Strategies for an efficient implementation of the Gauss–Bessel quadrature for the evaluation of multicenter integral over STFs

Abstract

In a previous work, a new Gauss quadrature was introduced with a view to evaluate multicenter integrals over Slater-type functions efficiently. The complexity analysis of the new approach, carried out using the three-center nuclear integral as a case study, has shown that for low-order polynomials its efficiency is comparable to the SD. The latter was developed in connection with multi-center integrals evaluated by means of the Fourier transform of B functions. In this work we investigate the numerical properties of the Gauss-Bessel quadrature and devise strategies for an efficient implementation of the numerical algorithms for the evaluation of multi-center integrals in the framework of the Gaussian transform/Gauss-Bessel approach. The success of these strategies are essential to elaborate a fast and reliable algorithm for the evaluation of multi-center integrals over STFs.

Evaluation of three-center two-electron repulsion integrals over Slater orbitals

“…The bottle-neck of these programs is the calculation of the three-and four-center repulsion integrals. The approximate methods used are: one-center expansion [7,8,9,10,11], translation [12,13], Gaussian expansion [14], Gauss transform [15,16,17], and Fourier transform [18,19,20,21,22,23] methods. The disadvantages of these methods are on one hand side the low accuracy achieved, what results in longer expansions and increased computational times, and on the other side the need of numerical integrations.…”