which are required for setting up the MF Hamiltonian as well as the self-energy. This step usually scales with N 4 b (with N b the number of basis functions). As one can see from Eq. ( ), GTOs occur as product functions φ α (r)φ β (r), of which N 2 b unique combinations exits. They can be approximated by a smaller auxiliary basis, ξ µ , which contains only N aux = 3N b to 5N b functions instead. Rewriting the 4-center integrals as a combination of 3-center and 2-center repulsion integrals