Tailored Gauss quadratures, a promising route for an efficient evaluation of multicenter integrals over B functions.
In the framework of the Fourier integral transform, complicated multicenter integrals, e.g., three-center nuclear attraction and exchange integrals, over B functions involve a multiple integral (double or triple), the innermost of which is a Hankel transform of an exponentially decreasing term. Because of the oscillatory nature of the Hankel transform and the order in which it occurs in the definition of multicenter integrals, i.e., innermost, an efficient evaluation of such a quantity requires highly performant algorithms. In this context, extrapolation techniques emerged, during the past decade, as a possible solution to the problem of evaluating the oscillating semi-infinite integral. With a view to improving the efficiency of future algorithms, this contribution introduces a new technique for the evaluation of the oscillating integral by means of a tailored Gaussian quadrature. Using the case of three-center nuclear attraction integrals as a working example, it is shown that the new approach allows the semi-infinite integral to be evaluated accurately if not exactly. Further, when the roots and weights of the quadrature are available, a complexity analysis of our algorithm shows encouraging results compared to nonlinear extrapolation techniques.
Rebabti
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Campus Saint Jean/University of Alberta, 8406-91 Street, Edmonton T6C 4G9, Canada.
Ghomari
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Bouferguene
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