Stereoisograms for three-membered heterocycles: II. Chirality, RS-stereogenicity, and ortho-stereogenicity on the basis of the proligand-promolecule model

Abstract

The stereoisogram approach is applied to promolecules derived from an oxirane skeleton. First, the four substitution positions of the oxirane skeleton are examined under the action of the RS-stereoisomeric group \(\mathbf{C}_{2v\widetilde{\sigma }\widehat{I}}\), where point groups for chirality (or enantiomeric relationships), RS-permutation groups for RS-stereogenicity (or RS-diastereomeric relationships), and ligand-reflection groups for sclerality (or holantimeric relationships) are integrated in a consistent way. A notation system for giving \(R_{\mathrm {a}}/S_{\mathrm {a}}\)-descriptors is proposed to specify the absolute configurations of oxirane derivatives on the basis of RS-stereogenicity (or RS-diastereomeric relationships) inherent in type-I, -III, or -V stereoisograms. The concept of chirality faithfulness is revised to give a rational judgement on whether \(R_{\mathrm {a}}/S_{\mathrm {a}}\)-descriptors are labelled in uppercase or lowercase letters. Pseudoasymmetry and extended pseudoasymmetry are discussed on the basis of type-V stereoisograms. Second, the stereoisomeric group \(\widetilde{\mathbf{C}}_{2v\widetilde{\sigma }\widehat{I}}\), which is a supergroup of the RS-stereoisomeric group \(\mathbf{C}_{2v\widetilde{\sigma }\widehat{I}}\), is used to characterize the cis/trans- or Z/E-isomerism, where multiple stereoisograms are introduced as graphic representations of stereoisomeric groups. The notation system of specifying Z/E-descriptors is modified to be applicable to oxirane derivatives by adopting ortho-stereogenicity (or ortho-diastereomeric relationships). Finally, the isoskeletal group \(\widetilde{\widetilde{\mathbf{C}}}_{2v\widetilde{\sigma }\widehat{I}}\), which is a supergroup of the stereoisomeric group \(\widetilde{\mathbf{C}}_{2v\widetilde{\sigma }\widehat{I}}\), is used to characterize total features of isomerism based on an oxirane skeleton. Multiple stereoisogram sets are introduced as graphic representations of such isoskeletal groups, where flowcharts for determining types of multiple stereoisogram sets are proposed.