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  • 1
    Electronic Resource
    Electronic Resource
    Amsterdam : Elsevier
    Journal of Computational Physics 13 (1973), S. 433-438 
    ISSN: 0021-9991
    Source: Elsevier Journal Backfiles on ScienceDirect 1907 - 2002
    Topics: Computer Science , Physics
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Amsterdam : Elsevier
    Journal of Computational Physics 40 (1981), S. 64-76 
    ISSN: 0021-9991
    Source: Elsevier Journal Backfiles on ScienceDirect 1907 - 2002
    Topics: Computer Science , Physics
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Amsterdam : Elsevier
    Journal of Computational Physics 22 (1976), S. 352-376 
    ISSN: 0021-9991
    Source: Elsevier Journal Backfiles on ScienceDirect 1907 - 2002
    Topics: Computer Science , Physics
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    Springer
    Theoretical chemistry accounts 31 (1973), S. 189-194 
    ISSN: 1432-2234
    Keywords: Gaussian quadrature ; Green's functions ; Singularities
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract An account is given of the use of Gaussian quadrature product formulae in the evaluation of certain six-dimensional, two-centre integrals involving one-electron Green's functions. These integrals occur in a new molecular variational principle recently proposed by Hall, Hyslop and Rees [1] from which an approximate energy may be derived which can be shown to be at least as good as that obtained from the Rayleigh-Ritz principle. Reductions in computing time are realized by removing certain singularities using a subtraction technique and also by using an empirically determined Richardson-type extrapolation formula.
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    Springer
    Mathematische Zeitschrift 42 (1937), S. 489-512 
    ISSN: 1432-1823
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
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  • 6
    Electronic Resource
    Electronic Resource
    Springer
    Minerva 2 (1964), S. 286-302 
    ISSN: 1573-1871
    Source: Springer Online Journal Archives 1860-2000
    Topics: Education , Nature of Science, Research, Systems of Higher Education, Museum Science
    Type of Medium: Electronic Resource
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  • 7
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 11 (1977), S. 325-339 
    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: A recursive numerical integration scheme based on the method of Clenshaw and Curtis is proposed for the efficient implementation of the variation-iteration procedure for the computation of approximate energies and wave functions for atomic systems. Extensive numerical tests are carried out to assess the accuracy and efficiency of the method and inaccuracies in some earlier calculations are pointed out.
    Additional Material: 5 Tab.
    Type of Medium: Electronic Resource
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  • 8
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 10 (1976), S. 669-681 
    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: In this paper an iterative generalization of the minimum principle proposed for electronic systems by Hall, Hyslop, and Rees is investigated. It is shown that this generalization still retains the advantage of using members of a larger class of trial wave-functions, for example those with discontinuities, as initial approximations to the wave-functions. This scheme has the advantage that, at each stage of iteration, an upper bound is obtained which is at least as good as that obtained previously.The theory is first applied to the hydrogen atom. It is then adapted to estimate the Hartree-Fock energy of the helium atom, the Hartree-Fock limit being obtained after a relatively small number of iterations.
    Additional Material: 3 Tab.
    Type of Medium: Electronic Resource
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  • 9
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 4 (1970), S. 5-20 
    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: In this paper the minimum principle proposed for atomic systems by Hall, Hyslop and Rees [1] is generalized to molecules. It is shown that this generalization retains the advantage of admitting the use of a larger class of trial wave functions, for example those with discontinuities, than is possible in the usual minimum energy principle. The further advantage that the upper bounds obtained by this treatment are always at least as good as those of the Rayleigh-Ritz method is also preserved.The theory is applied to the H2+ ion, potential energy curves are obtained for various “cut-off” wave functions, and the equilibrium internuclear distance is calculated. The optimization of the “cut-off” region so that the upper bound is minimized is also discussed.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
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  • 10
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 3 (1969), S. 195-204 
    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: In this paper a variational principle proposed by Hall [1] is shown to be a minimum principle for coulombic systems. Into this principle it is possible to admit a larger class of trial wave functions than is possible in the conventional variational treatment, including wave functions with discontinuities. It is further shown that the upper bounds given by this treatment are always at least as good as that given by the Rayleigh-Ritz method.The theory is then applied to the hydrogen atom and upper bounds to the energy are calculated for various “cutoff” wave functions. It is usually possible to define an optimum “cut off” distance which minimizes the upper bound.
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
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