ACE algorithm for the rapid evaluation of the electron-repulsion integral over Gaussian-type orbitals

✍ Scribed by Kazuhiro Ishida

• Publisher: John Wiley and Sons
• Year: 1996
• Tongue: English
• Weight: 602 KB
• Volume: 59
• Category: Article
• ISSN: 0020-7608
• DOI: 10.1002/(sici)1097-461x(1996)59:3<209::aid-qua4>3.0.co;2-1

✦ Synopsis

A new series of general formulas to evaluate the electron-repulsion integral (ERI) can be derived from modifying the Gauss-Rys quadrature formula. These named as "accompanying coordinate expansion (ACE) formulas" are capable of evaluating very fast EMS, especially for contracted Gaussian-type orbitals (GTOs). According to the degree of the contraction of GTOs, the optimum formula can be selected among these ACES. Numerical examples are shown for ( PSI ps) and ( ppI p p ) ERIs as typical examples.

It is found that the present ACE algorithm is numerically stable and is most efficient among all algorithms in the literature in the floating-point-operation (FLOP) count for all varieties of the degree of contraction.