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Aspects of form and general topology: Alpha Space Asymptotic Linearity Theorem and the spectral symmetry of alternants

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Abstract

A theoretical device and a technique have been developed by which one can study, in a unifying manner, additive properties of hydrocarbons and the symmetric property of the spectrum of alternants. By using functionals introduced in the approach via the aspects of form and general topology, a special version of the Asymptotic Linearity Theorem (for the study of additivity problems of the zero-point vibrational energy of hydrocarbons and the total pi-electron energy of alternants) has been obtained in parallel with a derivation of the spectral symmetry of alternants.

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References

  1. S. Arimoto, Phys. Lett. 113A (1985)126.

    Google Scholar 

  2. S. Arimoto, Phys. Lett. 124A (1987)131.

    Google Scholar 

  3. S. Àrimoto, Phys. Lett. 124A (1987)275.

    Google Scholar 

  4. S. Arimoto and G.G. Hall, Int. J. Quant. Chem. 41 (1992)613.

    Google Scholar 

  5. S. Arimoto and M. Spivakovsky, J. Math. Chem. 13 (1993)217.

    Google Scholar 

  6. T.L. Cottrell, J. Chem. Soc. (1948) 1448.

  7. K.S. Pitzer and E. Catalano, J. Am. Chem. Soc. 78 (1956)4844.

    Google Scholar 

  8. H. Shingu and T. Fujimoto, J. Chem. Phys. 31 (1959)556.

    Google Scholar 

  9. H. Shingu and T. Fujimoto, Bull. Japan Petroleum Inst. 1 (1959)11.

    Google Scholar 

  10. T. Fujimoto and H. Shingu, Nippon Kagaku Zasshi 82 (1961)789, 794, 945, 948.

    Google Scholar 

  11. T. Fujimoto and H. Shingu, Nippon Kagaku Zasshi 83 (1962)19.

    Google Scholar 

  12. T. Fujimoto and H. Shingu, Nippon Kagaku Zasshi 83 (1962)23, 359, 364.

    Google Scholar 

  13. J.M. Schulman and R.L. Disch, Chem. Phys. Lett. 133 (1985)291.

    Google Scholar 

  14. M.C. Flanigan, A. Kormornicki and J.W. McIver, Jr., in:Electronic Structure Calculation, ed. G.A. Segel (Plenum Press, New York, 1977).

    Google Scholar 

  15. G.G. Hall, Proc. Roy. Soc. A229 (1955)251.

    Google Scholar 

  16. G.G. Hall, Int. J. Math. Fduc. Sci. Technol. 4 (1973)233.

    Google Scholar 

  17. G.G. Hall, Bull. Inst. Math. Appl. 17 (1981)70.

    Google Scholar 

  18. J. Aihara, J. Am. Chem. Soc. 98 (1976)2750.

    Google Scholar 

  19. A. Graovac, I. Gutman and N. Trinajstić,Topological Approach to the Chemistry of Conjugated Molecules (Springer, Berlin, 1977).

    Google Scholar 

  20. I. Gutman and N. Trinajstić, Chem. Phys. Lett. 20 (1973)257.

    Google Scholar 

  21. A.T. Balaban,Chemical Applications of Graph Theory (Academic Press, New York, 1976).

    Google Scholar 

  22. A. Tang, Y. Kiang, G. Yan and S. Tai,Graph Theoretical Molecular Orbitals (Science Press, Beijing, 1986).

    Google Scholar 

  23. Y. Jiang, A. Tang and R. Hoffmarm, Theor. Chim. Acta 66 (1984)183.

    Google Scholar 

  24. A. Motoyama and H. Hosoya, J. Math. Phys. 18 (1977)1485.

    Google Scholar 

  25. H. Hosoya and A. Motoyama, J. Math. Phys. 26 (1985)157.

    Google Scholar 

  26. R.B. Mallion and D.H. Rouvray, J. Math. Chem. 5 (1990)1.

    Google Scholar 

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Authors and Affiliations

  1. Department of Chemistry, University of Saskatchewan, S7N OWO, Saskatoon, Saskatchewan, Canada

    Shigeru Arimoto

  2. Department of Mathematics, University of Saskatchewan, S7N OWO, Saskatoon, Saskatchewan, Canada

    Keith Taylor

Authors
  1. Shigeru Arimoto
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  2. Keith Taylor
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On leave from: Institute for Fundamental Chemistry, 34-4 Nishihiraki-cho, Takano, Sakyo-ku, Kyoto 606, Japan.

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Arimoto, S., Taylor, K. Aspects of form and general topology: Alpha Space Asymptotic Linearity Theorem and the spectral symmetry of alternants. J Math Chem 13, 249–264 (1993). https://doi.org/10.1007/BF01165569

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  • DOI: https://doi.org/10.1007/BF01165569

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