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Highly accurate numerical results for three‐center nuclear attraction and two‐electron Coulomb and exchange integrals over Slater‐type functions
Author(s) -
Safouhi Hassan
Publication year - 2004
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.20209
Subject(s) - slater integrals , nonlinear system , order of integration (calculus) , transformation (genetics) , convergence (economics) , trigonometric integral , coulomb , basis function , numerical integration , type (biology) , fourier transform , volume integral , mathematics , physics , electron , mathematical analysis , quantum mechanics , chemistry , integral equation , gene , economic growth , ecology , biochemistry , biology , economics , trigonometry
The present work focuses on the recent progress in nonlinear transformation methods for improving the convergence of highly oscillatory integrals and in their applications for an efficient and rapid numerical evaluation of molecular electronic integrals over Slater‐type functions (STFs). The nonlinear D transformation, which is probably the most effective general approach for increasing the rate of convergence of semi‐infinite oscillatory integrals, is presented. Molecular integrals over STFs are expressed as finite linear combinations of integrals over B functions. The basis set of B functions is suitable to apply the Fourier transform method, which led to analytic expressions, involving highly oscillatory functions, for molecular integrals. Efficient algorithms based on the D transformation are now developed for a numerical evaluation of molecular integrals over STFs. Numerical results that we obtained with linear and nonlinear molecules, and which are in agreement with those obtained using existing codes (Alchemy, STOP, and ADGGSTNGINT), show that the algorithms described in this work are relevant. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2004