ALGEBRA OF STEREOGENIC PAIRING EQUILIBRIA .3. CHIRAL DISCRIMINATION

The model for pairing equilibria between skeletal analogues is applied when the two moieties are enantiomers. For 3-D skeletons with a minimum number of sites positioned according to a C(i), C(s), C2h, C2v, C3v, D2h, S4, D3h, or T(d) symmetry, the homochiral pairings are found to be more favored than the heterochiral ones, regardless of the nature (real number or vector) of the ligand parameter. The same statement is true for real ligand parameters if the skeletal symmetry is C4v or D4h. Moreover, these pairings occur in equal amounts only if the molecule is achiral. These propositions are proven by using algebraic tools. The chemical pairing constant K serves to define a chirality index chi-p which is a consistent measure of "topographical chirality" over classes of skeletal analogues with different arrays of ligand parameters. The study of the families of molecules characterized by the same chirality index is outlined.