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Remark on the moment expansion of total π-electron energy

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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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References

  1. 1.

    Coulson CA (1940) Proc Cambridge Phil Soc 36:201

  2. 2.

    Ruedenberg K (1954) J Chem Phys 22:1878

  3. 3.

    Hall GG (1955) Proc Roy Soc (London) A229:251

  4. 4.

    Graovac A, Gutman I, Trinajstić N (1977) Topological approach to the chemistry of conjugated molecules. Springer, Berlin Heidelberg New York

  5. 5.

    Heilbronner E, Bock H (1968) Das HMO-Modell und seine Anwendung. Verlag Chemie, Weinheim

  6. 6.

    Gutman I (1992) Top Curr Chem 162 (in press)

  7. 7.

    Stepanov NF, Tatevsky VM (1961) Zh Strukt Khim 2:241

  8. 8.

    Stepanov NF, Tatevsky VM (1961) Zh Strukt Khim 2:452

  9. 9.

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

  10. 10.

    Jiang Y, Tang A, Hoffmann R (1984) Theor Chim Acta 66:183

  11. 11.

    Schmalz TG, Živković T, Klein DJ (1988) Stud Phys Theor Chem 54:173

  12. 12.

    Jiang Y, Zhang H (1989) Theor Chim Acta 75:279

  13. 13.

    Jiang Y, Zhu H, Zhang H, Gutman I (1989) Chem Phys Lett 159:159

  14. 14.

    Jiang Y, Zhang H (1990) Pure Appl Chem 62:451

  15. 15.

    Babić D, Graovac A, Gutman I (1991) Theor Chim Acta 79:403

  16. 16.

    Gutman I, Hall GG, Marković S, Stanković Z, Radivojević V (1991) Polyc Arom Comp (in press)

  17. 17.

    Dias JR (1985) Theor Chim Acta 68:107

  18. 18.

    Hall GG (1986) Theor Chim Acta 70:323

  19. 19.

    Marković S (1991) Theor Chim Acta (in press)

  20. 20.

    Marković S, Gutman I (1991) J Mol Struct (Theochem) 235:81

  21. 21.

    P. O. Löwdin (1990) J Math Chem 4:401

  22. 22.

    Gutman I, Trinajstić N (1972) Chem Phys Lett 17:535

  23. 23.

    Gutman I, Polansky OE (1986) Mathematical concepts in organic chemistry. Springer, Berlin Heidelberg New York

  24. 24.

    Gutman I (1977) J Chem Phys 66:1652

  25. 25.

    McClelland BJ (1971) J Chem Phys 54:640

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Gutman, I. Remark on the moment expansion of total π-electron energy. Theoret. Chim. Acta 83, 313–318 (1992). https://doi.org/10.1007/BF01113057

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Key words

  • Hückel theory
  • Total π-electron energy
  • Moments