A novel Rys quadrature algorithm for use in the calculation of electron repulsion integrals

作者：Shizgal Bernie D^*

来源：Computational and Theoretical Chemistry, 2015, 1074: 178-184.

DOI：10.1016/j.comptc.2015.10.023

• Rys polynomials
• Quadrature weights and points
• Half-range and full-range polynomials
• Jacobi matrix

The half-range Rys polynomials, R-n(x), are orthonormal with respect to weight function w(x) = e(-cx2) on the interval x is an element of[0, 1] and defined with the set of coefficients, alpha(n) and beta(n), in the three term recurrence relation for the polynomials. Full range Rys polynomials, J(n)(x), are orthonormal with respect to w(x) = e(-cx2) on the interval x is an element of[-1, 1]. They are defined with the set of (beta) over cap (n) recurrence coefficients as (alpha) over cap (n) = 0. The Gauss-Rys quadrature defined with the Rys polynomials are used to evaluate electron repulsion integrals in quantum chemistry computer codes. The present paper proposes a new algorithm for the efficient computation of the Rys quadrature weights and points versus the parameter c in the weight function. The method is based on the full range Rys polynomials and a novel method for the calculation of the positive quadrature points and related weights.

• 出版日期2015-12-15