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Mathematical stereochemistry /

Chirality and stereogenicity are closely related concepts and their differentiation and description is still a challenge in chemoinformatics. A new stereoisogram approach, developed by the author, is introduced in this book, providing a theoretical framework for mathematical aspects of modern stereo...

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Detalles Bibliográficos
Clasificación:	Libro Electrónico
Autor principal:	Fujita, Shinsaku, 1944-
Formato:	Electrónico eBook
Idioma:	Inglés
Publicado:	Berlin ; Boston : De Gruyter, [2015]
Temas:	Stereochemistry. Chemistry > Mathematics. Stéréochimie. SCIENCE / Chemistry / Physical & Theoretical.
Acceso en línea:	Texto completo

Tabla de Contenidos:

1. Introduction
1.1 Two-Dimensional versus Three-Dimensional Structures
1.1.1 Two-Dimensional Structures in Early History of Organic Chemistry
1.1.2 Three-Dimensional Structures After Beginning of Stereochemistry
1.1.3 Arbitrary Switching Between 2D-Based and 3D-Based Concepts
1.2 Problematic Methodology for Categorizing Isomers and Stereoisomers
1.2.1 Same or Different
1.2.2 Dual Definition of Isomers
1.2.3 Positional Isomers as a Kind of Constitutional Isomers
1.3 Problematic Methodology for Categorizing Enantiomers and Diastereomers
1.3.1 Enantiomers
1.3.2 Diastereomers
1.3.3 Chirality and Stereogenicity
1.4 Total Misleading Features of the Traditional Terminology on Isomers
1.4.1 Total Misleading Flowcharts
1.4.2 Another Flowchart With Partial Solutions
1.4.3 More Promising Way
1.5 Isomer Numbers
1.5.1 Combinatorial Enumeration as 2D Structures
1.5.2 Importance of the Proligand-Promolecule Model
1.5.3 Combinatorial Enumeration as 3D Structures
1.6 Stereoisograms
1.6.1 Stereoisograms as Diagrammatic Expressions of RS-Stereoisomeric Groups
1.6.2 Theoretical Foundations and Group Hierarchy
1.6.3 Avoidance of Misleading Standpoints of R/S-Stereodescriptors
1.6.4 Avoidance of Misleading Standpoints of pro-R/pro-S-Descriptors
1.6.5 Global Symmetries and Local Symmetries
1.6.6 Enumeration under RS-Stereoisomeric Groups
1.7 Aims of Mathematical Stereochemistry
References
2. Classification of Isomers
2.1 Equivalence Relationships of Various Levels of Isomerism
2.1.1 Equivalence Relationships and Equivalence Classes
2.1.2 Enantiomers, Stereoisomers, and Isomers
2.1.3 Inequivalence Relationships
2.1.4 Isoskeletomers as a Missing Link for Consistent Terminology.
2.1.5 Constitutionally-Anisomeric Relationships vs. Constitutionally-Isomeric Relationships
2.2 Revised Flowchart for Categorizing Isomers
2.2.1 Design of a Revised Flowchart for Categorizing Isomers
2.2.2 Illustrative Examples
2.2.3 Restriction of the Domain of Isomerism
2.2.4 Harmonization of 3D-Based Concepts with 2D-Based Concepts
References
3. Point-Group Symmetry
3.1 Stereoskeletons and the Proligand-Promolecule Model
3.1.1 Configuration and Conformation
3.1.2 The Proligand-Promolecule Model
3.2 Point Groups
3.2.1 Symmetry Axes and Symmetry Operations
3.2.2 Construction of Point Groups
3.2.3 Subgroups of a Point Group
