4 scale is optimally handled by just two interactions on level 1 instead of the equivalent, but less efficient interaction with 128 nodes on level 4. Further optimization of this approach is possible by considering subtractive as well as additive schemes.