Asymmetry revisited by Fujita’s stereoisogram approach. Part 1: Asymmetry under point-group symmetry and under RS-permutation-group symmetry

Abstract

Three kinds of symmetries are derived from stereoisograms, i.e., point-group symmetry, RS-permutation-group symmetry, and ligand-reflection-group symmetry. Among them, point-group symmetry is correlated to chirality as the first kind of handedness, while RS-permutation-group symmetry is correlated to RS-stereogenicity as the second kind of handedness. Thereby, asymmetry under point-group symmetry (denoted as asymmetry(P)) is differentiated from asymmetry under RS-permutation-group symmetry (denoted as asymmetry(RSP)), where tetrahedral derivatives are used as probes. The term asymmetry or hypo-chirality (newly coined) should be used to refer to the asymmetry(P), which is useful to discuss geometric features. For the purpose of supporting R/S-stereodescriptors, the term RS-stereogenic center (or more generally RS-stereogenic unit) based on the concept of RS-stereogenicity should be used in place of van’t Hoff’s ‘asymmetric carbon atom’ or its successor term ‘stereogenic center’, where the assignability of R/S-stereodescriptors is discussed by referring to the asymmetry(RSP) restricted to tetrahedral derivatives.