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Computation of electron repulsion integrals using the rys quadrature method
Author(s) -
Rys J.,
Dupuis M.,
King H. F.
Publication year - 1983
Publication title -
journal of computational chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.907
H-Index - 188
eISSN - 1096-987X
pISSN - 0192-8651
DOI - 10.1002/jcc.540040206
Subject(s) - computation , quadrature (astronomy) , basis function , basis (linear algebra) , slater integrals , gaussian , angular momentum , gauss–kronrod quadrature formula , gauss–jacobi quadrature , order of integration (calculus) , trigonometric integral , gaussian quadrature , numerical integration , set (abstract data type) , mathematics , computer science , mathematical analysis , physics , algorithm , classical mechanics , nyström method , quantum mechanics , integral equation , geometry , optics , trigonometry , programming language
Following an earlier proposal to evaluate electron repulsion integrals over Gaussian basis functions by a numerical quadrature based on a set of orthogonal polynomials (Rys polynomials),\documentclass{article}\pagestyle{empty}\begin{document} $$ (\eta \eta \parallel \eta \eta) = 2(\rho/\pi)^{1/2} \sum\limits_{\alpha = 1, N} I_x(u_{\alpha})I_{y}(u_{\alpha}) I_z(u_{\alpha})W_{\alpha} $$ \end{document} a computational procedure is outlined for efficient evaluation of the two‐dimensional integrals I x , I y , and I z . Compact recurrence formulas for the integrals make the method particularly fitted to handle high‐angular‐momentum basis functions. The technique has been implemented in the HONDO molecular orbital program.