3.2.4 Maximum Chiral Subgroup of a Point Group
3.2.5 Global and Local Point-Group Symmetries
3.3 Point-Group Symmetries of Stereoskeletons
3.3.1 Stereoskeletons of Ligancy 4
3.3.2 Stereoskeletons of Ligancy 6
3.3.3 Stereoskeletons of Ligancy 8
3.3.4 Stereoskeletons Having Two or More Orbits
3.4 Point-Group Symmetries of (Pro)molecules
3.4.1 Derivation of Molecules from a Stereoskeleton via Promolecules
3.4.2 Orbits in Molecules and Promolecules Derived from Stereoskeletons
3.4.3 The SCR Notation
3.4.4 Site Symmetries vs. Coset Representations for Symmetry Notations
References
4. Sphericities of Orbits and Prochirality
4.1 Sphericities of Orbits
4.1.1 Orbits of Equivalent Proligands
4.1.2 Three Kinds of Sphericities
4.1.3 Chirality Fittingness for Three Modes of Accommodation
4.2 Prochirality
4.2.1 Confusion on the Term 'Prochirality'
4.2.2 Prochirality as a Geometric Concept
4.2.3 Enantiospheric Orbits vs. Enantiotopic Relationships
4.2.4 Chirogenic Sites in an Enantiospheric Orbit
4.2.5 Prochirality Concerning Chiral Proligands in Isolation.
4.2.6 Global Prochirality and Local Prochirality
References
5. Foundations of Enumeration Under Point Groups
5.1 Orbits Governed by Coset Representations
5.1.1 Coset Representations
5.1.2 Mark Tables
5.1.3 Multiplicities of Orbits
5.2 Subduction of Coset Representations
5.2.1 Subduced Representations
5.2.2 Unit Subduced Cylce Indices (USCIs)
References
6. Symmetry-Itemized Enumeration Under Point Groups
6.1 Fujita's USCI Approach
6.1.1 Historical Comments
6.1.2 USCI-CFs for Itemized Enumeration
6.1.3 Subduced Cycle Indices for Itemized Enumeration
6.2 The FPM Method of Fujita's USCI Approach
6.2.1 Fixed-Point Vectors (FPVs) and Multiplicity Vectors (MVs)
6.2.2 Fixed-Point Matrices (FPMs) and Isomer-Counting Matrices (ICMs)
6.2.3 Practices of the FPM Method
6.3 The PCI Method of Fujita's USCI Approach
6.3.1 Partial Cycle Indices With Chirality Fittingness (PCI-CFs)
6.3.2 Partial Cycle Indices Without Chirality Fittingness (PCIs)
6.3.3 Practices of the PCI Method
6.4 Other Methods of Fujita's USCI Approach
6.4.1 The Elementary-Superposition Method
6.4.2 The Partial-Superposition Method
6.5 Applications of Fujita's USCI Approach
6.5.1 Enumeration of Flexible Molecules
6.5.2 Enumeration of Molecules Interesting Stereochemically
6.5.3 Enumeration of Inorganic Complexes
6.5.4 Enumeration of Organic Reactions
References
7. Gross Enumeration Under Point Groups
7.1 Counting Orbits
7.2 Pólya's Theorem of Counting
7.3 Fujita's Proligand Method of Counting
7.3.1 Historical Comments
7.3.2 Sphericities of Cycles
7.3.3 Products of Sphericity Indices
7.3.4 Practices of Fujita's Proligand Method
7.3.5 Enumeration of Achiral and Chiral Promolecules
References.
8. Enumeration of Alkanes as 3D Structures
8.1 Surveys With Historical Comments
8.2 Enumeration of Alkyl Ligands as 3D Planted Trees
8.2.1 Enumeration of Methyl Proligands as Planted Promolecules
8.2.2 Recursive Enumeration of Alkyl ligands as Planted Promolecules
8.2.3 Functional Equations for Recursive Enumeration of Alkyl ligands
