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  • Atomic, Molecular and Optical Physics  (2)
  • Characteristic polynomial  (2)
  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Theoretical chemistry accounts 63 (1983), S. 473-495 
    ISSN: 1432-2234
    Keywords: Characteristic polynomial ; Chebyshev polynomial ; Topological index ; Structure factor ; Graph
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract The structural dependency (effect of branching and cyclisation) of an alternative form, the Chebyshev expansion, for the characteristic polynomial were investigated systematically. Closed forms of the Chebyshev expansion for an arbitrary star graph and a bicentric tree graph were obtained in terms of the “structure factor” expressed as the linear combination of the “step-down operator”. Several theorems were also derived for non-tree graphs. Usefulness and effectiveness of the Chebyshev expansion are illustrated with a number of examples. Relation with the topological index (Z G ) was discussed.
    Type of Medium: Electronic Resource
    Library Location Call Number Volume/Issue/Year Availability
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Theoretical chemistry accounts 63 (1983), S. 473-495 
    ISSN: 1432-2234
    Keywords: Characteristic polynomial ; Chebyshev polynomial ; Topological index ; Structure factor ; Graph
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract The structural dependency (effect of branching and cyclisation) of an alternative form, the Chebyshev expansion, for the characteristic polynomial were investigated systematically. Closed forms of the Chebyshev expansion for an arbitrary star graph and a bicentric tree graph were obtained in terms of the “structure factor” expressed as the linear combination of the “step-down operator”. Several theorems were also derived for non-tree graphs. Usefulness and effectiveness of the Chebyshev expansion are illustrated with a number of examples. Relation with the topological index (Z G ) was discussed.
    Type of Medium: Electronic Resource
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
  • 3
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 6 (1972), S. 801-817 
    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: General expressions are obtained for the energies of complex and real forms of any hydrogenic orbital (n, l, m) in a cluster of point charges of any geometry. This is a perturbation calculation of hydrogenic Rydberg orbitals in a one-electron hard core approximation. A model calculation of 3d-electrons of carbene, ethylene and benzene with varying charge distribution is given.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
    Library Location Call Number Volume/Issue/Year Availability
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  • 4
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 15 (1979), S. 243-257 
    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 structures of the ground state of linear and highly branched polyenes with up to 80 π-electrons are calculated with particular reference to the alternation of the bond orders. The MO methods adopted are HMO, PPP, variable-β, γ, and its improved version. The effect of the electron correlation through singly and doubly excited configurations is estimated with a second-order perturbation calculation. The calculated bond orders systematically vary with the degree of approximation used. Most of the bond order values can be grouped into either a single or double bond region. In certain series of highly branched polyenes the bond orders of double and single bonds at the root of branching, respectively, get smaller and larger as the size of the molecule increases and sometimes their difference gets diminishingly small. The origin of these abnormal bond orders is discussed in terms of the π-electron flow networks.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
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