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Mathematical stereochemistry / Shinsaku Fujita.

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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Bibliographic Details
Online Access: Full Text (via Knovel)
Main Author: Fujita, Shinsaku, 1944-
Format: eBook
Language:English
Published: Berlin ; Boston : De Gruyter, [2015]
Subjects:
Stereochemistry.
Chemistry > Mathematics.
Table of Contents:
  • 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.

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