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Theoretical Chemistry Accounts

, Volume 121, Issue 5–6, pp 279–288 | Cite as

Narcissistic reaction pathways: an example of Maxwell’s theorem of geometrical optics applied to the intrinsic reaction coordinate model

  • Miquel LlunellEmail author
  • Pere Alemany
  • Josep Maria Bofill
Regular Article

Abstract

Maxwell’s theorem and the concept of stigmatic transformations that appear in the theory of geometrical optics are extended to the intrinsic reaction coordinate model when it is applied to the specific case of narcissistic reactions. Open image in new window

Keywords

Reaction path Narcissistic reaction Chirality measures Chiral path Helicenes 

Notes

Acknowledgments

Financial support from the Spanish Ministerio de Ciencia y Tecnología, DGI projects CTQ2005-08123-C02-01/BQU and CTQ2005-01117/BQU, and in part from the Generalitat de Catalunya projects 2005SGR-00036 and 2005SGR-00111 is fully acknowledged. M. L. gratefully acknowledges the Ramón y Cajal Program.

References

  1. 1.
    Eliel EL, Wilen SH (1994) Stereochemistry of organic compounds. Wiley, New YorkGoogle Scholar
  2. 2.
    Salem L (1971) Acc Chem Res 4:322. doi: 10.1021/ar50045a005 CrossRefGoogle Scholar
  3. 3.
    Fukui K (1981) Int J Quantum Chem Quantum Chem Symp 15:633Google Scholar
  4. 4.
    Luneburg RK (1944) Mathematical theory of optics, chap II. Brown University, ProvidenceGoogle Scholar
  5. 5.
    Heidrich D (ed) (1995) The reaction path in chemistry: current approaches and perspectives. Kluwer, DordrechtGoogle Scholar
  6. 6.
    Crehuet R, Bofill JM (2005) J Chem Phys 122:234105. doi: 10.1063/1.1927521 CrossRefGoogle Scholar
  7. 7.
    Courant R, Hilbert D (1953) Methods of mathematical physics. Wiley, New YorkGoogle Scholar
  8. 8.
    Dewar MJS, Zoebisch EG, Healy EF, Stewart JJP (1985) J Am Chem Soc 107:3902. doi: 10.1021/ja00299a024 CrossRefGoogle Scholar
  9. 9.
    Grimme S, Peyerimhoff SD (1996) Chem Phys 204:411. doi: 10.1016/0301-0104(95)00275-8 CrossRefGoogle Scholar
  10. 10.
    Janke RH, Haufe G, Würthwein EU, Borkent JH (1996) J Am Chem Soc 118:6031. doi: 10.1021/ja950774t CrossRefGoogle Scholar
  11. 11.
    González C, Schlegel HB (1989) J Chem Phys 90:2154. doi: 10.1063/1.456010 CrossRefGoogle Scholar
  12. 12.
    Frisch MJ, et al (2003) Gaussian03, Revision B.4. Gaussian Inc., WallingfordGoogle Scholar
  13. 13.
    Schmidt MW, Baldridge KK, Boatz JA, Elbert ST, Gordon MS, Jensen JH et al (1993) J Comput Chem 14:1347. doi: 10.1002/jcc.540141112 CrossRefGoogle Scholar
  14. 14.
    Mauksch M, Schleyer PvR (1997) Angew Chem Int Ed 36:1856CrossRefGoogle Scholar
  15. 15.
    Llunell M, Alemany P, Bofill JM (2008) Chemphyschem 9:1117. doi: 10.1002/cphc.200800052 CrossRefGoogle Scholar
  16. 16.
    Avnir D, Zabrodsky Hel-Or H, Mezey PG (1998) In: Schleyer PvR (ed) Encylopedia of computational chemistry. Wiley, New YorkGoogle Scholar
  17. 17.
    Zabrodsky H, Peleg S, Avnir D (1992) J Am Chem Soc 114:7843. doi: 10.1021/ja00046a033 CrossRefGoogle Scholar
  18. 18.
    Pinto Y, Salomon Y, Avnir D (1998) J Math Chem 23:13. doi: 10.1023/A:1019148619809 CrossRefGoogle Scholar
  19. 19.
    Alvarez S, Alemany P, Avnir D (2005) Chem Soc Rev 34:313. doi: 10.1039/b301406c CrossRefGoogle Scholar
  20. 20.
    Martin RH (1974) Angew Chem Int Ed 13:649CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  • Miquel Llunell
    • 1
    Email author
  • Pere Alemany
    • 1
  • Josep Maria Bofill
    • 2
  1. 1.Departament de Química Física, Institut de Química Teòrica i Computacional (IQTC)Universitat de BarcelonaBarcelonaSpain
  2. 2.Departament de Química Orgànica, Institut de Química Teòrica i Computacional (IQTC)Universitat de BarcelonaBarcelonaSpain

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