Extension of accompanying coordinate expansion and recurrence relation method for general-contraction basis sets

An algorithm of the accompanying coordinate expansion and recurrence relation (ACE-RR), which is used for the rapid evaluation of the electron repulsion integral (ERI), has been extended to the general-contraction (GC) scheme. The present algorithm, denoted by GC-ACE-RR, is designed for molecular calculations including heavy elements, whose orbitals consist of many primitive functions with and without higher angular momentum such as d- and f-orbitals. The performance of GC-ACE-RR was assessed for (ss|ss)-, (pp|pp)-, (dd|dd)-, and (ff|ff)-type ERIs in terms of contraction length and the number of GC orbitals. The present algorithm was found to reduce the central processing unit time compared with the ACE-RR algorithm, especially for higher angular momentum and highly contracted orbitals. Compared with HONDOPLUS and GAMESS program packages, GC-ACE-RR computations for ERIs of three-dimensional gold clusters Au _n (n=1, 2, ..., 10, 15, 20, and 25) are more than 10 times faster. © 2014 Wiley Periodicals, Inc. The rapid evaluations of electron repulsion integrals (ERIs) have been a challenging problem in quantum chemistry, especially for molecules containing heavy elements for which general-contraction (GC) basis functions with high angular momentum are used. Accompanying coordinate expansion and recurrence relation method is extended to the GC scheme. This article shows the procedure of the ERI evaluations and the efficiency of this method in comparison with other methods.