Rapid algorithm for computing the electron repulsion integral over higher order Gaussian-type orbitals: Accompanying coordinate expansion method

• Published in: Journal of computational chemistry Vol. 19; no. 8; pp. 923 - 934
• Main Author: Ishida, Kazuhiro
• Format: Journal Article
• Language: English
• Published: New York John Wiley & Sons, Inc 01.06.1998
• Subjects: accompanying coordinate expansion method; electron repulsion integral; molecular integral; rapid algorithm
• ISSN: 0192-8651; 1096-987X
• DOI: 10.1002/(SICI)1096-987X(199806)19:8<923::AID-JCC11>3.0.CO;2-8

A general algorithm for rapidly computing the electron repulsion integral (ERI) is derived for the ACE‐b3k3 formula, which has been derived previously. [K. Ishida, Int. J. Quantum Chem., 59, 209 (1996)]. A computer program code that is universal for all types of Gaussian‐type orbitals (GTOs) up to h‐type can be constructed by the use of this general algorithm. It is confirmed that the ACE‐b3k3 algorithm is numerically very stable even for higher order GTOs. It is found that, in a floating‐point‐operation (FLOP) count assessment, the ACE‐b3k3 algorithm is the fastest among all methods available in the literature for (dd|dd), (ff|ff), (gg|gg), and (hh|hh) ERIs when the degree of contraction of the GTO is high. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 923–934, 1998