Compact representation of helium wave functions in perimetric and hyperspherical coordinates

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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 languageEnglish (US)
Article number022504
Pages (from-to)225041-2250410
Number of pages2025370
JournalPhysical Review A - Atomic, Molecular, and Optical Physics
Volume69
Issue number2
StatePublished - Feb 2004

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All Science Journal Classification (ASJC) codes

  • Atomic and Molecular Physics, and Optics

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