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Analysis of atomic integrals involving explicit correlation factors for the three-electron case. I. Connection to the hypergeometric function \(_{3}{{\varvec{F}}}_{2}\)

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Abstract

This work considers the solution of atomic three-electron integrals that involve explicit inter-electronic separation factors. The traditional Sack expansion is replaced by an alternative expansion, which avoids the breakup of the radial integrals into a number of factors depending on the lesser and greater of the inter-electronic separation distances. The present approach avoids the N! increase in the number of required auxiliary functions, where N is the number of electrons. The new approach leads to additional infinite summations, but these summations either converge very quickly in a serial calculation, or can be effectively dealt with using the massively parallel architecture of a graphics processing unit. The new auxiliary functions that arise are discussed in detail.

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Acknowledgments

Preliminary support from the National Science Foundation and from the Donors of the Petroleum Research Fund, administered by the American Chemistry Society, is greatly appreciated. We also thank the Office of University Research, University of Wisconsin-Eau Claire for support. I.P. acknowledges a grant from the Spanish Ministerio de Educación (PRX12/00683), which provided financial assistance for his visit. We thank Morgan Leider for constructive comments on Cuda coding.

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Authors and Affiliations

  1. Department of Chemistry, University of Wisconsin-Eau Claire, Eau Claire, WI, 54702, USA

    Chong H. Leong, Ignacio Porras & Frederick W. King

  2. Departamento de Física Atómica, Molecular y Nuclear, Facultad de Ciencias, Universidad de Granada, 18071, Granada, Spain

    Ignacio Porras

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  1. Chong H. Leong
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  2. Ignacio Porras
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  3. Frederick W. King
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Correspondence to Ignacio Porras.

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Leong, C.H., Porras, I. & King, F.W. Analysis of atomic integrals involving explicit correlation factors for the three-electron case. I. Connection to the hypergeometric function \(_{3}{{\varvec{F}}}_{2}\) . J Math Chem 54, 1514–1552 (2016). https://doi.org/10.1007/s10910-016-0633-8

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