Premium
Recent progress in the accurate and rapid evaluation of all Coulomb integrals over slater‐type orbitals
Author(s) -
Safouhi Hassan,
Hoggan Philip
Publication year - 2001
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.1412
Subject(s) - atomic orbital , coulomb , ab initio , bar (unit) , physics , slater integrals , nonlinear system , mathematical physics , center (category theory) , chemistry , quantum mechanics , crystallography , electron , meteorology
One of the main objectives in ab initio Slater research is rapid and accurate evaluation of the two‐, three‐, and four‐center Coulomb integrals. General expressions for these integrals were obtained and evaluated for the first time using the single center strategy and requisite orbital translations. The alternative strategy using the Fourier transform of the B functions basis has been thoroughly explored by the Steinborn group. The analytical expressions of these integrals have been shown to be adapted to the use of nonlinear transformations to accelerate their convergence. A complete study of D ‐ (due to Levin and Sidi) and \documentclass{article}\pagestyle{empty}\begin{document}$\bar{D}$\end{document} ‐transformations (due to Sidi) for all these integrals has led to the improved HD and \documentclass{article}\pagestyle{empty}\begin{document}$H\bar{D}$\end{document} methods, which greatly simplified the application of the above nonlinear transformations. The results presented show that the \documentclass{article}\pagestyle{empty}\begin{document}$H\bar{D}$\end{document} method gives unprecedented accuracy with speedup by a factor of 5 over the \documentclass{article}\pagestyle{empty}\begin{document}$\bar{D}$\end{document} approach and over 70 over the initial STOP method for four center terms. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem, 2001