HOMEIER, HHH and STEINBORN, EO (1991) IMPROVED QUADRATURE METHODS FOR 3-CENTER NUCLEAR ATTRACTION INTEGRALS WITH EXPONENTIAL-TYPE BASIS FUNCTIONS. INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, 39 (4). pp. 625-645. ISSN 0020-7608,
Full text not available from this repository.Abstract
The numerical properties of a two-dimensional integral representation [J. Grotendorst and E.O. Steinborn, Phys. Rev. A 38, 3857 (1988)] of the three-center nuclear attraction integral with a special class of exponential-type orbitals (ETO'S), the B functions [E. Filter and E.O. Steinborn, Phys. Rev. A 18, 1 (1978)] are examined. B functions span the space of ETO'S. The commonly occurring ETO'S can be expressed in terms of simple finite sums of B functions. Hence, molecular integrals for other ETO'S, like the more common Slater-type orbitals, may be found as finite linear combinations of integrals with B functions. The main advantage of B functions is the simplicity of their Fourier transform that makes the derivation of relatively simple general formulas for molecular integrals with the Fourier transform method possible. The integrand of the integral representation mentioned above shows sharp peaks causing, in the case of highly asymmetric charge distributions, slow convergence of the quadrature method used by Grotendorst and Steinborn. New quadrature schemes are presented that use quadrature rules based on Mobius transformations. These rules are well suited for the numerical quadrature of functions that possess a sharp peak at or near a single boundary of integration [H. H. H. Homeier and E. O. Steinborn, J. Comput. Phys., 87, 61 (1990)]. Numerical results are presented that illustrate the fact that convergence of the new quadrature schemes is about a factor two faster in case of highly asymmetric charge distributions.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | REDUCED BESSEL-FUNCTIONS; 2-ELECTRON MULTICENTER INTEGRALS; FOURIER-TRANSFORM METHOD; ONE-ELECTRON; COULOMB INTEGRALS; NUMERICAL PROPERTIES; EFFICIENT EVALUATION; OVERLAP INTEGRALS; 2-CENTER PRODUCT; ATOMIC ORBITALS; |
| Depositing User: | Dr. Gernot Deinzer |
| Last Modified: | 19 Oct 2022 08:46 |
| URI: | https://pred.uni-regensburg.de/id/eprint/55037 |
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