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  • Biochemistry  (7)
  • 1-Factor enumeration  (1)
  • Benzenoid π-network polymers  (1)
  • 1
    Electronic Resource
    Electronic Resource
    Dimer coverings and Kekulé structures on honeycomb lattice strips (1986)
    Springer
    Theoretical chemistry accounts 69 (1986), S. 409-423 
    Details
    ISSN: 1432-2234
    Keywords: Kekulé structure enumeration ; Dimer covering enumeration ; 1-Factor enumeration ; Benzenoid π-network polymers ; Long-range order ; Bond localization ; Edge reactivity ; Graph theory ; Transfer matrices
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract The problem of covering every site of a subsection of the honeycomb lattice with disjoint edges is considered. It is pointed out that a type of long-range order associated to such coverings can occur, so that different phases can arise as a consequence of the subsection's boundaries. These features are quantitatively investigated via a new analytic solution for a class of strips of arbitrary widths, arbitrary lengths, and arbitrary long-range-order values. Relations to work on the dimer covering problem of statistical mechanics and especially to the resonance theory of benzenoid hydrocarbons are noted.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00526700
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  • 2
    Electronic Resource
    Electronic Resource
    Many-body conjugated-circuit computations (1991)
    New York, NY [u.a.] : Wiley-Blackwell
    Journal of Computational Chemistry 12 (1991), S. 1260-1264 
    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 powerful algorithm for calculating conjugated-circuit expectations for planar graphs is enunicated. The utility for systematizing quantitative resonance-theoretic computations on conjugated hydrocarbons, and related species, is emphasized.
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/jcc.540121014
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  • 3
    Electronic Resource
    Electronic Resource
    Analytical approach to very large benzenoid polymers (1995)
    New York, NY [u.a.] : Wiley-Blackwell
    Journal of Computational Chemistry 16 (1995), S. 517-526 
    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 rigorous evaluation of conjugated-circuit resonance energies for families of structurally related benzenoid hydrocarbons of increasing size. Local and global aromatic properties of such molecules are investigated with particular interest in modeling high polymers. Using the algebra of large numbers, exact formulas for contributions from individual benzene rings of polymers with up to 25,000 repeating units (close to half a million carbon atoms) were derived. All arithmetic procedures were carried out in terms of whole numbers retaining all digits, of which there were sometimes more than 105. © 1995 by John Wiley & Sons, Inc.
    Additional Material: 8 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/jcc.540160415
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  • 4
    Electronic Resource
    Electronic Resource
    Transfer-Matrix Method for Subgraph Enumeration: Applications to Polypyrene FusenesResearch supported by the Robert A. Welch Foundation of Houston, Texas. (1986)
    New York, NY [u.a.] : Wiley-Blackwell
    Journal of Computational Chemistry 7 (1986), S. 443-456 
    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 frequently encountered problem in chemical applications is that of a weighted enumeration (or summation over) a class of extended subgraphs of a given system graph, which might represent a chemical structure. Some aspects of a powerful transfer-matrix method are described for treating such graphtheoretic weighted enumeration problems. This method is seen to be particularly amenable for system graphs which are long in one direction and narrow in transverse directions. When the system graph is uniform (i.e., translationally symmetric) along one extended direction, asymptotic results can be readily extracted.A second point of emphasis here is that the weighted enumeration problems of the type studied here naturally arise in computing matrix elements over cluster expanded wave functions, though most applications so far framed in the literature differ from this. Size consistency and size-extensivity aspects of this application are noted in terms of the transfer-matrix approach.Polypyrene fusene strips of varying lengths are considered as applications of the transfer-matrix methods for two weighted enumeration problems. Different graph-theoretic problems are noted to arise for low-order cluster expanded wave functions, such as in fact occur in both the Herndon-Simpson and the Pauling-Wheland resonance theories. For higher-order wave function ansätze the graph-theoretic problems would simply have more complicated weights and transfer matrices, which for the present examples are very small (i.e., 2 by 2 and 3 by 3).
    Additional Material: 12 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/jcc.540070407
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  • 5
    Electronic Resource
    Electronic Resource
    The graph isomorphism problem (1991)
    New York, NY [u.a.] : Wiley-Blackwell
    Journal of Computational Chemistry 12 (1991), S. 1243-1251 
    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 chemically and graph-theoretically relevant problem is that of determining whether a pair of graphs G and G′ are isomorphic. A two-stage computational test is developed. In the first stage an “eigenvalue-eigenprojector” tabular graph-theoretic invariant is computed, whence if the two tables differ, G and G′ must be nonisomorphic. The second stage, utilizing the tables of the first stage, orders the vertices, thereby leading to a special labeling for them, whence if the associated adjacency matrices for G and G′ are equal, it must be that G and G′ are isomorphic. The computational implementation, and testing of the algorithm is described.
    Additional Material: 10 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/jcc.540121012
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  • 6
    Electronic Resource
    Electronic Resource
    Sixty-atom carbon cages (1991)
    New York, NY [u.a.] : Wiley-Blackwell
    Journal of Computational Chemistry 12 (1991), S. 1265-1269 
    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: The enumeration of all 60-atom carbon cages associated to trivalent polyhedra with five-and six-sided faces is addressed. This isomer problem is computationally solved to give 1790 cages, with a further resolution into subclasses of cages with differing numbers p of abutting pairs of pentagonal faces. The individual cages are generated, and then there are computed various graph-theoretic invariants, including Hückel MO energies, HOMO-LUMO gaps, Kekulé structure counts, and conjugated-circuit counts. Associated properties as a function of p are reported and found to be in concert with earlier qualitative arguments. It is found that the most stable of these cages is the unqiue p = 0 Buckminsterfullerene structure.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/jcc.540121015
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  • 7
    Electronic Resource
    Electronic Resource
    Innate degree of freedom of a graph (1987)
    New York, NY [u.a.] : Wiley-Blackwell
    Journal of Computational Chemistry 8 (1987), S. 516-521 
    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: For a Kekulé structure we consider the smallest number of placements of double bonds such that the full Kekulé structure on the given parent graph is fully determined. These numbers for each Kekulé structure of the parent graph sum to a novel structural invariant F, called the degree of freedom of the graph. Some qualitative characteristics are identified, and it is noted that apparently it behaves differently from a couple of other invariants related to Kekulé structures.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/jcc.540080432
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  • 8
    Electronic Resource
    Electronic Resource
    Generation of carbon-cage polyhedra (1991)
    New York, NY [u.a.] : Wiley-Blackwell
    Journal of Computational Chemistry 12 (1991), S. 1252-1259 
    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: The problem of the generation of polyhedra with degree-3 vertices, and faces each of which is pentagonal or hexagonal, is addressed in order to characterize carbon in order to characterize clusters of ca. 30 or more atoms. Following Eulerian type arguments such polyhedra are subcategorized in terms of numbers of different types of local structures. An algorithm to generate such polyhedra is developed, and its computer implementation is described. Results for smaller than 80-vertex cages of subcategories anticipated to be more chemically relevant are reported. The singular position of the truncated-icosahedron (buckminsterfullerene) structure is noted.
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/jcc.540121013
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