Shinsaku Fujita
Symmetry and Combinatorial Enumeration in Chemistry
Shinsaku Fujita
Symmetry and Combinatorial Enumeration in Chemistry
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Mit der Gruppentheorie führt der Autor Chemiestudenten in die Stereochemie ein. Er erklärt einheitlich und sehr verständlich stereochemische Probleme und die Methode der Abzählung chemischer Isomere.
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Mit der Gruppentheorie führt der Autor Chemiestudenten in die Stereochemie ein. Er erklärt einheitlich und sehr verständlich stereochemische Probleme und die Methode der Abzählung chemischer Isomere.
Produktdetails
- Produktdetails
- Verlag: Springer / Springer Berlin Heidelberg / Springer, Berlin
- Artikelnr. des Verlages: 978-3-540-54126-4
- 1991.
- Seitenzahl: 384
- Erscheinungstermin: 5. September 1991
- Englisch
- Abmessung: 235mm x 155mm x 21mm
- Gewicht: 560g
- ISBN-13: 9783540541264
- ISBN-10: 3540541268
- Artikelnr.: 26384216
- Verlag: Springer / Springer Berlin Heidelberg / Springer, Berlin
- Artikelnr. des Verlages: 978-3-540-54126-4
- 1991.
- Seitenzahl: 384
- Erscheinungstermin: 5. September 1991
- Englisch
- Abmessung: 235mm x 155mm x 21mm
- Gewicht: 560g
- ISBN-13: 9783540541264
- ISBN-10: 3540541268
- Artikelnr.: 26384216
1 Introduction.- 2 Symmetry and Point Groups.- 2.1 Symmetry Operations and Elements.- 2.2 Conjugacy Glasses in Point Groups.- 2.3 Subgroups of Point Groups.- 2.4 Conjugate and Normal Subgroups of Point Groups.- 2.5 Non-Redundant Set of Subgroups for a Point Group.- 3 Permutation Groups.- 3.1 Permutations and Cycles.- 3.2 Permutation Groups.- 3.3 Transitivity and Orbits..- 3.4 Symmetric Groups.- 3.5 Parity.- 3.6 Alternating Groups.- 4 Axioms and Theorems of Group Theory.- 4.1 Axioms and Multiplication Tables.- 4.2 Subgroups.- 4.3 Cosets.- 4.4 Equivalence Relations.- 4.5 Conjugacy Classes.- 4.6 Conjugate and Normal Subgroups.- 4.7 Subgroup Lattices.- 4.8 Cyclic Groups.- 5 Coset Representations and Orbits.- 5.1 Coset Representations.- 5.2 Transitive Permutation Representations.- 5.3 Mark Tables.- 5.4 Permutation Representations and Orbits.- 6 Systematic Classification of Molecular Symmetries.- 6.1 Assignment of Coset Representations to Orbits.- 6.2 SCR Notation.- 7 Local Symmetries and Forbidden Coset Representations.- 7.1 Blocks and Local Symmetries.- 7.2 Forbidden Coset Representations.- 8 Chirality Fittingness of an Orbit.- 8.1 Ligands.- 8.2 Behavior of Cosets on the Action of a CR.- 8.3 Chirality Fittingness of an Orbit.- 9 Subduction of Coset Representations.- 9.1 Subduction of Coset Representations.- 9.2 Subduced Mark Table.- 9.3 Chemical Meaning of Subduction.- 9.4 Unit Subduced Cycle Indices.- 9.5 Unit Subduced Cycle Indices with Chirality Fittingness.- 9.6 Desymmetrization Lattice.- 10 Prochirality.- 10.1 Desymmetrization of Enantiospheric Orbits.- 10.2 Prochirality.- 10.3 Further Desymmetrization of Enantiospheric Orbits.- 10.4 Chiral syntheses.- 11 Desymmetrization of Para-Achiral Compounds.- 11.1 Chiral Subduction of Homospheric Orbits.- 11.2 Desymmetrization of Homospheric Orbits.