Our new PCHB excitation generator relies on the decay of Hamiltonian matrix elements from vanishing integrals. We assume the MOs to be suitably localized and separated enough from each other so that a distance R between the MOs can be defined. We have to emphasize that the following discussion does not apply to delocalized orbitals. For the decay of the two-electron integrals g AIBJ we need to define the following quantities: S IA and R IA are defined as before, S JB and R BJ are the absolute overlaps and distances between φ J and φ B , and R ovl,AI,BJ is the distance between the overlap distributions φ A φ I and φ B φ J . With this notation the two-electron integrals g AIBJ decay for large distances as O S AI S BJ R ovl,AI,BJ . We will now look at specific important integrals. In the case of the classical Coulomb term g IIJJ we have S II = S JJ = 1 which implies a decay of g IIJJ with O 1 R IJ (note R ovl,II,JJ = R IJ in this case). This decay can be related to classical electrostatics, since the orbitals depending on the same electronic coordinate can be combined into the classical electron density ρ I = φ * I φ I and decays, like classical point charges, with O( 1 R IJ ) for a large enough distance between the MOs φ I and φ J . Now we look at specific examples of non-classical two-electron integrals, that appear in the single-excitation matrix elements, namely g AIRR or g ARRI . The integral g AIRR decays with S AI hence exponentially with R AI .