Integrated Discussion on Stereogenicity and Chirality for Restructuring Stereochemistry

To discuss the difference between stereogenicity and chirality, we propose the concept of RS-stereoisomeric groups. Beginning with this concept, we have further proposed the concepts of holantimers, stereoisograms, and RS-stereogenicity. Thereby, we have clarified that the concept of RS-stereogenicity, but not conventional stereogenicity, is closely related to chirality. Thus, five RS-stereogenicity types are defined and examined to discuss the difference between stereogenicity and chirality. Combinatorial enumerations have also been studied by considering the RS-stereogenicity.     

Symmetry-itemized enumeration of quadruplets of RS-stereoisomers. II. The partial-cycle-index method of the USCI approach combined with the stereoisogram approach

The symmetry-itemized enumeration of quadruplets of stereoisograms is discussed by starting from a tetrahedral skeleton, where the partial-cycle-index (PCI) method of the unit-subduced-cycle-index approach (Fujita in Symmetry and combinatorial enumeration of chemistry. Springer, Berlin, 1991) is combined with the stereoisogram approach (Fujita in J Org Chem 69:3158–3165, 2004, Tetrahedron 60:11629–11638, 2004). Such a tetrahedral skeleton as contained in the quadruplet of a stereoisogram belongs to an RS-stereoisomeric group denoted by $\mathbf{T}_{d\widetilde{\sigma }\widehat{I}}$ , where the four positions of the tetrahedral skeleton accommodate achiral and chiral proligands to give quadruplets belonging to subgroups of $\mathbf{T}_{d\widetilde{\sigma }\widehat{I}}$ according to the stereoisogram approach. The numbers of quadruplets are calculated as generating functions by applying the PCI method. They are itemized in terms of subgroups of $\mathbf{T}_{d\widetilde{\sigma }\widehat{I}}$ , which are further categorized into five types. Quadruples for stereoisograms of types I–V are ascribed to subgroups of $\mathbf{T}_{d\widetilde{\sigma }\widehat{I}}$ , where their features are discussed in comparison between RS-stereoisomeric groups and point groups.     

Stereoisograms for reorganizing the theoretical foundations of stereochemistry and stereoisomerism. Part 3: rational avoidance of misleading standpoints for pro-R/pro-S-descriptors

The stereoisogram approach is introduced to settle the misleading terminology due to ‘prochirality’ in modern stereochemistry. After the term prochirality is redefined as having a purely geometric meaning, a method based on probe stereoisograms and another method based on equivalence classes (orbits) are introduced to determine prochirality and/or pro-RS-stereogenicity. Enantiotopic and RS-diastereotopic relationships appearing in probe stereoisograms are respectively used to determine prochirality and pro-RS-stereogenicity, where ‘stereoheterotopic’ relationships used in modern stereochemistry are abandoned. Alternatively, an enantiospheric orbit for specifying prochirality and an RS-enantiotropic orbit for specifying pro-RS-stereogenicity are emphasized by using coset representations and Young tableaux. The pro-R/pro-S-system is clarified to be based on pro-RS-stereogenicity and not on prochirality.     

Group-theoretical discussion on the E/Z-nomenclature for ethylene derivatives. Discrimination between RS-stereoisomeric groups and stereoisomeric groups

The hierarchy of point groups, RS-stereoisomeric groups, stereoisomeric groups, and isoskeletal groups is discussed to comprehend the chirality, RS-stereogenicity, stereogenicity, and isoskeletal isomerism for ethylene derivatives. The RS-stereoisomeric groups for ethylene derivatives have been clarified not to coincide with their stereoisomeric groups, so that diastereomers (E/Z-isomers) are not identical with RS-diastereomers. To discuss the relationship among RS-diastereomers, m-diastereomers, and isoskeletal isomers, we have proposed the concepts of extended stereoisograms and extended stereoisogram sets, where the term "m-diastereomers" is coined to show its difference from the traditional term "diastereomer". Thereby, ethylene derivatives are classified into Types II-II/II-II/II-II, IV-IV/IV-IV/IV-IV, etc. on the basis of relevant stereoisograms (Types I to V). The stereoisomerism of ethylenes has been concluded to be treated in terms of m-diastereomers characterized by the E/Z-nomenclature but not to be treated in terms of RS-diastereomers characterized by the RS-nomenclaure.     

Combinatorial approach to group hierarchy for stereoskeletons of ligancy 4

Fujita’s proligand method developed originally for combinatorial enumeration under point groups (Fujita in Theor Chem Acc 113:73–79, 2005) is extended to meet the group hierarchy, which stems from the stereoisogram approach for integrating geometric aspects and stereoisomerism in stereochemistry (Fujita in J Org Chem 69:3158–3165, 2004). Thereby, it becomes applicable to enumeration under respective levels of the group hierarchy. Combinatorial enumerations are conducted to count inequivalent pairs of (self-)enantiomers under a point group, inequivalent quadruplets of RS-stereoisomers under an RS-stereoisomeric group, inequivalent sets of stereoisomers under a stereoisomeric group, and inequivalent sets of isoskeletomers under an isoskeletal group. In these enumerations, stereoskeletons of ligancy 4 are used as examples, i.e., a tetrahedral skeleton, an allene skeleton, an ethylene skeleton, an oxirane skeleton, a square planar skeleton, and a square pyramidal skeleton. Two kinds of compositions are used for the purpose of representing molecular formulas in an abstract fashion, that is to say, the compositions for differentiating proligands having opposite chirality senses and the compositions for equalizing proligands having opposite chirality senses. Thereby, the classifications of isomers are accomplished in a systematic fashion.     