- 11.3 Chemoselective and Stereoselective Processes.- 12 Topicity and Stereogenicity.- 12.1 Topicity Based On Chirality Fittingness of an Orbit.- 12.2 Stereogenicity.- 13 Counting Orbits.- 13.1 The Cauchy-Frobenius Lemma.- 13.2 Configurations.- 13.3 The Pólya-Redfield Theorem.- 14 Obligatory Minimum Valencies.- 14.1 Isomer Enumeration under the OMV Restriction.- 14.2 Unit Cycle Indices.- 15 Compounds with Achiral Ligands Only.- 15.1 Compounds with Given Symmetries.- 15.2 Compounds with Given Symmetries and Weight.- 16 New Cycle Index.- 16.1 New Cycle Indices Based On USCIs.- 16.2 Correlation of New Cycle Indices to Pólya's Theorem.- 16.3 Partial Cycle Indices.- 17 Cage-Shaped Molecules with High Symmetries.- 17.1 Edge Strategy.- 17.2 Tricyclodecanes with Td and Its Subsymmetries.- 17.3 Use of Another Ligand-Inventory.- 17.4 New Type of Cycle Index.- 18 Elementary Superposition.- 18.1 The USCI Approach.- 18.2 Elementary Superposition.- 18.3 Superposition for Other Indices.- 19 Compounds with Achiral and Chiral Ligands.- 19.1 Compounds with Given Symmetries.- 19.2 Compounds with Given Symmetries and Weights.- 19.3 Compounds with Given Weights.- 19.4 Special Cases.- 19.5 Other Indices.- 20 Compounds with Rotatable Ligands.- 20.1 Rigid Skeleton and Rotatable Ligands.- 20.2 Enumeration of Rotatable Ligands.- 20.3 Enumeration of Non-Rigid Isomers.- 20.4 Total Numbers.- 20.5 Typical Procedure for Enumeration.- 21 Promolecules.- 21.1 Molecular Models.- 21.2 Proligands and Promolecules.- 21.3 Enumeration of Promolecules.- 21.4 Molecules Based on Promolecules.- 21.5 Prochiralities of Promolecules and Molecules.- 21.6 Concluding Remarks.- 22 Appendix A. Mark Tables.- A.1 Td Point Group and Its Subgroups.- A. 2 D3h Point Group and Its Subgroups.- 23Appendix B. Inverses of Mark Tables.- B. 1 Td Point Group and Its Subgroups.- B. 2 D3h Point Group and Its Subgroups.- 24 Appendix C. Subduction Tables.- C. 1 Td Point Group and Its Subgroups.- C. 2 D3h Point Group and Its Subgroups.- 25 Appendix D. Tables of USCIs.- D. 1 Td Point Group and Its Subgroups.- D. 2 D3h Point Group and Its Subgroups.- 26 Appendix E. Tables of USCI-CFs.- E. 1 Td Point Group and Its Subgroups.- E.2 D3h Point Group and Its Subgroups.- 27 Index.
1 Introduction.- 2 Symmetry and Point Groups.- 2.1 Symmetry Operations and Elements.- 2.2 Conjugacy Glasses in Point Groups.- 2.3 Subgroups of Point Groups.- 2.4 Conjugate and Normal Subgroups of Point Groups.- 2.5 Non-Redundant Set of Subgroups for a Point Group.- 3 Permutation Groups.- 3.1 Permutations and Cycles.- 3.2 Permutation Groups.- 3.3 Transitivity and Orbits..- 3.4 Symmetric Groups.- 3.5 Parity.- 3.6 Alternating Groups.- 4 Axioms and Theorems of Group Theory.- 4.1 Axioms and Multiplication Tables.- 4.2 Subgroups.- 4.3 Cosets.- 4.4 Equivalence Relations.- 4.5 Conjugacy Classes.- 4.6 Conjugate and Normal Subgroups.- 4.7 Subgroup Lattices.- 4.8 Cyclic Groups.- 5 Coset Representations and Orbits.- 5.1 Coset Representations.- 5.2 Transitive Permutation Representations.- 5.3 Mark Tables.- 5.4 Permutation Representations and Orbits.- 6 Systematic Classification of Molecular Symmetries.