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  • 1
    Electronic Resource
    Electronic Resource
    The convergence of CI calculations for atomic and molecular electronic bound states in a basis of floating Gauss orbitals (1985)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 83 (1985), S. 5754-5759 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The energy convergence of CI calculations for atomic and molecular electronic bound states in a basis set of floating orbitals, which may depend on the number of basis functions used in a calculation, is investigated. Applying a generalization of the Müntz–Szász theorem, a condition for the choice of floating orbital exponents with respect to Gaussians results, which guarantees convergence of energies and wave functions to the right limits in any state, as the number of basis orbitals increases to infinity. This condition is discussed for the special choice of even-tempered Gaussians.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.449652
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    A generalization of the Müntz–Szász theorem to floating exponents with applications to Gauss- and Slater-type functions (1985)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 83 (1985), S. 5749-5753 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The Müntz–Szász condition for completeness of the monomials xλn in L2 is extended to floating functions, where the exponents λn may depend on the number of basis functions used in an approximation. The generalized condition is rewritten for Gauss- and Slater-type functions and then discussed, especially with respect to even-tempered functions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.449651
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    The convergence of the Rayleigh-Ritz Method in quantum chemistry (1977)
    Springer
    Theoretical chemistry accounts 44 (1977), S. 9-26 
    Details
    ISSN: 1432-2234
    Keywords: Criteria of convergence ; Completeness of basis sets ; Energy space ; CI calculations
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract 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 L 2-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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00548026
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    Paper (German National Licenses)
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  • 4
    Electronic Resource
    Electronic Resource
    The convergence of the Rayleigh-Ritz Method in quantum chemistry (1977)
    Springer
    Theoretical chemistry accounts 44 (1977), S. 27-43 
    Details
    ISSN: 1432-2234
    Keywords: Convergence of the RRM/CI calculation ; Complete basis sets ; Orbital exponents ; Two-electron functions
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: 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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00548027
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    Paper (German National Licenses)
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  • 5
    Electronic Resource
    Electronic Resource
    Completeness and linear independence of basis sets used in quantum chemistryThis material constitutes part of the doctoral thesis of one of the authors (B.K.). (1977)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 11 (1977), S. 943-957 
    Details
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Infinite sets of functions in Hilbert space are characterized by their completeness properties and the extent of linear independence. Different measures of linear independence such as orthonormality, Gram's determinant, the special measure of linear independence, and the asymptotic dimension are related to each other and with the degrees of completeness such as overcompleteness, exact completeness, and incompleteness as far as possible.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560110607
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    Paper (German National Licenses)
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