Systematic Characterization of Prochirality, Prostereogenicity, and Stereogenicity by Means of the Sphericity Concept

A systematic method for characterizing prochirality, prostereogenicity, and stereogenicity is described. Any set of equivalent ligands is regarded as an orbit governed by a coset represention, by which the orbit is classified into homospheric, enantiospheric, or hemispheric. A molecule containing at least one enantiospheric orbit is defined to be prochiral (Rule A). After the definition of the topicity terms, a prostereogenic center is defined as a center or atom having two ligands that are indistinguishable in isolation and not homotopic (i.e. either enantiotopic, diastereotopic or heterotopic) in a molecule (Rule B). Then, Rule C for characterizing a stereogenic center is defined subsidiarily from Rule B; these rules are discussed by using several molecules of stereochemical interest.