Experimental tests of chirality algebra

Most chiral molecules can be dissected into a collection of ligands attached to an underlying skeleton. Application of permutation group theory and group representation theory to such a model can lead to chirality functions which can be used to approximate pseudoscalar measurements such as optical rotation or circular dichroism. Such chirality functions have been tested experimentally for the following skeletons: (1) The polarized triangle of phosphines and phosphine oxides; (2) the tetrahedron of methane derivatives; (3) the disphenoid of allene and 2, 2-spirobiindane derivatives; (4) the polarized rectangle of [2, 2]-metacyclophanes; (5) the polarized pentagon of heterodisubstituted ferrocenes. The success of this method is fair to good for the polarized triangle, tetrahedron, and disphenoid skeletons but deteriorates rapidly for the polarized rectangle and polarized pentagon skeletons, in accord with the greater group-theoretical complexity of the latter skeletons.