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  • 1
    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
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  • 2
    ISSN: 1432-2234
    Keywords: Polymers ; Oligomers ; Benzenoids ; Resonance ; Conjugation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Summary We have initiated a comparative study of several families of structurally closely related large benzenoid hydrocarbons of increasing number of fused benzene rings. Local and global properties of such molecules have been studied with a particular interest in investigating the closeness of finite-size molecules for modelling infinite polymeric structures having the same structural patterns. We focus in this report on two questions: (1) how large is a finite molecule which well approximates an infinite system? and (2) how do terminal groups influence local properties in the central part of the molecule as we approach the infinite system. Emphasis in this report is on extraction of high-accuracy limiting values for selected molecular properties from limited data on a few smaller members of structurally related molecules.
    Type of Medium: Electronic Resource
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  • 3
    ISSN: 1432-2234
    Keywords: π-network polymers ; Valence-bond model ; Resonance theory ; Long-range order ; Bond localization ; Solitonic excitations ; Transfer matrices
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract The poly-polyphenanthrene family of extended π-network strips with members ranging from polyacetylene to graphite is considered in terms of the locally correlated valence-bond or Heisenberg Hamiltonian. Resonance theory wavefunctions which provide a variational upper bound to the ground state energy are developed in a graph-theoretic formalism extendable to more general localized wavefunction cluster expansions. The graph-theoretic formalism facilitates the use of general transfer matrix techniques, which are especially powerful in application to quasi-one-dimensional systems such as are illustratively treated here. It is argued that these strips exhibit states of different long-range spin-pairing orderings. Novel properties associated with these different resulting phases are briefly indicated, including the possibilities of solitonic excitations and the reactivity at the ends of the strips. The qualitative arguments are supported by numerical calculations for strips up to width 8.
    Type of Medium: Electronic Resource
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