where P and Q denotes the elements of the auxiliary basis, whereas (pq|P) and (P|Q) stand for the three-and two-centered Coulomb integrals, respectively. The (P|Q) -1 is a simplified notation for the corresponding element of the inverse of the two-center Coulomb integral matrix. In actual practice, the inverse matrix is factorized and rewritten as the product of the inverse square root matrices. The four-centered ERIs can then be recasted as ( )