B.7 Angular Momentum Problem

The fundamental integral is essentially an integral without angular momentum (i.e., it is an integral of the type $[ss\vert ss]$ ). Angular momentum, usually depicted by $L$ , 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 relations[Obara and Saika(1986), Obara and Saika(1988)] and the newly developed tensor equations[Adams et al.(1997)Adams, Adamson, and Gill] are the basis for the modern approaches.