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 C 2v σ 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 a /S 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 a /S 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 C 2v σ I , which is a supergroup of the RS-stereoisomeric group C 2v σ I , is used to characterize the cis/transor 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 C 2v σ I , which is a supergroup of the stereoisomeric group C 2v σ 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.

Type-itemized enumeration of quadruplets of RS-stereoisomers: II—cycle indices with chirality fittingness modulated by type-V quadruplets

“…The corresponding RSstereoisomeric group C 2v σ I is constructed on the basis of the point group C 2v , as shown in Table 1. The four positions of the oxirane skeleton 1 belong to a C 2v (/C 1 )-orbit under the point group C 2v , while they are regarded as belonging to a C 2v σ I (/C I )-orbit under the RS-stereoisomeric group C 2v σ I [27][28][29]. Each operation of C 2v σ I is represented by a product of cycles, which is characterized by a product of sphericity indices (PSI) as listed in the PSI-column of Table 1.…”

“…On the other hand, the achiral promolecules 9 and 10 construct a quadruplet of type V, where they do not exhibit cis/trans-isomerism (Z /E-isomerism). From a viewpoint of Fujita's stereoisogram approach [27][28][29], the stereoisomerism at issue is represented by the following scheme:…”

“…2 is essentially equivalent to to the list of Fig. 26 of [28]. However, it should be noted that the numbering of four positions of the oxirane skeletons in Fig.…”

“…2 is based on the action of the RS-stereoisomeric group C 2v σ I , while the numbering in Fig. 26 of [28] is based on the action of the corresponding isoskeletal (isoskeletomeric) group (cf. Fig.…”

“…Type-itemized enumerations of quadruplets have been conducted according to three kinds of relationships contained in stereoisograms [21,22]. More recently, symmetry-itemized enumerations of quadruplets have been conducted by extending Fujita's USCI approach [10], where tetrahedral derivatives [23,24], allene derivatives [25,26], and three-membered heterocycles [27][28][29] are combinatorially enumerated after the preparation of necessary data (e.g., mark tables, inverse mark tables, subductions of coset representations). Because such necessary data to symmetry-itemized enumerations are not so easily obtained in general, type-itemized enumerations are still important as succinct methods.…”