The computation of radial integrals with nonclassical quadratures for quantum chemistry and other applications

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• 作者：Bernie D. Shizgal ; Nicholas Ho ; Xingwei Yang
• 关键词：Radial integrals ; Quadratures ; Mappings ; Gauss–Maxwell quadrature
• 刊名：Journal of Mathematical Chemistry
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：55
• 期：2
• 页码：413-422
• 全文大小：
• 刊物类别：Chemistry and Materials Science
• 刊物主题：Physical Chemistry; Theoretical and Computational Chemistry; Math. Applications in Chemistry;
• 出版者：Springer International Publishing
• ISSN：1572-8897
• 卷排序：55

文摘

The computation of radial integrals on the semi-infinite axis is an important computationally intensive feature of quantum chemistry computer codes with additional applications to physics and engineering. There have been numerous algorithms proposed to evaluate these integrals efficiently. Many of these approaches involve the transformation of the semi-infinite axis, \(r \in [0,\infty )\), to the finite interval, \(x \in [-1,1]\), and the use of the Gauss–Legendre or Gauss–Chebyshev quadratures to evaluate the integrals. These mappings redistribute the quadrature points in many different ways. The approach in this paper is to compute the radial integrals with the Gauss–Maxwell nonclassical quadrature defined by the weight function \(w(r)=r^2e^{-r^2}\) appropriate for the semi-infinite interval and to also use scaling of the quadrature points. We carry out numerical experiments with simple model radial integrands and compare with the results of previous workers.