Interaction between the atom under consideration and distant leaves via the structure factors is analogous to the FMM approach, where calculation is done without needing any allto-all communication as in PME. Unlike FMM, the structure factor calculation involves relatively simple evaluation of sine and cosine functions, or complex exponentials. In SGT, the target accuracy can be controlled by adjusting the Gauss-Hermite-spherical-t cubature where using more cubature nodes increases the accuracy.