Molecular symmetry andab initio calculations: IV. Symmetry-matrix and symmetry-supermatrix in calculations of two-electron repulsion integrals
✍ Scribed by Cao, Xiaoping; Wang, Yan
- Publisher
- John Wiley and Sons
- Year
- 1997
- Tongue
- English
- Weight
- 168 KB
- Volume
- 18
- Category
- Article
- ISSN
- 0192-8651
No coin nor oath required. For personal study only.
✦ Synopsis
The product of two Gaussians having different centers is itself a one-center Gaussian, thus multicenter integrals with a Cartesian Gaussian basis can be reduced to one-center integrals. Recurrence relations for overlap integrals and Ž . electron repulsion integrals ERIs are derived at these centers. The calculations of overlap integrals and ERIs are carried out step by step from the highest Ž . Ž . symmetry case one center to required cases different centers by using the translation of Cartesian Gaussians. Full exploitation of symmetry in calculation processes can result in optimal use of these recurrence relations. Compared with the recently published algorithms, based on the recurrence relations derived by w Ž .x Obara and Saika J. Chem. Phys., 84, 3963 1986 , the floating point operations Ž . Ž . FLOPs for ERI calculations having four different centers can be reduced by a factor of ca. 2. A significant extra saving in calculations and storage can be obtained if atoms, linear, or planar molecules are discussed.