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Test of the Conventional Quantum Chemistry Methods on the Hydrogen Atom

  • T. L. Bailey
  • J. L. Kinsey

Abstract

This paper is a numerical study of the reliability and accuracy of some of the conventional methods of quantum chemistry by their application to the problem of the hydrogen atom, a case where the quantities of interest are known exactly. The variation principle, δ<H> = 0, is used to approximate energy eigenvalues and the corresponding eigenfunctions. As basis functions, two simple sets are chosen: a) Gaussians, exp(-kηr2); k = 1, 2,...N, and b) exponentials, exp(-kηr); k = 1, 2...N. N is the order of the basis set and η is the scale factor. Scaled functions φk are obtained from the unscaled ones φk in the usual way /1/:
$${\bar \phi _k} = {\eta ^{3/2}}{\phi _k}\left( {\eta r} \right)$$
Both sets become complete in the interval 0≤r≤∞ when N→∞ and, for both, all the necessary integrals are elementary.

Keywords

Excited State Lower Bound Quantum Chemistry Variation Principle Numerical Accuracy 
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References

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Copyright information

© Springer Science+Business Media New York 1976

Authors and Affiliations

  • T. L. Bailey
    • 1
  • J. L. Kinsey
    • 1
  1. 1.Quantum Chemistry Group For Research in Atomic, Molecular and Solid-State TheoryUppsala UniversityUppsalaSweden

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