Algorithm for the storage of Clebsch-Gordan and Gaunt coefficients with the same selection rule and its application to multicenter integrals

Common algorithm is presented for the generation and storage of all unique, non-zero Clebsch-Gordan and Gaunt coefficients for which the sum of the three angular momentum quantum numbers is a non-negative even integer. This algorithm is especially useful for the fast computation of arbitrary multicenter integrals over Slater type orbitals (STOs) appearing in the Hartree-Fock-Roothaan and Hylleraas approaches. The storage algorithm obtained for the Clebsch-Gordan and Gaunt coefficients is utilized, as for examples, in the computation of two-electron multicenter integrals occurring in the Hartree-Fock-Roothaan equations of a molecule.