Promolecules with a subsymmetry of D.infin.h. Combinatorial enumeration and stereochemical properties

Fujita, Shinsaku

doi:10.1021/ci00008a015

Cited by 29 publications

(5 citation statements)

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“…The point group O h (order 48) has 33 subgroups up to conjugacy, which have been discussed in terms of a non-redundant set of subgroups (SSG) [31]:…”

Section: Partial Cycle Indices With Chirality Fittingness (Pci-cfs) Under the Point Group O Hmentioning

confidence: 99%

Application of GAP (groups, algorithms and programming) system to stereoisograms for characterizing RS-stereoisomers of cubane derivatives

Fujita¹

2021

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The PCI (Partial-Cycle-Index) method of Fujita’s USCI (Unit-Subduced-CycleIndex) approach has been applied to symmetry-itemized enumerations of cubane derivatives, where groups for specifying three-aspects of symmetry, i.e., the point group for chirality/achirality, the RS-stereogenic group for RS-stereogenicity/RS-astereogenicity, and the LR-permutation group for sclerality/ascrelarity are considered as the subgroups of the RS-stereoisomeric group . Five types of stereoisograms are adopted as diagrammatical expressions of , after combined-permutation representations (CPR) are created as new tools for treating various groups according to Fujita’s stereoisogram approach. The use of CPRs under the GAP (Groups, Algorithms and Programming) system has provided new GAP functions for promoting symmetry-itemized enumerations. The type indices for characterizing stereoisograms (e.g., for a type-V stereoisogram) have been sophisticated into RS-stereoisomeric indices (e.g., for a cubane derivative with the composition ). The type-V stereoisograms for cubane derivatives with the composition are discussed under extended pseudoasymmetry as a new concept.

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“…The point group O h (order 48) has 33 subgroups up to conjugacy, which have been discussed in terms of a non-redundant set of subgroups (SSG) [31]:…”

Section: Partial Cycle Indices With Chirality Fittingness (Pci-cfs) Under the Point Group O Hmentioning

confidence: 99%

Application of GAP (groups, algorithms and programming) system to stereoisograms for characterizing RS-stereoisomers of cubane derivatives

Fujita¹

2021

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“…1), even if the corresponding different sets of generators are used. This is because the mark table and the USCI-CF table reported in a previous article [33] are based on SSG D6h (Eq. 1).…”

Section: Concordant Construction Of a Standard Mark Table And A Standard Usci-cf Table For D 6hmentioning

confidence: 99%

Standard mark table and standard USCI-CF table of the point group D6h. Unification of candidates derived from different D6h-skeletons

Fujita¹

2021

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Combined-permutation representations (CPRs) for characterizing -skeletons (a benzene skeleton, a Haworth-projected skeleton, a superphane skeleton, and a coronene skeleton) are constructed by starting from respective sets of generators, where the permutation of each generator is combined with a mirror-permutation of 2-cycle to treat both achiral and chiral substituents under the GAP system. Thereby, the CPR of degree 8 (= 6 + 2) for the benzene skeleton, the CPR of degree 14 (= 12 + 2) for the Haworth-projected skeleton, the CPR of degree 14 (= 12 + 2) for the superphane skeleton, the CPR of degree 14 (= 12 + 2) for the coronene skeleton are generated to give primary mark tables (tables of marks) based on these CPRs. These primary mark tables generated by the GAP system are different in the sequence of subgroups from each other, although they stem from the same point group . They are unified into a single standard mark table by means of a newly-devised GAP function MarkTableforUSCI. Moreover, another newly-devised GAP function constructUSCITable is employed to construct a standard USCI-CF (unit-subduced-cycle-index-with-chirality-fittingness) table concordantly. After a set of PCI-CFs (partial cycle indices with chirality fittingness) is calculated for each skeleton, symmetry-itemized combinatorial enumeration is conducted by means of the PCI method of Fujita’s USCI approach (S. Fujita, Symmetry and Combinatorial Enumeration in Chemistry, Springer-Verlag, Berlin-Heidelberg, 1991).

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“…positions that can be assigned to a CR D ∞ h (/ C ∞ v ) 57,58 . This versatile approach enables the characterization of the average nature of such flexible derivatives as tartaric acids57 and ferrocenes 59…”

Section: Relevant Topicsmentioning

confidence: 99%

Sphericity Governs Both Stereochemistry in a Molecule and Stereoisomerism Among Molecules

Fujita

2002

The Chemical Record

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The concept of sphericity and relevant fundamental concepts that we have proposed have produced a systematized format for comprehending stereochemical phenomena. Permutability of ligands in conventional approaches is discussed from a stereochemical point of view. After the introduction of orbits governed by coset representations, the concepts of subduction and sphericity are proposed to characterize desymmetrization processes, with a tetrahedral skeleton as an example. The stereochemistry and stereoisomerism of the resulting promolecules (molecules formulated abstractly) are discussed in terms of the concept of sphericity as a common mathematical and logical framework. Thus, these promolecules are characterized by point group and permutation group symmetry. Prochirality, stereogenicity, prostereogenicity, and relevant topics are described in terms of the concept of sphericity.

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Promolecules with a subsymmetry of D.infin.h. Combinatorial enumeration and stereochemical properties

Cited by 29 publications

References 20 publications

Application of GAP (groups, algorithms and programming) system to stereoisograms for characterizing RS-stereoisomers of cubane derivatives

Application of GAP (groups, algorithms and programming) system to stereoisograms for characterizing RS-stereoisomers of cubane derivatives

Standard mark table and standard USCI-CF table of the point group D6h. Unification of candidates derived from different D6h-skeletons

Sphericity Governs Both Stereochemistry in a Molecule and Stereoisomerism Among Molecules

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