Abstract
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.
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References
D. Avnir and A.Y. Meyer, J. Mol. Struct. (Theochem) 226 (1991) 211.
L.D. Barron, in: New Developments in Molecular Chirality, ed. P. Mezey (Kluwer, Dordrecht, 1991) pp. 1–55.
A.B. Buda, T. Auf der Heyde and K. Mislow, Angew. Chem. Int. Ed. Engl. 31 (1992) 989–1007.
A.B. Buda and K. Mislow, J. Am. Chem. Soc. 114 (1992) 6006–6012.
E.L. Eliel, S.H. Wilen and L.N. Mander, Stereochemistry of Organic Compounds (Wiley–Interscience, New York, 1994).
G. Gilat, J. Phys. A 22 (1989) L545–L550.
G. Gilat, Found. Phys. Lett. 3 (1990) 189–196.
G. Gilat, J. Math. Chem. 15 (1994) 197–205.
G. Gilat, J. Math. Chem. 16 (1994) 37–48.
G. Gilat, in: Concepts in Chemistry: A Contemporary Challenge, ed. D.H. Rouvray (Wiley, New York, 1996) pp. 325–351.
O. Katzenelson, H. Zabrodsky Hel-Or and D. Avnir, Chem. Eur. J. 2 (1996) 175–181.
W.T. Kelvin, Baltimore Lectures on Molecular Dynamics and the Wave Theory of Light (C.J. Clay, London, 1904) p. 619.
A.I. Kitaigorodskii, Organic Chemical Crytallography (Consultant Bureau, New York, 1961).
V.E. Kuzmin and I.B. Stelmakh, Zh. Strukt. Khim. 28 (1987) 45.
W.J. Laugh, ed., Chiral Liquid Chromatography (Chapman and Hall, New York, 1989).
P. Le Guennec, Two-dimensional theory of chirality; (I) Absolute chirality, (II) Relative chirality and the chirality of complex fields, J. Math. Phys., submitted.
J. Maruani, G. Gilat and R. Veysseyre, C. R. Acad. Sci. Paris 319(II) (1994) 1165–1172.
S.F. Mason, Molecular Optical Activity and the Chiral Discriminations (Cambridge University Press, Cambridge, 1982).
P. Mezey, ed., New Developments in Molecular Chirality (Kluwer, Dordrecht, 1991).
K. Mislow and P. Bickart, Isr. J. Chem. 15 (1976/1977) 1.
J.D. Morrison, ed., Asymmetric Synthesis, Vol. 1, Analytical Methods (Academic Press, New York, 1983).
A. Rassat, C. R. Acad. Sci. Paris B 299 (1984) 53.
H. Zabrodsky, S. Peleg and D. Avnir, J. Am. Chem. Soc. 114 (1992) 7843–7851.
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Le Guennec, P. On the concept of chirality. Journal of Mathematical Chemistry 23, 429–439 (1998). https://doi.org/10.1023/A:1019197930712
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DOI: https://doi.org/10.1023/A:1019197930712