8.2.4 Achiral Alkyl Ligands and Pairs of Enantiomeric Alkyl Ligands
8.3 Enumeration of Alkyl Ligands as Planted Trees
8.3.1 Alkyl Ligands or Monosubstituted Alkanes as Graphs
8.3.2 3D Structures vs. Graphs for Characterizing Alkyl Ligands or Monosubstituted Alkanes
8.4 Enumeration of Alkanes (3D-Trees) as 3D-Structural Isomers
8.4.1 Alkanes as Centroidal and Bicentroidal 3D-Trees
8.4.2 Enumeration of Centroidal Alkanes (3D-Trees) as 3D-Structural Isomers
8.4.3 Enumeration of Bicentroidal Alkanes (3D-Trees) as 3D-Structural Isomers
8.4.4 Total Enumeration of Alkanes as 3D-Trees
8.5 Enumeration of Alkanes (3D-Trees) as Steric Isomers
8.5.1 Centroidal Alkanes (3D-Trees) as Steric Isomers
8.5.2 Bicentroidal Alkanes (3D-Trees) as Steric Isomers
8.5.3 Total Enumeration of Alkanes (3D-Trees) as Steric Isomers
8.6 Enumeration of Alkanes (Trees) as Graphs or Constitutional Isomers
8.6.1 Alkanes as Centroidal and Bicentroidal Trees
8.6.2 Enumeration of Centroidal Alkanes (Trees) as Constitutional Isomers
8.6.3 Enumeration of Bicentroidal Alkanes (Trees) as Constitutional Isomers
8.6.4 Total Enumeration of Alkanes (Trees) as Graphs or Constitutional Isomers
References
9. Permutation-Group Symmetry
9.1 Historical Comments
9.2 Permutation Groups
9.2.1 Permutation Groups as Subgroups of Symmetric Groups
9.2.2 Permutations vs. Reflections
9.3 RS-Permutation Groups.
9.3.1 RS-Permutations and RS-Diastereomeric Relationships
9.3.2 RS-Permutation Groups vs. Point Groups
9.3.3 Formulation of RS-Permutation Groups
9.3.4 Action of RS-Permutation Groups
9.3.5 Misleading Features of the Conventional Terminology
9.4 RS-Permutation Groups for Skeletons of Ligancy 4
9.4.1 RS-Permutation Group for a Tetrahedral Skeleton
9.4.2 RS-Permutation Group for an Allene Skeleton
9.4.3 RS-Permutation Group for an Ethylene Skeleton
References
10. Stereoisograms and RS-Stereoisomers
10.1 Stereoisograms as Integrated Diagrammatic Expressions
10.1.1 Elementary Stereoisograms of Skeletons with Position Numbering
10.1.2 Stereoisograms Based on Elementary Stereoisograms
10.2 Enumeration Under RS-Stereoisomeric Groups
10.2.1 Subgroups of the RS-Stereoisomeric Group C3v sI
10.2.2 Coset Representations
10.2.3 Mark Table and its Inverse
10.2.4 Subduction for RS-Stereoisomeric Groups
10.2.5 USCI-CFs for RS-Stereoisomeric Groups
10.2.6 SCI-CFs for RS-Stereoisomeric Groups
10.2.7 The PCI Method for RS-Stereoisomeric Groups
10.2.8 Type-Itemized Enumeration by the PCI Method
10.2.9 Gross Enumeration Under RS-Stereoisomeric Groups
10.3 Comparison with Enumeration Under Subgroups
10.3.1 Comparison with Enumeration Under Point Groups
10.3.2 Comparison with Enumeration Under RS-Permutation Groups
10.3.3 Comparison with Enumeration Under Maximum-Chiral Point Subgroups
10.4 RS-Stereoisomers as Intermediate Concepts
References
11. Stereoisograms for Tetrahedral Derivatives
11.1 RS-Stereoisomeric Group Td sI and Elementary Stereoisogram
11.2 Stereoisograms of Five Types for Tetrahedral Derivatives
11.2.1 Type-I Stereoisograms of Tetrahedral Derivatives.

Mathematical stereochemistry /

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