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  • 1
    Digitale Medien
    Digitale Medien
    Springer
    Theoretical chemistry accounts 63 (1983), S. 473-495 
    ISSN: 1432-2234
    Schlagwort(e): Characteristic polynomial ; Chebyshev polynomial ; Topological index ; Structure factor ; Graph
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Chemie und Pharmazie
    Notizen: 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.
    Materialart: Digitale Medien
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  • 2
    Digitale Medien
    Digitale Medien
    Springer
    Theoretical chemistry accounts 63 (1983), S. 473-495 
    ISSN: 1432-2234
    Schlagwort(e): Characteristic polynomial ; Chebyshev polynomial ; Topological index ; Structure factor ; Graph
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Chemie und Pharmazie
    Notizen: 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.
    Materialart: Digitale Medien
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  • 3
    Digitale Medien
    Digitale Medien
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 60 (1996), S. 1851-1863 
    ISSN: 0020-7608
    Schlagwort(e): Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Chemie und Pharmazie
    Notizen: Using the information on the interatomic separations in a molecule, one can construct structural invariants that are the components of a molecular profile. The entries in the profile are derived by averaging different powers of the interatomic separations, suitably normalized so that the increasing powers do not dominate the sequence. Although only a few hundreds of structures have been so analyzed, no two different chemical structures were found to be characterized by the same sequences. A critical test for the conjecture that molecular profiles are unique is to consider structurally closely related systems that are very similar and have several similar properties. In this contribution we investigated the cuboctahedron and the accompanying polyhedron obtained by rotating half of the cuboctahedron against the other half, resulting in the so-called twist cutoctahedron. We show that even this pair of closely related structures has different profiles. We have also examined the generalized molecular profiles obtained by inserting n additional points along each edge of the polyhedra. The convergence of the profiles as n increases is discussed. It appears thus that these generalized molecular profiles, called line profiles or bond profiles, are likely to lead to a unique characterization of structures in which not only the geometry of atoms is recorded but also the geometry of the connectivity of the structure. © 1996 John Wiley & Sons, Inc.
    Zusätzliches Material: 4 Ill.
    Materialart: Digitale Medien
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  • 4
    Digitale Medien
    Digitale Medien
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 50 (1994), S. 369-384 
    ISSN: 0020-7608
    Schlagwort(e): Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Chemie und Pharmazie
    Notizen: Recursive formulas are derived for generating the conjugated-circuit polynomials for circuits up to size n = 6, 10, or 14 on regular chain polyhex graphs. These counting polynomials are of use for a simple valence-bond resonance-theoretic derived model: the conjugated-circuit model. © 1994 John Wiley & Sons, Inc.
    Zusätzliches Material: 11 Ill.
    Materialart: Digitale Medien
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  • 5
    Digitale Medien
    Digitale Medien
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 49 (1994), S. 215-237 
    ISSN: 0020-7608
    Schlagwort(e): Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Chemie und Pharmazie
    Notizen: We introduce generalized bond orders defined in terms of weighted Kekule valence structures. The weights were determined by the contributions of linearly independent and minimal conjugated circuits in individual Kekule valence structure. When special values for the contributions of conjugated circuits of different size are assumed, one obtains quantities that show considerable similarity to the Pauling and the Clar's bond orders. Pauling bond orders are obtained when one assumes that all conjugated circuits make equal contribution to bond orders. © 1994 John Wiley & Sons, Inc.
    Zusätzliches Material: 10 Ill.
    Materialart: Digitale Medien
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  • 6
    Digitale Medien
    Digitale Medien
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 52 (1994), S. 215-225 
    ISSN: 0020-7608
    Schlagwort(e): Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Chemie und Pharmazie
    Notizen: We consider the paradoxical situation arising in the standard multiple regression analysis in that as the standard error of prediction decreases by introduction of additional variables (descriptors) at the same time the standard error of the coefficients of the regression analysis increases, often to the point of the coefficients having no statistical validity. We trace the origin of this paradoxical situation to intercorrelation of the variables. A remedy to this curve-fitting paradox is in the introduction of orthogonal variables or descriptors. © 1994 John Wiley & Sons, Inc.
    Zusätzliches Material: 3 Tab.
    Materialart: Digitale Medien
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  • 7
    Digitale Medien
    Digitale Medien
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 56 (1995), S. 61-73 
    ISSN: 0020-7608
    Schlagwort(e): Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Chemie und Pharmazie
    Notizen: We have undertaken the task of characterizing conformations of nine-membered rings. Each of the 16 symmetrical conformations of puckered nine-membered rings considered is characterized by distance-dependent Dk structural invariants, referred to as molecular profiles. In this way we succeeded to map a three-dimensional molecular object by a one-dimensional mathematical object, a sequence. The quantity D1 represents the average row sum of the distance matrix and is proportional to the average interatomic separations in a molecule. The corresponding Dk values give the average of the row sums for the kth power of interatomic separations normalized by the factorial k!. Hence, derived molecular profiles are independent of the orientation of a molecule or labeling of its atoms, i.e., derived molecular profiles are structural invariants. Properties of the derived profile sequences for the nine-membered rings are analyzed and discussed. Molecular profiles were used to establish which pairs of nine-membered ring conformers are the least similar and which are the most similar - a task that is difficult to do by mere inspection of the corresponding molecular models and cannot be considered using standard graph theoretical schemes that are devoid of information pertaining to the relative orientation of molecular groups in the 3-dimensional space. © 1995 John Wiley & Sons, Inc.
    Zusätzliches Material: 5 Ill.
    Materialart: Digitale Medien
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  • 8
    Digitale Medien
    Digitale Medien
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 22 (1982), S. 441-441 
    ISSN: 0020-7608
    Schlagwort(e): Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Chemie und Pharmazie
    Materialart: Digitale Medien
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  • 9
    Digitale Medien
    Digitale Medien
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 30 (1986), S. 203-218 
    ISSN: 0020-7608
    Schlagwort(e): Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Chemie und Pharmazie
    Notizen: We consider the question of predicting the stability of hypothetical structures that are too large for ab initio calculations, too complex for simple MO calculations, and too few for reliable semiempirical SCF MO schemes. The problem is illustrated on a polycyclic conjugated cation having 21 carbon atoms. The analysis is general and applies to conjugated hydrocarbons and their ions for which it is not apparent whether they exhibit aromatic characteristics (and, if they do, to what extent). For the investigated polycyclic cation we find that to a large extent its aromatic components are cancelled by its antiaromatic components resulting in an essentially nonaromatic system. The analysis, which is based on close examination of various contributing conjugated circuits, allows one to examine the partial role of the individual Kekulé valence structures as well as to foretell the nature of both the positively and the negatively charged system. We conclude that the particular cation should be stable but represents a challenge as it would be a cation with a rather small resonance energy. In contrast, the corresponding anion is relatively stable and, at least from a theoretical point of view, is less interesting.
    Zusätzliches Material: 2 Ill.
    Materialart: Digitale Medien
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  • 10
    Digitale Medien
    Digitale Medien
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 21 (1982), S. 647-663 
    ISSN: 0020-7608
    Schlagwort(e): Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Chemie und Pharmazie
    Notizen: Using a canonical numbering of vertices for the graph corresponding to a particular rearrangement of tetragonal-pyramidal complexes, all 120 permutations defining the symmetry for the rearrangement are derived. An examination of the permutations points to the symmetric group S5, which has previously been found for isomerizations of trigonal-bipyramidal complexes and in the rearrangement of homotetrahedryl cations.
    Zusätzliches Material: 7 Ill.
    Materialart: Digitale Medien
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