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Analysis of some integrals arising in the atomic four-electron problem

J. Chem. Phys. 99, 3622 (1993); doi:10.1063/1.466160

Issue Date: 1 September 1993

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Frederick W. King
Department of Chemistry, University of Wisconsin–Eau Claire, Eau Claire, Wisconsin 54702
An analysis is presented for the evaluation of the one-center integrals of the form [integral]r<sup>i</sup><sub>1</sub>r<sup>j</sup><sub>2</sub>r<sup>k</sup><sub>3</sub>r<sup>l</sup><sub>4</sub>r<sup>m</sup><sub>12</sub> r<sup>n</sup><sub>13</sub>r<sup>p</sup><sub>14</sub>r<sup>q</sup><sub>23</sub>r<sup>s</sup><sub>24</sub> r<sup>t</sup><sub>34</sub>e<sup> - ar</sup><sub>1</sub>−br2−cr3−dr4 dr1 dr2 dr3 dr4 which arise in the solution of the atomic four-electron problem when a Hylleraas expansion is employed. A majority of the cases that arise can be solved by a reduction of the four-electron integrals to integrals arising in the three-electron problem. A second general approach is developed which is able to handle almost all cases that arise in practical calculations. The Journal of Chemical Physics is copyrighted by The American Institute of Physics.
History: Received 16 April 1993; accepted 18 May 1993
Permalink: http://link.aip.org/link/?JCPSA6/99/3622/1
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EDITORIALLY RELATED

  1. Comment on "Analysis of some integrals arising in the atomic four-electron problem" [J. Chem. Phys. 99, 3622 (1993)]
    Frank E. Harris et al.
    J. Chem. Phys. 120, 3040 (2004)
  2. Reply to "Comment on `Analysis of some integrals arising in the atomic four-electron problem' " [J. Chem Phys. 99, 3622 (1993)]
    Frederick W. King
    J. Chem. Phys. 120, 3042 (2004)

KEYWORDS and PACS

Keywords
PACS
  • 31.20.-d
    Electronic structure of atoms and molecules: theory Specific calculations and results
  • 02.30.-f
    Mathematical methods in physics Function theory, analysis
  • YEAR: 1993

PUBLICATION DATA

ISSN:
0021-9606 (print)   1089-7690 (online)
Publisher:
AIP is a member of CrossRef AIP

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