The exchanged version g ARRI decays with O S AR S RI R ovl,AR,RI . Due to the triangle inequality in Euclidean space we can write R AR + R RI ≥ R AI and R ovl,AR,RI ≥ 1 2 R AI , which then gives an overall exponential decay of the integral g ARRI with R AI . As shown in equation 6, the integrals g AIRR or g ARRI are the only ones appearing in the single excitation matrix elements; thus, we expect an exponential decay with R AI . This observation is crucial for the weighted singles excitation generator.