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  • Computational Chemistry and Molecular Modeling  (7)
  • Characteristic polynomial  (2)
  • 1
    Electronic Resource
    Electronic Resource
    Analysis of the topological dependency of the characteristic polynomial in its chebyshev expansion (1983)
    Springer
    Theoretical chemistry accounts 63 (1983), S. 473-495 
    Details
    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
    URL: http://dx.doi.org/10.1007/BF02394808
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Analysis of the topological dependency of the characteristic polynomial in its chebyshev expansion (1983)
    Springer
    Theoretical chemistry accounts 63 (1983), S. 473-495 
    Details
    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
    URL: http://dx.doi.org/10.1007/BF00552651
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    Studies on Rydberg orbitals. IV. Basic formulas for the one-electron perturbation calculation of molecular Rydberg excited states (1972)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 6 (1972), S. 801-817 
    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: 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
    URL: http://dx.doi.org/10.1002/qua.560060502
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    Paper (German National Licenses)
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  • 4
    Electronic Resource
    Electronic Resource
    Semiempirical MO study on the abnormal bond orders of large networks of highly branched polyenes (1979)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 15 (1979), S. 243-257 
    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: 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
    URL: http://dx.doi.org/10.1002/qua.560150208
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    Paper (German National Licenses)
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  • 5
    Electronic Resource
    Electronic Resource
    Graph generators (1987)
    New York, NY [u.a.] : Wiley-Blackwell
    Journal of Computational Chemistry 8 (1987), S. 522-535 
    Details
    ISSN: 0192-8651
    Keywords: Computational Chemistry and Molecular Modeling ; Biochemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Computer Science
    Notes: We consider the construction of highly symmetrical vertex transitive graphs. Some such graphs represent the degenerate rearrangements in which a molecule or an ion is formed by breaking and making bonds so that the final and the initial skeleton is identical. The approach is closely related to Cayley's graphs for selected groups. We restrict the choice of generators to symmetric matrices. Successive multiplications of such matrices generate other permutation matrices of the same dimension, each new matrix representing a new vertex for a transitive graph under the construction. In particular we restrict our discussion to matrices of dimension 3 and 4 and proceed to construct systematically all transitive graphs using 4 × 4 symmetric matrices as generators.
    Additional Material: 9 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/jcc.540080433
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    Paper (German National Licenses)
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  • 6
    Electronic Resource
    Electronic Resource
    Operator technique for obtaining the recursion formulas of characteristic and matching polynomials as applied to polyhex graphs (1983)
    New York, NY [u.a.] : Wiley-Blackwell
    Journal of Computational Chemistry 4 (1983), S. 585-593 
    Details
    ISSN: 0192-8651
    Keywords: Computational Chemistry and Molecular Modeling ; Biochemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Computer Science
    Notes: A simple and efficient method, called an operator technique, for obtaining the recurrence relation of a given counting polynomial, e.g., characteristic PG(x) or matching MG(x) polynomial, for periodic networks is proposed. By using this technique the recurrence relations of the PG(x) and MG(x) polynomials for the linear zigzag-type and kinked polyacene graphs were obtained. For the lower members of these series of graphs, the coefficients of PG(x) and MG(x) polynomials are tabulated.
    Additional Material: 6 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/jcc.540040418
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    Paper (German National Licenses)
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  • 7
    Electronic Resource
    Electronic Resource
    On the construction of the matching polynomial for unbranched catacondensed benzenoids (1989)
    New York, NY [u.a.] : Wiley-Blackwell
    Journal of Computational Chemistry 10 (1989), S. 683-697 
    Details
    ISSN: 0192-8651
    Keywords: Computational Chemistry and Molecular Modeling ; Biochemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Computer Science
    Notes: An algorithm for obtaining the matching polynomial of an arbitrary catacondensed unbranched benzenoid molecule is presented. It is based on multiplication of only three 5 x 5 transfer matrices I, J, K, and an appropriate terminal vector. The choice of the matrices is dictated by the history of the growth of the hexagonal “animals” (i.e., by the pattern of the successive fusions of the benzene rings). The approach also gives the number of Kekule valance structures, the count of conjugated circuits, the values of the topological index Z, and the characteristic polynomials.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/jcc.540100510
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  • 8
    Electronic Resource
    Electronic Resource
    Computational algorithms for matching polynomials of graphs from the characteristic polynomials of edge-weighted graphs (1989)
    New York, NY [u.a.] : Wiley-Blackwell
    Journal of Computational Chemistry 10 (1989), S. 698-710 
    Details
    ISSN: 0192-8651
    Keywords: Computational Chemistry and Molecular Modeling ; Biochemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Computer Science
    Notes: Computational algorithms are described which provide for constructing the set of associated edge-weighted directed graphs such that the average of the characteristic polynomials of the edge-weighted graphs gives the matching polynomial of the parent graph. The weights were chosen to be unities or purely imaginary numbers so that the adjacency matrix is hermitian. The computer code developed earlier by one of the authors (K.B.) is generalized for complex hermitian matrices. Applications to bridged and spirographs, some lattices and all polycyclic graphs containing up to four cycles are considered.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/jcc.540100511
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    Paper (German National Licenses)
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  • 9
    Electronic Resource
    Electronic Resource
    Analysis of the π-electronic structure of infinitely large networks. I. Some remarks on the characteristic polynomial and density of states of large polycyclic aromatic hydrocarbons (1987)
    New York, NY [u.a.] : Wiley-Blackwell
    Journal of Computational Chemistry 8 (1987), S. 358-366 
    Details
    ISSN: 0192-8651
    Keywords: Computational Chemistry and Molecular Modeling ; Biochemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Computer Science
    Notes: General expressions of the characteristic polynomials of various series of cyclic and linear polymers of polycyclic aromatic hydrocarbons are presented, i.e., polyacene, zigzag-polyacene, 1,4-dimethylbenzene polymer, polyperylene, etc. The densities of states of cyclic and linear polymers with the same repetitive units are shown. In some cases the allowed region of the energy levels of these polymers is found not to be the same. Several related problems are discussed.
    Additional Material: 10 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/jcc.540080412
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    Paper (German National Licenses)
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