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A combined technique for computation of energy-effect of cycles in conjugated molecules

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Abstract

A direct method for computation of the energy-effect (ef) of cycles in conjugated molecules is elaborated, based on numerical calculation of the (complex) zeros of certain graph polynomials. Accordingly, the usage of the Coulson integral formula can be avoided, and thus the ef-values can be calculated for arbitrary cycles of arbitrary conjugated systems.

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Notes

  1. The quantities \(\lambda _k \), \(k=1,2,\ldots ,n\), are in fact the eigenvalues of the adjacency matrix. The usual way of their computation is matrix diagonalization. On the other hand, the quantities \(\lambda _k^{ref} \), \(k=1,2,\ldots ,n\), are not eigenvalues, and can only be obtained by calculating the zeros of the underlying polynomial.

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Authors and Affiliations

  1. Center for Separation Processes Modeling and Nano-Computations, School of Chemical Engineering, College of Engineering, University of Tehran, P. O. Box 11365-4563, Tehran, Iran

    H. Fatoorehchi & H. Abolghasemi

  2. Faculty of Science, University of Kragujevac, P. O. Box 60, 34000, Kragujevac, Serbia

    I. Gutman

  3. State University of Novi Pazar, Novi Pazar, Serbia

    I. Gutman

  4. Oil and Gas Center of Excellence, University of Tehran, Tehran, Iran

    H. Abolghasemi

Authors
  1. H. Fatoorehchi
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  2. I. Gutman
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  3. H. Abolghasemi
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Correspondence to I. Gutman.

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Fatoorehchi, H., Gutman, I. & Abolghasemi, H. A combined technique for computation of energy-effect of cycles in conjugated molecules. J Math Chem 53, 1113–1125 (2015). https://doi.org/10.1007/s10910-015-0473-y

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  • DOI: https://doi.org/10.1007/s10910-015-0473-y

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