### Abstract

A basis set representation which includes an explicit treatment of the Fock expansion in hyperspherical coordinates, was used for variational calculations of the ground-state energy of helium. The Fock functions provided the exact analytic structure of the true wave function when two electrons coalesced near the nucleus. The modified Gauss-Laguerre quadrature allowed an accurate numerical evaluation of integrals containing logarithms of the hyperradius. The results demonstrate that the convergence rate of a nearly orthogonal basis set, such as the triple product of Laguerre polynomials in perimetric coordinates, may be improved through the addition of a few specially designed basis functions.

Original language | English (US) |
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Article number | 022504 |

Pages (from-to) | 225041-2250410 |

Number of pages | 2025370 |

Journal | Physical Review A - Atomic, Molecular, and Optical Physics |

Volume | 69 |

Issue number | 2 |

State | Published - Feb 2004 |

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### All Science Journal Classification (ASJC) codes

- Atomic and Molecular Physics, and Optics

### Cite this

*Physical Review A - Atomic, Molecular, and Optical Physics*,

*69*(2), 225041-2250410. [022504].