Theoretica chimica acta

, Volume 59, Issue 5, pp 533–549 | Cite as

Convergence of the Rayleigh—Ritz method in self-consistent-field and multiconfiguration self-consistent-field calculations

  • Giacomo Fonte
Original Investigation


We investigate the analytical convergence of SCF and MCSCF calculations, when the dimension of the subspaces to which the orbitals are restricted tends to infinity. We show that the completeness only inL2(R3;C2) of the orbital bases does not ensure the convergence of the Ritz-energy, neither in SCF nor in MCSCF calculations, but that this convergence — as well as the convergence of the Ritz-orbitals in SCF calculations — is on the contrary guaranteed if the orbital bases are complete in the Sobolev spaceW1,2(R3;C2). Some consequences on the choice of the orbital exponents of Slater and Gauss functions are also discussed.

Key words

Convergence of the Rayleigh-Ritz method SCF and MCSCF calculations Completeness of orbital bases 


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Copyright information

© Springer-Verlag 1981

Authors and Affiliations

  • Giacomo Fonte
    • 1
  1. 1.Centro Siciliano di Fisica Nucleare e di Struttura della MateriaIstituto di Fisica Nucleare, Sezione di CataniaCataniaItaly

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