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Gauss–Bessel quadrature: A tool for the evaluation of Barnett–Coulson/Löwdin functions
Author(s) -
Bouferguene Ahmed,
Safouhi Hassan
Publication year - 2006
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.21079
Subject(s) - bessel function , numerical integration , convergence (economics) , gaussian quadrature , representation (politics) , logarithm , quadrature (astronomy) , gauss , mathematics , cusp (singularity) , gauss–kronrod quadrature formula , mathematical analysis , integral equation , physics , quantum mechanics , nyström method , geometry , optics , political science , law , economics , economic growth , politics
In previous work, we analyzed the numerical efficiency of several algorithms that can be used to evaluate the so‐called Barnett–Coulson/Löwdin functions (BCLFs). It was shown that series representations of these functions are generally not recommended in the neighborhood of the cusp because of their poor convergence (logarithmic convergence). In the present work, we propose to evaluate BCLFs using its symmetric integral representation combined with a tailored Gauss quadrature. The new method is shown to be capable of achieving acceptable accuracy, as illustrated by the numerical values obtained for two‐center overlap integrals, which agree with previously published results. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2006