New recurrence relations for the rapid evaluation of electron repulsion integrals based on the accompanying coordinate expansion formula

An algorithm for the rapid computation of electron repulsion integrals (ERI) over Gaussian basis functions based on accompanying coordinate expansion (ACE) formula was discussed. The algorithm used angular momentum reduced expression and introduced two types of recurrence relations to ACE formulas. It was found that the algorithm was suitable for calculation of ERI for the same exponent but different angular momentum functions. Analysis showed that the algorithm was capable of calculating ERIs with highly contracted Gaussian basis function.