- 6.1 Assignment of Coset Representations to Orbits.- 6.2 SCR Notation.- 7 Local Symmetries and Forbidden Coset Representations.- 7.1 Blocks and Local Symmetries.- 7.2 Forbidden Coset Representations.- 8 Chirality Fittingness of an Orbit.- 8.1 Ligands.- 8.2 Behavior of Cosets on the Action of a CR.- 8.3 Chirality Fittingness of an Orbit.- 9 Subduction of Coset Representations.- 9.1 Subduction of Coset Representations.- 9.2 Subduced Mark Table.- 9.3 Chemical Meaning of Subduction.- 9.4 Unit Subduced Cycle Indices.- 9.5 Unit Subduced Cycle Indices with Chirality Fittingness.- 9.6 Desymmetrization Lattice.- 10 Prochirality.- 10.1 Desymmetrization of Enantiospheric Orbits.- 10.2 Prochirality.- 10.3 Further Desymmetrization of Enantiospheric Orbits.- 10.4 Chiral syntheses.- 11 Desymmetrization of Para-Achiral Compounds.- 11.1 Chiral Subduction of Homospheric Orbits.- 11.2 Desymmetrization of Homospheric Orbits.- 11.3 Chemoselective and Stereoselective Processes.- 12 Topicity and Stereogenicity.- 12.1 Topicity Based On Chirality Fittingness of an Orbit.- 12.2 Stereogenicity.- 13 Counting Orbits.- 13.1 The Cauchy-Frobenius Lemma.- 13.2 Configurations.- 13.3 The Pólya-Redfield Theorem.- 14 Obligatory Minimum Valencies.- 14.1 Isomer Enumeration under the OMV Restriction.- 14.2 Unit Cycle Indices.- 15 Compounds with Achiral Ligands Only.- 15.1 Compounds with Given Symmetries.- 15.2 Compounds with Given Symmetries and Weight.- 16 New Cycle Index.- 16.1 New Cycle Indices Based On USCIs.- 16.2 Correlation of New Cycle Indices to Pólya's Theorem.- 16.3 Partial Cycle Indices.- 17 Cage-Shaped Molecules with High Symmetries.- 17.1 Edge Strategy.- 17.2 Tricyclodecanes with Td and Its Subsymmetries.- 17.3 Use of Another Ligand-Inventory.- 17.4 New Type of Cycle Index.- 18 Elementary Superposition.- 18.1 The USCI Approach.- 18.2 Elementary Superposition.- 18.3 Superposition for Other Indices.- 19 Compounds with Achiral and Chiral Ligands.- 19.1 Compounds with Given Symmetries.- 19.2 Compounds with Given Symmetries and Weights.- 19.3 Compounds with Given Weights.- 19.4 Special Cases.- 19.5 Other Indices.- 20 Compounds with Rotatable Ligands.- 20.1 Rigid Skeleton and Rotatable Ligands.- 20.2 Enumeration of Rotatable Ligands.- 20.3 Enumeration of Non-Rigid Isomers.- 20.4 Total Numbers.- 20.5 Typical Procedure for Enumeration.- 21 Promolecules.- 21.1 Molecular Models.- 21.2 Proligands and Promolecules.- 21.3 Enumeration of Promolecules.- 21.4 Molecules Based on Promolecules.- 21.5 Prochiralities of Promolecules and Molecules.- 21.6 Concluding Remarks.- 22 Appendix A. Mark Tables.- A.1 Td Point Group and Its Subgroups.- A. 2 D3h Point Group and Its Subgroups.- 23Appendix B. Inverses of Mark Tables.- B. 1 Td Point Group and Its Subgroups.- B. 2 D3h Point Group and Its Subgroups.- 24 Appendix C. Subduction Tables.- C. 1 Td Point Group and Its Subgroups.- C. 2 D3h Point Group and Its Subgroups.- 25 Appendix D. Tables of USCIs.- D. 1 Td Point Group and Its Subgroups.- D. 2 D3h Point Group and Its Subgroups.- 26 Appendix E. Tables of USCI-CFs.- E. 1 Td Point Group and Its Subgroups.- E.2 D3h Point Group and Its Subgroups.- 27 Index.