Abstract
The half-range Rys polynomials, Rn(x), are orthonormal with respect to weight function w(x)=e-cx2 on the interval x∈[0,1] and defined with the set of coefficients, αn and βn, in the three term recurrence relation for the polynomials. Full range Rys polynomials, Jn(x), are orthonormal with respect to w(x)=e-cx2 on the interval x∈[-1,1]. They are defined with the set of β̂n recurrence coefficients as α̂n=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.
Published Version
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