CHIRALITY POLYNOMIALS

Chirality algebra uses ideas from permutation group theory and group representation theory to derive chirality polynomials having appropriate transformation properties for estimation of the magnitude and sign of a given pseudoscalar property (e.g. optical rotation, circular dichroism) for a given skeleton using parameters which depend only upon the ligands located at the specific sites of the skeleton, the particular skeleton, and the particular pseudoscalar property. For all but the simplest skeletons, a qualitatively complete chirality polynomial describing all chirality phenomena associated with the skeleton contains more than one component and thus requires more than one set of ligand parameters. Qualitatively complete chirality polynomials are reviewed for the most important transitive skeletons (i.e. skeletons in which all sites are equivalent), including the polarized triangle, tetrahedron, disphenoid (allene), polarized square, polarized rectangle, polarized pentagon, octahedron, trigonal prism (cyclopropane), and polarized heptagon skeletons.