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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Theoretical chemistry accounts 45 (1977), S. 79-87 
    ISSN: 1432-2234
    Keywords: Acyclic polyenes ; Graph theory
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract The main result of the present work is the proof that among acyclic polyenes C n H n+2, the linear isomer H2C=(CH) n−2=CH2 has maximal HMO π-electron energy. The 1,1-divinyl isomer (H2C=CH)2C(CH) n−6=CH2 has maximal π-energy among branched acyclic systems. Among trees withn vertices, the star has minimal energy. A number of additional inequalities for HMO total π-electron energy of acyclic conjugated systems are proved.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Theoretical chemistry accounts 47 (1978), S. 217-222 
    ISSN: 1432-2234
    Keywords: Graph theory ; Free valence ; Localization energy ; Polarizability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract Lower and upper bounds are derived for bond number, localization energy and atom self-polarizability of alternant hydrocarbons. It is proved that in acyclic polyenes the maximal bond number is 1, √2 and √3, respectively for primary, secondary and tertiary carbon atoms.
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  • 3
    ISSN: 1432-2234
    Keywords: Hückel theory ; Resonance energy ; Acyclic walks ; Moments
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Summary The new concept of the resonance energy in conjugated hydrocarbons introduced by Jiang Y, Zhang H (1989) Theor Chim Acta 75:279 is further developed. This model is based on expansion of the π-electron energy in terms of moments which are also equal to numbers of closed walks in a molecular graph. The reference system is established by counting only acyclic walks, i.e. those tracing only on acyclic subgraphs. Because acyclic walks could be counted only up to some finite length, the energy of the reference system has been evaluated by truncating higher terms in the expansion. In this paper a finite expression for the energy of the same reference system is derived, thus allowing its exact evaluation. The exact values differ significantly from the truncated ones. This difference, as well as the discrepancy between exact results and chemical experience, are discussed.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    Springer
    Theoretical chemistry accounts 83 (1992), S. 313-318 
    ISSN: 1432-2234
    Keywords: Hückel theory ; Total π-electron energy ; Moments
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Summary The truncated expansion of the function |x| was frequently used to express the total Hückel π-electron energy (E) in terms of moments. We now present an identity which connectsE with an infinite series of moments. This series is convergent. Lower and upper bounds forE are obtained, based on the same infinite moment expansion.
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  • 5
    Electronic Resource
    Electronic Resource
    Springer
    Theoretical chemistry accounts 34 (1974), S. 129-136 
    ISSN: 1432-2234
    Keywords: Cato-condensed hydrocarbons ; Molecular graphs
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract A simple algorithm for the determination of the number of zeros in the molecular graphs of alternant cata-condensed conjugated hydrocarbons is derived. For non-branched hydrocarbons it is shown that, from the topological point of view, only four types of ring systems exist. The given algorithm enables the derivation of a number of general regularities relating the structural features of the molecule with its stability.
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  • 6
    Electronic Resource
    Electronic Resource
    Springer
    Theoretical chemistry accounts 35 (1974), S. 355-359 
    ISSN: 1432-2234
    Keywords: Graph theory ; Ulam's conjecture
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract A definition of the topological formula for total π-electron energy (E) is given and its necessary analytical from is shown to be a linear combination of graph invariants. It is demonstrated that no exact topological formula for E can exist, i.e. that E cannot be expressed as a function of graph invariants. The proof of the nonexistence of the topological formula is based on Ulam's conjecture.
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  • 7
    Electronic Resource
    Electronic Resource
    Springer
    Theoretical chemistry accounts 48 (1978), S. 279-286 
    ISSN: 1432-2234
    Keywords: Acyclic polynomial ; Graph theory ; Topological index
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract Graphical methods are developed for recursive evaluation of the acyclic polynomial. Analytical formulas of the acyclic polynomials for several specific series of graphs are given. Mathematical properties of the derivatives of the acyclic polynomial are given.
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  • 8
    Electronic Resource
    Electronic Resource
    Springer
    Theoretical chemistry accounts 50 (1979), S. 287-297 
    ISSN: 1432-2234
    Keywords: Graph theory ; Heteroconjugated molecules
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract A graph-theoretical analysis of certain π-electron properties of alternant molecules with one heteroatom is given. Topological formulas for total π-electron energy, π-electron charge density, bond order and various polarizabilities are derived. The main results of the paper are summarized in Rules 1-7.
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  • 9
    Electronic Resource
    Electronic Resource
    Springer
    Theoretical chemistry accounts 56 (1980), S. 89-92 
    ISSN: 1432-2234
    Keywords: Graph theory ; Topological resonance energy
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract The topological resonance energy (TRE) is nowadays considered as one of the most reliable indices of stability and aromaticity of conjugated molecules. Seven groups of examples are constructed showing that the TRE concept leads sometimes to obviously false chemical conclusions.
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  • 10
    Electronic Resource
    Electronic Resource
    Springer
    Theoretical chemistry accounts 66 (1984), S. 43-49 
    ISSN: 1432-2234
    Keywords: Cyclic conjugation-graph theory
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract A novel approach to the theory of cyclic conjugation is proposed, which is free of some disadvantages of the previously used methods. It is shown that in the general case the effect of cyclic conjugation is an additive function of individual ring effects. An expression for the effect of an individual ring on total π- electron energy is obtained. Some difficulties of the theory are pointed out.
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