The fundamental integral is essentially an integral without angular momentum
(i.e., it is an integral of the type ). Angular momentum,
usually depicted by , has been problematic for efficient ERI formation,
evident in the above time line. Initially, angular momentum was calculated by
taking derivatives of the fundamental ERI with respect to one of the Cartesian
coordinates of the nuclear center. This is an extremely inefficient route, but
it works and was appropriate in the early development of ERI methods. Recursion
J. Chem. Phys.
(1986), 84, pp. 3963. , 827 J. Chem. Phys.
(1988), 89, pp. 1540. and the newly developed tensor equations 22 J. Chem. Phys.
(1997), 107, pp. 124. are the basis for the modern approaches.