Hyper-radial functions that are used for calculation of electron repulsion integrals over the Slater-type orbitals has recenty been introduced by A. Bagci and G. A. Aucar in,
https://arxiv.org/abs/2212.13911 .
The electron repulsion integrals are useful in both non−relativistic and relativistic calculations of many−electron systems. They involve hyper−geometric functions. Due to the non−trivial structure of infinite series that are used to define them, the hyper−geometric functions are practically difficult to compute. Convergence of their series are strictly depends on the values of parameters. Computational issues such as cancellation or round−off error emerge. The relationships free from hyper-geometric functions for expectation values of Coulomb potential are obtanied via Hyper-radial functions. Considering the efforts performed for accurate computation of special functions, our method is favorable in terms of cost−permanence factor. This is because its bi−directional form prompts to integrate the methodological developments with current state−of−art computer science. Recurrence relationships obtained for Hyper-radial functions exhibit a significant improvement in computational speed and a considerable reduction in complexity for electron repulsion integrals.
Further details will be accessible with the publication of relevant paper.
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