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.     

Conceptual defects of modern stereochemistry. Comprehensive remedy by stereoisograms based on RS-stereoisomerism for mediating between enantiomerism and stereoisomerism

The recognition of chirality as a single kind of handedness is a conceptual defect of modern stereochemistry, which has caused serious confusion in its theoretical foundations and stereochemical nomenclature. To remedy this defect, RS-stereogenicity is developed as another kind of handedness. These two kinds of handedness are integrated to give RS-stereoisomerism, which is formulated diagrammatically by stereoisograms. During the process of the remedy, the lack of the concept of ligand reflections has been revealed as another conceptual defect. The lack of the concept of orbits (equivalence classes) has been found to be one more defect, which has caused a misleading classification of isomers. By adopting the concept of orbits, the revised hierarchy of isomerism is developed, i.e., isomers $?$ isoskeletomers $?$ stereoisomers $?$ RS-stereoisomers $?$ enantiomers $?$ 3D-structures. Thereby, the theoretical foundations of modern stereochemistry are restructured rationally.     

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.     

Pseudoasymmetrie in der organischen Chemie

The geometrical foundations of ‘pseudoasymmetry’ and several other related concepts of organic stereochemistry such as ‘prochirality’ and ‘propseudoasymmetry’ in two- and three-dimensional space have been explored. As a consequence some modifications of the R,S system for specification of molecular chirality and stereoisomerism are proposed.     

Die Isomerie: Grundlagen der Chemie

Studies in the field of isomerism have often created misunderstandings, confusion and controversies, but have also led to new impulses for the development of structure theory, new analytical methods and synthesis of novel compounds. Problems of isomerism are present in nearly all fields of chemistry and have stimulated creation of new concepts and enriched the chemical nomenclature. Presently, probably the most ambitious studies in structure chemistry deal with the elucidation of conformational isomerism of large bio‐molecules such as proteins in liquid and solution.     

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.     

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.     

Control of Diels-Alder Addition,Stereo- and Regioselectivity by Remote Substituents and Tricarbonyl(diene)iron Moieties

A stereoselective synthesis of tricarbonyl-[((1RS,2RS,4RS,5RS,6RS)-C-5,6,C-η-(5,6,7,8,-tetramethylidenbicyclo[2.2.2]octan-2-ol)]iron ( 11 ),and of its tosylate 12 and benzoate 13 is reported. The bulk of the ‘endo’-Fe(CO))³ moiety and of the ester groups in 13 renders its Diels-Alder additions to methyl propynoate ( 15 )), butynone ( 16 ), and 1-cyanovinyl acetate highly ‘para’ regioselective. The cycloadditions of diene-alcohol 11 are either ‘meta’- or ‘para’-regioselective depending on the nature of the dienophile. In the presence of BF ₃. Et ₂O, the addition of 11 to methyl vinyl ketone is highly stereo- (Alder mode) and ‘para’-regioselective, giving adduct 52 (tricarbonyl [((1 RS,4RS,8RS,9RS,10RS,12RS)-C,9,10,C-η-(12-hydroxy-9,10-dimethylidenetricyclo[6.2.2.0^2,7]dodec-2(7)-en-4 yl methyl ketone)]iron) whose structure has been established by single-crystal X-ray crystallography.     

Gas-phase NMR studies of chemical equilibria: 1—Methodology

Methods for obtaining ¹H NMR spectra of gases are discussed. Particular attention is paid to the nature of the tube and to the use of ‘second sample’ field/frequency locking. The question of the chemical shift reference is examined, and some results for tetramethylsilane gas are presented. Representative spectra are shown for three types of organic equilibria in the gas phase: keto-enol tautomerism, addition of methanol to acetaldehyde and Z-E isomerism of acetaldoxime.     

GC/MS and 1H-NMR Analysis of Phytanic Acid Synthesized from Natural trans-Phytol and a Synthetic Phytol Standard

Phytanic acid (3,7,11,15-tetramethylhexadecanoic acid) is a bioactive multi-branched fatty acid mainly synthesized by ruminants from trans-phytol which is found esterified in chlorophyll. Many clinical and biochemical studies were carried out with phytol and phytanic acid, but the stereochemistry of both compounds has not been detailed in either case. In this study, we released trans-phytol from a sample of fresh grass and isolated the natural product from the unsaponifiable matter by means of high-speed counter-current chromatography (HSCCC). The trans-phytol obtained by this measure was used as starting material for the synthesis of phytanic acid. The starting material and the products of this synthesis were compared to the compounds generated in parallel from commercial phytol labeled as “cis-/trans-mixture”. While the phytanic acid produced from trans-phytol from the grass sample was enantiopure on C-7 and C-11, the commercial phytol standard proved to be racemic. These differences could be elaborated by means of the trimethylsilylether of phytol and the methyl esters of phytanic acid. Likewise, ¹H-NMR of phytanic acid methyl ester was suitable to distinguish the natural 3R,7R,11R-/3S,7R,11R-diastereomers from all racemic 3RS,7RS,11RS-phytanic acid by means of the signal dispersion of the multiplets at ~2.1 and ~2.3 ppm. Our results indicate that racemic phytol has been used in different chemical, analytical and biochemical studies. Due to the extraordinary relevance of stereoisomerism, future studies should take advantage of the natural products, i.e. trans-phytol and phytanic acid, with R-configuration on C-7 and C-11. Moreover, the specific composition of the compounds used in studies should be addressed in future studies.     

烃同分异构体的计数

能否系统精确地解决高中化学学习中的同分异构体计数问题?本文在高中数学化学的背景知识之上,引入生成函数以及Pólya计数定理,在不考虑立体异构的前提下,从烷基的同分异构体计数入手,逐步推导烷烃、一烯烃、一炔烃苯的衍生物、二取代烷烃以及二烯烃的同分异构体计数的公式,并将计算结果与手工枚举进行对比,进一步证明其正确性。我们还归纳性地发掘了同分异构体计数的渐进特征并提出了以上烃类同分异构体计数的近似公式。对比国外的成果,本文尽力避免引入过多的数学概念,降低门槛,适合高中生阅读,加深对于烃结构的理解,培养计算思维;对比国内相同主题的研究,本文的推导形式清晰简洁,拓展性较强。     

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’).