Resolutions of the Coulomb operator. VI. Computation of auxiliary integrals

We discuss the efficient computation of the auxiliary integrals that arise when resolutions of two-electron operators (specifically, the Coulomb operator T. Limpanuparb, A. T. B. Gilbert, and P. M. W. Gill, J. Chem. Theory Comput. 7, 830 (2011)10.1021/ct200115t and the long-range Ewald operator T. Limpanuparb and P. M. W. Gill, J. Chem. Theory Comput. 7, 2353 (2011)10.1021/ct200305n) are employed in quantum chemical calculations. We derive a recurrence relation that facilitates the generation of auxiliary integrals for Gaussian basis functions of arbitrary angular momentum and propose a near-optimal algorithm for its use.