Theoretica chimica acta

, Volume 44, Issue 1, pp 9–26 | Cite as

The convergence of the Rayleigh-Ritz Method in quantum chemistry

I. the criteria of convergence
  • Bruno Klahn
  • Werner A. Bingel
Original Investigations


Two sufficient criteria for the convergence of the Rayleigh-Ritz Method (RRM) with respect to the eigenvalues (“E-convergence”) of non-relativistic electronic Hamiltonians of molecules are discussed and compared. Moreover, a necessary and sufficient criterion is given. By example (Sect. 9) it is shown that the L2-completeness of the basis is not sufficient to guarantee E-convergence. The convergence of the wave functions in different norms (“Ψ-convergence”) is also investigated. In particular, sufficient conditions for the one-particle basis functions (orbitals) are given, such that a CI calculation in this basis is both E- and Ψ-convergent.

Key words

Criteria of convergence Completeness of basis sets Energy space CI calculations 


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Copyright information

© Springer-Verlag 1977

Authors and Affiliations

  • Bruno Klahn
    • 1
  • Werner A. Bingel
    • 1
  1. 1.Theoretical Chemistry GroupUniversity of GöttingenGöttingenFederal Republic of Germany

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