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  • 1
    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
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  • 2
    Electronic Resource
    Electronic Resource
    New York, NY [u.a.] : Wiley-Blackwell
    Journal of Computational Chemistry 12 (1991), S. 1252-1259 
    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
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  • 3
    Electronic Resource
    Electronic Resource
    New York, NY [u.a.] : Wiley-Blackwell
    Journal of Computational Chemistry 12 (1991), S. 1265-1269 
    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
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  • 4
    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 Herndon-Simpson model for a particular catacondensed polyphene chain is considered as a nontrivial many-body Hamiltonian, defined on a space with a basis of orthonormal Kekulé structures. An Explicitly correlated cluster expanded resonance-theoretic wave function is described for this model, and its quality is judged by calculation of the standard deviation for the energy expectation. The quality is found to be high. Indeed, for a particular parameter ratio within the range of experimental interest, the wave function ansatz is found to be exact. This very accurate solution is then used to gauge the quality of the common ansatz with equally weighted Kekulé structures, and it is found to be reasonably good.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
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  • 5
    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: Within the framework of the AMO-EHF approximation for the Hubbard model, it is shown that the band gap ΔE of an arbitrary regular alternant 1D π-system (polymer), having a singlet ground state, is different from zero, i.e., the ground state is a dielectric one. At least one of the three components of the energy gap - the topological, Δtop; the geometrical, Δgeom; or the correlation, Δcorr (combined via the equation ΔE = {Δcorr2 + (Δtop + Δgeom))2}1/2 - is different from zero. Numerical results for several 1D alternant polymers with conjugated π-systems are given. © 1994 John Wiley & Sons, Inc.
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
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  • 6
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    ISSN: 0020-7608
    Keywords: Chemistry ; Theoretical, Physical and Computational Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Heteroatomic cages (BN/2NN/2) with borons and nitrogens fully replacing alternant sets of carbons in cages are built graph-theoretically and investigated via the semiempirical MNDO Hamiltonian. The comparison with their parent carbon cages CN is made in terms both of electronic and of geometric changes. Infinite classes first of octahedral symmetry and second of hexagonal-bipyramidal symmetry fullerenoid cages are considered in detail. The difference in the electronegativities for boron and nitrogen implies the opening of HOMO-LUMO gaps for alternant BN clusters. In general, the borons prefer planar geometry (sp2 hybridization) while the nitrogens prefer pyramidalization (sp3 hybridization). © 1997 John Wiley & Sons, Inc.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
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