title: Strategies for Evaluation of Rys Roots and Weights.
abstract: The Rys quadrature method for evaluating molecular integrals requires accurate numerical values of the nodes of a Rys polynomial and associated weight factors. The numerical value of a Rys polynomial for a specified value of its argument can be evaluated by three-term recursion using α and β coefficients. We review existing integration schemes for computing these recurrence parameters, discuss issues related to computational efficiency and numerical precision, and propose a slightly new integration method using Gauss-Rys quadrature. We discuss the advantages and disadvantages of using Golub's matrix method for the computation of roots and weights.
authors.affiliation: Department of Chemistry University at Buffalo State University of New York Buffalo, New York 14260, United States.
authors.forename: Harry F
authors.initials: HF
authors.lastname: King