Recurrence relations for matrix elements of few-body correlated wave functions

Authors

  • Frank E. Harris

    Corresponding author
    1. Department of Physics, University of Utah, Salt Lake City, Utah 84112
    2. Quantum Theory Project, University of Florida, Gainesville, Florida 32611
    • Department of Physics, University of Utah, Salt Lake City, Utah 84112
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Abstract

This article considers the matrix elements arising from the use of wave functions containing exponentials in all the interparticle distances. Special cases (with some vanishing parameters) correspond to the use of the Hylleraas basis. For the three-body (sometimes called two-electron) correlated wave function, we present new recurrence relations that complement the formula of Sack, Roothaan, and Kolos. One of these is a sum rule that could also be used for downward recursion; the other is suitable for recursion in the usual (upward) recursive process. Formulas connecting matrix elements in the four-body (three-electron) problem are also derived; their use confirms the recurrence relations recently published by Pachucki, Puchalski, and Remiddi for the Hylleraas basis and provides a new sum rule for matrix elements in the general correlated exponential basis. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005

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