Journal of Mathematical Chemistry

, Volume 23, Issue 3–4, pp 429–439 | Cite as

On the concept of chirality

  • Patrick Le Guennec


In the literal sense of Kelvin’s classical definition, chirality is a dichotomous concept. In this letter, we report on theoretical results which tend to alter profoundly this conception of chirality in a class of spaces of chiral systems. The example space considered here is the space of 2D square‐integrable complex fields. Our results show that, in such spaces, chirality can be considered as a continuous, extensive and local geometrical phenomenon. The presented analysis, based on a theory of symmetry groups structure, provides a rigorous description of “the way”, “the place where”, and “the extent to which” an element of such spaces lacks indirect symmetries. Kelvin’s definition is shown to describe the exterior signs of this phenomenon. A major interest of this theory is that all results can be applied to molecular wavefunctions and orbitals. Then there is hope that such results provide a renewed insight in basic stereochemical issues related to chirality.


Symmetry Group Chiral Molecule Molecular Electronic Density Molecular Chirality Chiral System 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    D. Avnir and A.Y. Meyer, J. Mol. Struct. (Theochem) 226 (1991) 211.CrossRefGoogle Scholar
  2. [2]
    L.D. Barron, in: New Developments in Molecular Chirality, ed. P. Mezey (Kluwer, Dordrecht, 1991) pp. 1–55.Google Scholar
  3. [3]
    A.B. Buda, T. Auf der Heyde and K. Mislow, Angew. Chem. Int. Ed. Engl. 31 (1992) 989–1007.CrossRefGoogle Scholar
  4. [4]
    A.B. Buda and K. Mislow, J. Am. Chem. Soc. 114 (1992) 6006–6012.CrossRefGoogle Scholar
  5. [5]
    E.L. Eliel, S.H. Wilen and L.N. Mander, Stereochemistry of Organic Compounds (Wiley–Interscience, New York, 1994).Google Scholar
  6. [6]
    G. Gilat, J. Phys. A 22 (1989) L545–L550.CrossRefGoogle Scholar
  7. [7]
    G. Gilat, Found. Phys. Lett. 3 (1990) 189–196.CrossRefGoogle Scholar
  8. [8]
    G. Gilat, J. Math. Chem. 15 (1994) 197–205.CrossRefGoogle Scholar
  9. [9]
    G. Gilat, J. Math. Chem. 16 (1994) 37–48.CrossRefGoogle Scholar
  10. [10]
    G. Gilat, in: Concepts in Chemistry: A Contemporary Challenge, ed. D.H. Rouvray (Wiley, New York, 1996) pp. 325–351.Google Scholar
  11. [11]
    O. Katzenelson, H. Zabrodsky Hel-Or and D. Avnir, Chem. Eur. J. 2 (1996) 175–181.Google Scholar
  12. [12]
    W.T. Kelvin, Baltimore Lectures on Molecular Dynamics and the Wave Theory of Light (C.J. Clay, London, 1904) p. 619.Google Scholar
  13. [13]
    A.I. Kitaigorodskii, Organic Chemical Crytallography (Consultant Bureau, New York, 1961).Google Scholar
  14. [14]
    V.E. Kuzmin and I.B. Stelmakh, Zh. Strukt. Khim. 28 (1987) 45.Google Scholar
  15. [15]
    W.J. Laugh, ed., Chiral Liquid Chromatography (Chapman and Hall, New York, 1989).Google Scholar
  16. [16]
    P. Le Guennec, Two-dimensional theory of chirality; (I) Absolute chirality, (II) Relative chirality and the chirality of complex fields, J. Math. Phys., submitted.Google Scholar
  17. [17]
    J. Maruani, G. Gilat and R. Veysseyre, C. R. Acad. Sci. Paris 319(II) (1994) 1165–1172.Google Scholar
  18. [18]
    S.F. Mason, Molecular Optical Activity and the Chiral Discriminations (Cambridge University Press, Cambridge, 1982).Google Scholar
  19. [19]
    P. Mezey, ed., New Developments in Molecular Chirality (Kluwer, Dordrecht, 1991).Google Scholar
  20. [20]
    K. Mislow and P. Bickart, Isr. J. Chem. 15 (1976/1977) 1.Google Scholar
  21. [21]
    J.D. Morrison, ed., Asymmetric Synthesis, Vol. 1, Analytical Methods (Academic Press, New York, 1983).Google Scholar
  22. [22]
    A. Rassat, C. R. Acad. Sci. Paris B 299 (1984) 53.Google Scholar
  23. [23]
    H. Zabrodsky, S. Peleg and D. Avnir, J. Am. Chem. Soc. 114 (1992) 7843–7851.CrossRefGoogle Scholar

Copyright information

© Kluwer Academic Publishers 1998

Authors and Affiliations

  • Patrick Le Guennec
    • 1
  1. 1.URA 1679Département de Chimie de l’École Normale SupérieureParis Cedex 05FranceE-mail:

Personalised recommendations