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Stability and reactivities based on moment analysis

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Abstract

The truncated expansion of a function ¦x¦ is used to obtain the total Hückel π-electron energy partitioned into various sums, in terms of moments as well as molecular fragments. The additivity is in general satisfactory for acyclic and cyclic systems, which exhibit a regularity called the generalized Hückel rule which indicates whether a fragment plays the role of stabilization or of destabilization. A unified treatment based on the energy partitioning is proposed for rationalizing aromaticity, reactivities and bond lengths of conjugated hydrocarbons. The relationships between molecular properties and topology can be deduced from inspecting, enumerating or summing the relative contributions of various fragments.

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References

  1. See, for example, Dewar MJS (1969) The molecular orbital theory of organic chemistry. McGraw-Hill, New York

    Google Scholar 

  2. Coulson CA (1946) Proc Roy Soc (London) A169; 413 (1939); Trans Faraday Soc 42:256 (1946)

  3. Foster JM, Boys SF (1960) Rev Mod Phys 32:300

    Google Scholar 

  4. Edmiston G, Ruedenberg K (1963) Rev Mod Phys 35:457; (1965) J Chem Phys 43:S97

    Google Scholar 

  5. Haydock R, Meine V, Kelly MJ (1972) J Phys C: Solid State Phys 5:2845; (1975) 8:2591

    Google Scholar 

  6. Burdett JK, Lee S, Sha WC (1984) Croat Chem Acta 57:1193

    Google Scholar 

  7. Burdett JK, Lee S (1985) J Am Chem Soc 107:3050, 3063

    Google Scholar 

  8. Burdett JK, Lee S, McLarnan TJ (1985) J Am Chem Soc 107:3083

    Google Scholar 

  9. Wall HS (1948) Analytic theory of continued fractions. Van Nostrand, New York

    Google Scholar 

  10. Whitehead RR, Watt A (1978) J Phys G Nucl Phys 4:835

    Google Scholar 

  11. Hall GG (1986) Theor Chim Acta 70:323 and the references therein

    Google Scholar 

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

    Google Scholar 

  13. Gutman I, Trinajstic N (1972) Chem Phys Lett 17:535; (1973) 20:257

    Google Scholar 

  14. Tang AC, Kiang YS, Yan GS, Dai SS (1986) Graph theoretical molecular Orbitals. Science Press, Beijing

    Google Scholar 

  15. Coislowski J (1985) Chem Phys Lett 112:243

    Google Scholar 

  16. Coulson CA (1940) Proc Cambridge Phil 36:201

    Google Scholar 

  17. Kiang YS, Tang AC (1986) Int J Quantum Chem 22:229

    Google Scholar 

  18. Jiang Y, Zhang H: to be submitted to Theor Chim Acta

  19. Hess Jr BA, Schaad LT (1971) J Am Chem Soc 93:305

    Google Scholar 

  20. Cao W, Jiang Y (1982) Acta Chim Sin 40:880

    Google Scholar 

  21. Schmalz TG, Zivkovic T, Klein DJ: to be published in Proceedings of Math/Chem/Comp 87, Yugoslavia, Elsevier

  22. Yoneda S, Shibata M, Kida S, Yoshida Z, Kai Y, Miki K, Kasai N (1984) Angew Chem Int Ed Engl 23:63

    Google Scholar 

  23. Kroto HW, Heath JR, O'Brien SC, Curl RF, Smalley RE (1985) Nature 318:162

    Google Scholar 

  24. Klein DJ, Schmalz TG, Seitz WA, Hite GE (1986) J Am Chem Soc 108:1301; and the references therein

    Google Scholar 

  25. Gutman I, Trinajstic N, Millan M (1977) J Am Chem Soc 99:1962

    Google Scholar 

  26. Gutman I, Petrovic S, Mohar B (1982) In: “ZBORNIK RADOVA, Prirodno-Matematickog Fakulteta 3”, Kragujevac: Univerzitet “Svetozar Markovic” U Kragujevcu, 1982; and the references therein

    Google Scholar 

  27. Gutman I (1980) Theor Chim Acta 56:89

    Google Scholar 

  28. Heilbronner E (1982) Chem Phys Lett 85:377

    Google Scholar 

  29. Fukui K, Yonezawa T, Nagata C (1957) J Chem Phys 27:1274

    Google Scholar 

  30. Clar E (1964) Polycyclic hydrocarbons. Academic Press, New York

    Google Scholar 

  31. Clar E (1972) The aromatic sextet. Wiley, London

    Google Scholar 

  32. Polansky OE, Derflinger G (1967) Int J Quantum Chem 1:379

    Google Scholar 

  33. Aida M, Hosoya H (1980) Tetrahedron 36:1317

    Google Scholar 

  34. Randic M (1980) Pure Appl Chem 52:1587

    Google Scholar 

  35. Sakurai K, Kitaura K, Nishimoto K (1986) Theor Chim Acta 69:23

    Google Scholar 

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Authors and Affiliations

  1. Institute of Theoretical Chemistry, Jilin University, Changchun, People's Republic of China

    Y. Jiang & H. Zhang

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  1. Y. Jiang
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  2. H. Zhang
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Also known as: Yuan-sun Kiang

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Jiang, Y., Zhang, H. Stability and reactivities based on moment analysis. Theoret. Chim. Acta 75, 279–297 (1989). https://doi.org/10.1007/BF00533194

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  • DOI: https://doi.org/10.1007/BF00533194

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