ON THE CONCEPT OF CHIRALITY

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 o f ''the way'', ''the place where'', and ''the extent to which'' an ele ment of such spaces lacks indirect symmetries. Kelvin's definition is shown to describe the exterior signs of this phenomenon. A major inter est of this theory is that all results can be applied to molecular wav efunctions and orbitals. Then there is hope that such results provide a renewed insight in basic stereochemical issues related to chirality.