Molecular chirality and chiral parameters

The fundamental issues of symmetry related to chirality are discussed and a pplied to simple situations relevant to liquid crystals. The authors show t hat any chiral measure of a geometric object is a pseudoscalar (invariant u nder proper rotations but changing sign under improper rotations) and must involve three-point correlations that only come into play when the molecule has at least four atoms. In general, a molecule is characterized by an inf inite set of chiral parameters. The authors illustrate the fact that these parameters can have differing signs and can vanish at different points as a molecule is continuously deformed into its mirror image. From this it is c oncluded that handedness is not an absolute concept but depends on the prop erty being observed. Within a simplified model of classical interactions, t he chiral parameter of the constituent molecules that determines the macros copic pitch of cholesterics is identified. [S0034-6861(99)00255-X].