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  • Computational Chemistry and Molecular Modeling  (35)
  • Restricted random walks  (2)
  • 1
    Digitale Medien
    Digitale Medien
    Springer
    Theoretical chemistry accounts 92 (1995), S. 97-106 
    ISSN: 1432-2234
    Schlagwort(e): Graphs ; Restricted random walks
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Chemie und Pharmazie
    Notizen: Summary In the first part of this contribution we outline the construction of a novel matrix associated with a graph, the entries of which give the probability of a random walk over the graphG starting at sitei to reach sitej inD ij steps. HereD ij is the distance between verticesi, j. The derived matrices, to be referred to as restricted random walk matrices and labeled as RRW matrices, are non-symmetric, for trees the entries being of the form 1/p, wherep is an integer equal to 1 or larger. In the second part of the report we consider a few invariants of the RRW matrices. We will illustrate the use of one such invariant in a regression analysis. We consider the variations of the entropies in isometric octanes with skeletal changes. The derived regression, based on a single descriptor, yields the standard error of 1.26 cal K−1 mol−1 that is the smallest yet reported in the literature.
    Materialart: Digitale Medien
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  • 2
    Digitale Medien
    Digitale Medien
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 8 (1974), S. 643-676 
    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: A brief survey of the maximum overlap method is presented and some computational aspects of the approach are discussed. The hybrid compositions and bond overlaps are reported for some thirty small ring compounds and a list of characteristic hybrids for various structural environments is given. The table of characteristic hybrids is extended to acyclic hydrocarbons and the transferability of the maximum overlap hybrids is demonstrated. Those aspects of the method which depend on geometrical properties of molecules have been considered in some details and the discussion is extended to some structural features of cyclic systems. In particular the asymmetry of bonds of spiro carbon atom is examined and rationalization of puckering of large macrocyclic systems is presented. In the summary it is pointed to the method and its potential to discuss structural aspects of molecules at the particular level of accuracy expected to be of great use in organic and physical organic chemistry. Further development and improvement of the method is mentioned, but already in the present form it can produce hybrids which may constitute a useful basis for other more ambitious semiempirical calculations.
    Zusätzliches Material: 6 Ill.
    Materialart: Digitale Medien
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  • 3
    Digitale Medien
    Digitale Medien
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 17 (1980), S. 549-586 
    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: The resonance energy of conjugated benzenoid systems is expressed as contributions arising from independent conjugated circuits. The scheme has been applied to numerous very large conjugated systems. In many cases, it was possible to find regularities in the increments for the resonance energy within a family of benzenoid systems as the number of benzene rings is increased.
    Zusätzliches Material: 15 Ill.
    Materialart: Digitale Medien
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  • 4
    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: While the concept of the graph center is unambiguous (and quite old) in the case of acyclic graphs, an attempt has been made recently to extend the concept to polycyclic structures using the distance matrix of a graph as the basis. In this work we continue exploring such generalizations considering in addition to the distance matrix, self-avoiding walks or paths as graph invariants of potential interest for discriminating distinctive vertex environments in a graph of polycyclic structures. A hierachy of criteria is suggested that offers a systematic approach to the vertex discrimination and eventually establishes in most cases the graph center as a single vertex, a single bond (edge), or a single group of equivalent vertices. Some applications and the significance of the concept of the graph center are presented.
    Zusätzliches Material: 3 Ill.
    Materialart: Digitale Medien
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  • 5
    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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  • 6
    Digitale Medien
    Digitale Medien
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 24 (1983), S. 435-452 
    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: For most structures (molecules, graphs, lattices) a count of random walks for nonequivalent sites will give different numbers, particularly for walks of many steps. Occasionally one finds the same count of walks for nonequivalent sites. These have been termed “unusual walks” and have been closely examined in the case of trivalent graphs. While it remains to be understood what structural factors are critical, some regularities have been observed and are discussed. Unusual walks within a single structure signal “isospectural” points in a graph. A number of structures possessing unusual walks have been displayed, and a few constructive steps which do not alter the “unusual” characteristics of selected vertices have been indicated.
    Zusätzliches Material: 11 Ill.
    Materialart: Digitale Medien
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  • 7
    Digitale Medien
    Digitale Medien
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 34 (1988), S. 267-285 
    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: In this paper we have addressed an important problem: how to develop a strategy for identification of the topological indices which are most important in establishing a model for structure-activity analysis. In particular we consider a rational selection of graph theoretical (topological) indices in QSAR. The approach is illustrated by the study of the toxicity of ethers on mice. The indices examined include the connectivity indices based on adjacency matrix, the conceptually related graph distance indices, and an information theoretic index based on partitioning of electrons in various domains. We have outlined the similarities and differences and discuss advantages and limitations among different approaches. Our emphasis is on the problem how to select in a rational way appropriate graph-theoretical descriptors and how to introduce higher “corrections” in order to improve derived correlation.
    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 37 (1990), S. 437-448 
    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 examined variations in bond orders in conjugated hydrocarbons that follow improvement in MO calculations on going from topological Hückel MO to self-consistent Pariser-Parr-Pople-type calculations. Differences in individual bond orders can be interpreted as pointing to increased weights of selected Kekulé valence structures. Significantly, so indicated valence structures are those with the largest number of formal Kekulé benzene rings or the largest contribution to molecular resonance energy in terms of conjugated circuits.
    Zusätzliches Material: 4 Ill.
    Materialart: Digitale Medien
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  • 9
    Digitale Medien
    Digitale Medien
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 26 (1984), S. 69-89 
    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: Isomerization of octahedral complexes XY6, by a mechanism known as diagonal twist (in which two ligands in cis positions, one to another, exchange sites) is considered. Construction of the corresponding isomerization graph is outlined (reported before by Balaban) and the problem of determining its symmetry is considered. Alternative routes for deducing the order of the automorphism group are described. The group is confirmed to be S6 and representative symmetry permutations (one for each of the 11 classes of S6) are shown. Alternative pictorial representations of the 15-vertex graph are also shown.
    Zusätzliches Material: 12 Ill.
    Materialart: Digitale Medien
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  • 10
    Digitale Medien
    Digitale Medien
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 26 (1984), S. 137-153 
    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: After a brief review of empirical and nonempirical schemes used in the study of molecular properties, the difficulties associated with structure-activity correlations are outlined. Part of the difficulty originates with the lack of precise definition of a structure. An analogy is made with similarly vague concepts of structural chemistry - the notion of aromaticity. This follows with the description of a characterization of structures by selected graph invariants. In particular we consider the count of weighted paths derived from suitable weighting of the individual bonds in a structure. We adopted the weighting factors (mn)-1/2 introduced originally for the definition of the connectivity index. The approach thus combines some features of the very successful connectivity index with features of path sequences, found very useful in comparative studies of related compounds. As an illustration of the combined approach we consider a set of some 40 therapeutically active substances, studied previously by others, and derive their clustering (classification) which is solely based on the count of weighted paths and is devoid of any empirical parametrization.
    Zusätzliches Material: 3 Ill.
    Materialart: Digitale Medien
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