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  • 1
    ISSN: 1432-2234
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Description / Table of Contents: Zusammenfasung Für eine Reihe von Zweizentren-Austauschintegralen zwischen Slaterorbitalen werden geschlossene analytische Ausdrücke mitgeteilt, wobei allerdings nur ls-, 2s- und 2pσ-Orbitale mit gleichen Exponenten behandelt werden. Schließlich wird noch eine asymptotische Entwicklung für großeR angegeben.
    Abstract: Resumé Obtention d'expressions analytiques compactes pour certaines intégrales d'échange bicentriques entre orbitales de Slater. On considère des intégrales impliquant des orbitales ls, 2s et 2pσ avec comme restriction l'égalité des exposants orbitaux. Un développement valable pour les grandes valeurs deR est aussi obtenu.
    Notes: Abstract Closed analytical expressions are derived for some two-centre exchange integrals between Slater orbitals. Integrals involving 1s, 2s and 2pσ orbitals are considered with the restriction that the two orbitals have the same exponent. An expansion formula accurate for large values ofR is also derived.
    Type of Medium: Electronic Resource
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  • 2
    ISSN: 1432-2234
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Description / Table of Contents: Zusammenfassung Das Theorem von Sachs [1] wird diskutiert und Kekulé- und Sachs-Graphen werden definiert. Die einfachen Folgerungen aus dem Theorem von Sachs, die in der Chemie von Interesse sind, werden abgeleitet. So wird gezeigt, daß die Paarregel von Coulson und Rushbrooke, die Hückelsche (4m+2)-Regel und die Regel von Longuet-Higgins und Dewar [2] leicht mit dem Sachsschen Theorem erhalten werden können. Die Abhängigkeit der Zahl der Kekulé-Strukturen von der molekularen Topologie wird ebenfalls gezeigt.
    Notes: Abstract The Sachs theorem [1] is discussed, and Kekulé and Sachs graphs are defined. The simple consequences of Sachs theorem which are of interest in chemistry are presented. Thus, it is shown that the pairing theorem, Hückel (4m+2) rule, and Longuet-Higgins and Dewar rule [2] can be obtained easily with the use of Sachs theorem. The dependence of the number of Kekulé structures on the molecular topology is also shown.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Springer
    Theoretical chemistry accounts 74 (1988), S. 349-361 
    ISSN: 1432-2234
    Keywords: Resonance theory ; Conjugated circuits ; Valence-bond theory ; Graphite ; Many-body theory
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract Computations for the “conjugated circuits” model which has previously only been treated for finite and quasi-one-dimensional conjugatedπ-networks are here extended to the graphite lattice. Many-body techniques give the resultant resonance energy per site as a function of a physically relevant long-range order parameter.
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  • 4
    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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  • 5
    Electronic Resource
    Electronic Resource
    Amsterdam : Elsevier
    Tetrahedron 29 (1973), S. 3449-3454 
    ISSN: 0040-4020
    Source: Elsevier Journal Backfiles on ScienceDirect 1907 - 2002
    Topics: Chemistry and Pharmacology
    Type of Medium: Electronic Resource
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  • 6
    Electronic Resource
    Electronic Resource
    Amsterdam : Elsevier
    Chemical Physics Letters 2 (1968), S. 369-370 
    ISSN: 0009-2614
    Source: Elsevier Journal Backfiles on ScienceDirect 1907 - 2002
    Topics: Chemistry and Pharmacology , Physics
    Type of Medium: Electronic Resource
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  • 7
    Electronic Resource
    Electronic Resource
    Amsterdam : Elsevier
    Chemical Physics Letters 14 (1972), S. 342-345 
    ISSN: 0009-2614
    Source: Elsevier Journal Backfiles on ScienceDirect 1907 - 2002
    Topics: Chemistry and Pharmacology , Physics
    Type of Medium: Electronic Resource
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  • 8
    ISSN: 1572-8897
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Mathematics
    Notes: Abstract The electronic structure of a π-network polymer with random numbers of two types of monomer units is considered in a “conjugated circuit” resonance-theoretic framework. A transfer-matrix technique for computing relevant ensemble-average energies is described and applied to a few example simple benzenoid systems. A type of long-range ordering is noted to be relevant, and some of its implications are discussed.
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  • 9
    ISSN: 1572-8897
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Mathematics
    Notes: Abstract In its simplest form, the low-rank perturbation (LRP) method solves the perturbed matrix eigenvalue equationsAΨ ≡ (B + V)Ψ =εΨ, whereA, B andV are nth-order Hermitian matrices, and where the eigenstates and the eigenvalues of the unperturbed matrixB are known. The method can be applied to arbitrary perturbations V, but it is numerically most efficient if the rank ρ ofV is “small”. A special case of low-rank perturbations are localized perturbations (e.g. replacement of one atom with another, creation and destruction of a chemical bond, local interaction of large molecules, etc.). In the case of local perturbations with a fixed localizability I, the operation count for the calculation of a single eigenvalue and/or a single eigenstate isO(l 2 n). In the more general case of a delocalized perturbation with a fixed rank p, the operation count for the derivation of all eigenvalues and/or all eigenstates is O(π 2 n 2). For largen, the performance of the LRP method is hence at least one order of magnitude better than the performance of other methods. The obtained numerical results demonstrate that the LRP method is numerically reliable, and that the performance of the method is in accord with predicted operation counts.
    Type of Medium: Electronic Resource
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  • 10
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    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: Neutral, ionic, and complete alternant systems are studied using the alternancy symmetry adapted (ASA) approach. This approach is based on an explicit construction of ASA operators that are up to the sign invariant with respect to the particle-hole symmetry transformation. These operators serve as building blocks of alternant systems, and they determine their characteristic properties. All Hamiltonians describing neutral alternant systems are explicitly constructed. Up to some minor restrictions, all Hamiltonians describing ionic and complete alternant systems are also explicitly constructed. Inversely, given a Hamiltonian Ĥ in a second quantization notation, one can easily check whether or not this Hamiltonian describes a neutral (ionic, complete) alternant system. All linear properties characteristic to neutral (ionic, complete) alternant systems are obtained. In particular, all one- and two-particle properties are derived in an explicit form. The properties obtained substantially generalize “classical” properties of alternant systems such as, in the case of neutral alternant systems, uniform charge density distribution, vanishing bond orders between atomic sites of the same parity, and alternancy selection rules for the electric dipole transitions.
    Type of Medium: Electronic Resource
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