Pseudoasymmetry, stereogenicity, and the RS-nomenclature comprehended by the concepts of holantimers and stereoisograms

The concepts of holantimer and stereoisogram are applied to comprehensive discussions on the term ‘pseudoasymmetry’, where the concept of RS-stereogenicity is used as a more definite concept than usual stereogenicity. Thereby, three relationships contained in each stereoisogram can be definitely specified: an enantiomeric relationship is related to chiral/achiral, an RS-diastereomeric relationship is related to RS-stereogenic/RS-astereogenic, and a holantimeric relationship is related to scleral/ascleral, which is coined to keep the terminology in a balanced fashion. Such stereoisograms are classified into five types (Types I-V) by virtue of the three relationships. Among them, Type I, III, and V are selected as a set of RS-stereogenic units: chiral/ascleral RS-stereogenic unit (or Type I unit), chiral/scleral RS-stereogenic unit (or Type III unit), and achiral/scleral RS-stereogenic unit (or Type V unit). Thereby, the term ‘pseudoasymmetric stereogenic units’ should be replaced by the term ‘achiral/scleral RS-stereogenic units’ (or ‘Type V units’).     

Hierarchical enumeration of Kekulé’s benzenes,Ladenburg’s benzenes,Dewar’s benzenes,and benzvalenes by using combined-permutation representations

The group hierarchy for each skeleton of ligancy 6 is formulated to be: point group (PG \({\varvec{G}}_{\sigma }\)) \(\subseteq \) RS-stereoisomeric group (RS-SIG \({\varvec{G}}_{\sigma \widetilde{\sigma }\widehat{I}}\)) \(\subseteq \) stereoisomeric group (SIG \(\widetilde{{\varvec{G}}}_{\sigma \widetilde{\sigma }\widehat{I}}\)) \(\subseteq \) isoskeletomeric group (ISG \(\widetilde{\widetilde{{\varvec{G}}}}_{\sigma \widetilde{\sigma }\widehat{I}}\) = \({\varvec{S}}^{[6]}_{\sigma \widehat{I}}\)), where we start from the PG \({\varvec{G}}_{\sigma }\) = \({\varvec{D}}_{6h}\) for the Kekulé benzene skeleton, from the PG \({\varvec{G}}_{\sigma }\) = \({\varvec{D}}_{3h}\) for the Ladenburg benzene skeleton, from the PG \({\varvec{G}}_{\sigma }\) = \({\varvec{C}}_{2v}\) for the Dewar benzene skeleton, or from the PG \({\varvec{G}}_{\sigma }\) = \({\varvec{C}}_{2v}\) for the benzvalene skeleton. After these groups are constructed as combined-permutation representations, the calculation of the respective cycle indices with chirality fittingness (CI-CFs) and the introduction of ligand-inventory functions are conducted to give generation functions for 3D-based enumerations (for PGs and RS-SIGs) and 2D-based enumerations (for SIGs and ISGs). The enumeration results are discussed by means of isomer-classification diagrams, in which equivalence classes under enantiomerism (for PGs), RS-stereoisomerism (for RS-SIGs), stereoisomerism (for SIGs), and isoskeletomerism (for ISGs) are illustrated schematically. The implicit connotations of the conventional terms “skeletal isomerism”, “positional isomerism”, and “constitutional isomerism” are discussed, where the effects of the concept of isoskeletomerism are emphasized.     

Alnumycins A2 and A3: new inverse-epimeric pairs stereoisomeric to alnumycin A1

Two new pairs of stereoisomeric alnumycin As, A2 {(2)-(1R,1′RS,4′SR,5′SR)} and A3 {(2)-(1R,1′RS,4′SR,5′RS)}, are described. Similar to alnumycin A1 {(2)-(1R,1′RS,4′RS,5′SR)}, each of these naturally occurring compounds is also a pair of C-1 inverse epimers. The relative configurations of the dioxane ring sidechains were assigned on the basis of ¹H NMR NOE contacts and molecular modeling using density functional theory (DFT) at the M06-2X/6-31G(d) level of theory. The absolute configurations of C-1 and the determination of inverse epimeric relationships were achieved by experimental electronic circular dichroism (ECD) measurements, with both aspects confirmed by using the chiral derivatizing agent (CDA) Mosher′s acid chloride {α-methoxy-α-trifluorophenylacetyl chloride (MTPACl)} to effect enantiodifferentiation. The absolute configurations of the dioxane ring using the CDA could only be effected in the case of alnumycin A1, the results of which were in agreement with previous assignments. The dioxane ring conformational mobility and the likely interaction between the MTPA groups coupled with the structural novelty of the diols in the dioxane ring with respect to CDA analysis precluded an absolute configuration assignment for alnumycins A2 and A3 based on empirical comparisons or by computational analysis of through-space NMR shieldings (TSNMRS) emanating from the phenyl groups of the MTPA moieties.