CHIRALITY FITTINGNESS OF AN ORBIT GOVERNED BY A COSET REPRESENTATION - INTEGRATION OF POINT-GROUP AND PERMUTATION-GROUP THEORIES TO TREAT LOCAL CHIRALITY AND PROCHIRALITY

Local chirality and prochirality are discussed by integrating point-group and permutation-group theories. Thereby, a compound of G symmetry is considered to consist of several orbits that are subject to coset representations (CRs). Such a CR is denoted by the symbol G(/Gi) which comes from a coset decomposition of the group G by its subgroup Gi. The local chirality for a member of a G(/Gi) orbit is determined to be Gi. The concept “chirality fittingness” is proposed to indicate symmetrical properties of the G(/Gi) orbit, in which the orbit is classified into one of three categories, i.e., homospheric, enantiospheric, and hemispheric. This terminology allows us to define a prochi ral compound as an achiral compound having at least one enantiospheric orbit. This membership criterion for prochirality is compared with the conventional substitution and symmetry criteria. The subduction of CRs affords a desymmetrization lattice for examining the existence and nonexistence of subgroups. Chemoselective achiral processes, chemoselective chiral processes, and stereoselective chiral processes are discussed in terms of the chirality fittingness of orbits. © 1990, American Chemical Society. All rights reserved.