Practical performance assessment of accompanying coordinate expansion recurrence relation algorithm for computation of electron repulsion integrals

We have developed a computer program for evaluation of electron repulsion integrals (ERIs) based on the accompanying coordinate expansion recurrence relation (ACE-RR) algorithm, which has been recently developed as an efficient algorithm for computation of ERIs using Pople-type basis sets (STO-3G and 6-31G, for example) and derivatives of ERIs [Kobayashi and Nakai, J Chem Phys 121:4050, 2004]. The computer program can be linked to GAMESS ab initio quantum chemistry program. The practical performance of the ACE-RR method is assessed by means of the central processing unit (CPU) time for the first direct self-consistent field cycle on a model system (4 x 4 x 4 cubic hydrogen lattice), taxol (C₄₇H₅₁NO₁₄), and valinomycin (C₅₄H₉₀N₆O₁₈) using Pople-type basis sets. The considerable efficiency of the present ACE-RR method is demonstrated by measuring the CPU time. The present ACE-RR method is comparable to or at most 30% faster than the Pople-Hehre method which is also designed for efficient computation of ERIs using Pople-type basis sets. Furthermore, the ACE-RR method is drastically faster than the Dupuis-Rys-King method in the case where the degree of contraction of Pople-type basis sets is high: 7.5 times faster in the case of valinomycin using STO-6G basis set, for example.