Rys - Gauss quadrature

The author s connection to the area covers the implementation of the Rys-Gauss quadrature evaluation of ERIs. However, this article is not intentionally biased towards any method. It is anticipated that after reading this article, readers will be able to form opinions on which method to use in a particular circumstance. [Pg.1338]

The Rys-Gauss quadrature developed by Dupuis, Rys, and King in the late 1970s is a method which at first glance seems to have little in common with the other integral schemes. " However, as can be demonstrated the formulae derived for the Rys-Gauss quadrature are connected to the formulae of the incomplete Gamma function based schemes. [Pg.1346]

One way of formulating the computation of the ERIs using the Rys-Gauss quadrature is (see Figure 5) ... [Pg.1347]

The Obara-Saika 8-term recurrence relation is related to the 3-term formula used in the Dupuis-King-Rys implementation of the Rys-Gauss quadrature. However, the differences are... [Pg.1347]

The computation of the incomplete Gamma functions is a vital part of evaluating of the ERIs for all integral methods except the Rys-Gauss quadrature. In the evaluation of Fm(T ) two formulae can be used depending on the value of the argument, T. Firstly, there is the asymptotic formula in which the Laplace formula (see equation 13) is utilized. [Pg.1350]

This expression is in the appropriate form for Gauss-Rys quadrature (9.11.19) and may thus be evaluated exactly as... [Pg.393]

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