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The convergence of the Rayleigh-Ritz Method in quantum chemistry

II. Investigation of the convergence for special systems of Slater, Gauss and two-electron functions

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Abstract

The convergence of the Rayleigh-Ritz Method (RRM) or of CI calculations, respectively, for the non-relativistic electronic Hamiltonian of molecules is investigated using the conventional basis sets of Quantum Chemistry, such as systems of Slater, Gauss and two-electron functions. Conditions for the choice of orbital exponents with respect to Slater and Gauss orbitals are especially given, such that the convergence is guaranteed. Inter alia, in Theorem 10 a proof of the convergence of the RRM for a Hylleraas basis in s,t,u-coordinates is presented, a question which is still being debated today.

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Klahn, B., Bingel, W.A. The convergence of the Rayleigh-Ritz Method in quantum chemistry. Theoret. Chim. Acta 44, 27–43 (1977). https://doi.org/10.1007/BF00548027

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Key words

  • Convergence of the RRM/CI calculation
  • Complete basis sets
  • Orbital exponents
  • Two-electron functions