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Journal of Mathematical Chemistry

, Volume 54, Issue 7, pp 1514–1552 | Cite as

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

  • Chong H. Leong
  • Ignacio Porras
  • Frederick W. King
Original Paper

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.

Keywords

Atomic three-electron integrals Sack expansion Hypergeometric functions 

Notes

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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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Chong H. Leong
    • 1
  • Ignacio Porras
    • 1
    • 2
  • Frederick W. King
    • 1
  1. 1.Department of ChemistryUniversity of Wisconsin-Eau ClaireEau ClaireUSA
  2. 2.Departamento de Física Atómica, Molecular y Nuclear, Facultad de CienciasUniversidad de GranadaGranadaSpain

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