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  • Atomic, Molecular and Optical Physics  (7)
  • Wiley-Blackwell  (7)
  • 1995-1999
  • 1965-1969  (7)
  • 1950-1954
  • 1969  (7)
  • 1953
  • 1
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 3 (1969), S. 13-15 
    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
    Additional Material: 1 Tab.
    Type of Medium: Electronic Resource
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  • 2
    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: The π-electronic properties of furan, oxazole, benzofuran, benzoxazole, anthranil, and dibenzofuran are calculated by the semiempirical self-consistent-field molecular orbital method. A single set of parameters is found which satisfactorily reproduces the π → π* electronic transition energies and other π-electronic properties.
    Additional Material: 1 Ill.
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  • 3
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 3 (1969), S. 711-722 
    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: The generalized algebraic eigenvalue problem (A - λB)x = 0 arises in the use of the variation method in quantum mechanics. If, within the limitations of the computer word-length, the basis set used to expand the trial wave function is linearly dependent, the matrix B becomes singular. Three different algorithms designed to deal with this difficulty have been investigated, paying special attention to the problem of identifying which members of the basis set are effectively linearly dependent. The advantages and limitations of each method are discussed.
    Additional Material: 1 Tab.
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  • 4
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 3 (1969), S. 699-710 
    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 generalization of a theorem on off-diagonal hypervirial relations is obtained and is used to demonstrate when to expect exact solutions of eigenvalue problems using the hypervirial method. Links are established between the hypervirial method and other approximation methods. The harmonic oscillator and hydrogen atom problems are given as examples.
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  • 5
    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.
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  • 6
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 3 (1969), S. 397-415 
    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: Two-center one-electron integrals needed in certain molecular correlated wave function calculations, using one-center expansion approximation, have been studied. The form of the basic correlated function used in this study is \documentclass{article}\pagestyle{empty}\begin{document}$$ h(r_{12}) = r_{12}^n e^{ - \zeta r_{12} } $$\end{document} The parent integral is expressed in terms of an angular integral, and an auxiliary radial integral depending upon the variables r1, r2, and r12. Several analytical formulas, and a recursive formula are derived for the auxiliary integral, and other related integrals. All these formulas are given in computationally useful forms. Logical flow charts and FORTRAN programs were constructed for computing the basic integrals discussed in the paper. Numerical values of some integrals, thus obtained, are tabulated for comparisons.
    Additional Material: 1 Tab.
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  • 7
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 3 (1969), S. 903-911 
    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: It is shown how the leading term for very large R of the Casimir-Polder potential, that is the term varying as R-7, arises in second-order perturbation theory applied to the interaction Hamiltonian - \documentclass{article}\pagestyle{empty}\begin{document}$ - \sum\limits_\sigma {\frac{1}{2}\alpha (\sigma){\rm E}^{ \bot ^2 } (\sigma)} $\end{document}. The generalization to anisotropic molecules is calculated and the angular dependence of the long range intermolecular potential in this case is given explicitly in terms of the principal polarizabilities and their corresponding directions of the two molecules.
    Additional Material: 1 Ill.
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