Mathematical concepts in organic chemistry:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin u.a.
Springer
1986
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | X, 212 S. Ill. |
| ISBN: | 3540162356 0387162356 |
Staff View
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| 245 | 1 | 0 | |a Mathematical concepts in organic chemistry |c Ivan Gutman ; Oskar E. Polansky |
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Record in the Search Index
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|---|---|
| adam_text | Contents
Introduction 1
Part A Chemistry and Topology 3
Chapter 1 Topological Aspects in Chemistry 5
1.1 Topology in Chemistry 5
1.2 Abstraction in Science and How Far One Can Go 8
Chapter 2 Molecular Topology 12
2.1 What is Molecular Topology? 12
2.2 Geometry, Symmetry, Topology 14
2.3 Definition of Molecular Topology 14
Part B Chemistry and Graph Theory 17
Chapter 3 Chemical Graphs 19
Chapter 4 Fundamentals of Graph Theory 23
4.1 The Definition of a Graph 23
4.1.1 Relations 23
4.1.2 The First Definition of a Graph 24
4.1.3 The Second Definition of a Graph 25
4.1.4 Vertices and Edges 26
4.1.5 Isomorphic Graphs and Graph Automorphisms 27
4.1.6 Special Graphs 28
4.2 Subgraphs 29
4.2.1 Sachs Graphs 30
4.2.2 Matchings 32
4.3 Graph Spectral Theory 33
4.3.1 The Adjacency Matrix 33
4.3.2 The Spectrum of a Graph 34
4.3.3 The Sachs Theorem 35
4.3.4 The/i Polynomial 38
4.4 Graph Operations 39
VIII Contents
Chapter 5 Graph Theory and Molecular Orbitals 42
Chapter 6 Special Molecular Graphs 46
6.1 Acyclic Molecules 46
6.1.1 Trees 46
6.1.2 The Path and the Star 47
6.1.3 The Characteristic Polynomial of Trees 48
6.1.4 Trees with Greatest Number of Matchings 51
6.1.5 The Spectrum of the Path 53
6.2 The Cycle 54
6.3 Alternant Molecules 55
6.3.1 Bipartite Graphs 56
6.3.2 The Pairing Theorem 57
6.3.3 Some Consequences of the Pairing Theorem 58
6.4 Benzenoid Molecules 59
6.4.1 Benzenoid Graphs 59
6.4.2 The Characteristic Polynomial of Benzenoid Graphs 61
6.5 Hydrocarbons and Molecules with Heteroatoms 62
6.5.1 On the Question of the Molecular Graph 62
6.5.2 The Characteristic Polynomial of Weighted Graphs 64
6.5.3 Some Regularities in the Electronic Structure of Heteroconjugated
Molecules 65
Part C Chemistry and Group Theory 67
Chapter 7 Fundamentals of Group Theory 69
7.1 The Symmetry Group of an Equilateral Triangle 70
7.2 Order, Classes and Representations of a Group 71
7.3 Reducible and Irreducible Representations 73
7.4 Characters and Reduction of a Reducible Representation 75
7.5 Subgroups and Sidegroups — Products of Groups 80
7.6 Abelian Groups 82
7.7 Abstract Groups and Group Isomorphism 84
Chapter 8 Symmetry Groups 85
8.1 Notation of Symmetry Elements and Representations 85
8.2 Some Symmetry Groups 86
8.2.1 Rotation Groups 87
8.2.2 Groups with More than One n Fold Axis, n 2 88
8.2.3 Groups of Collinear Molecules 89
8.3 Transformation Properties and Direct Products of Irreducible Representa¬
tions 90
8.3.1 Transformation Properties 90
8.3.2 Rules Concerning the Direct Product of Irreducible Representations 94
8.4 Some Applications of Symmetry Groups 95
8.4.1 Electric Dipole Moment 96
Contents IX
8.4.2 Polarizability 96
8.4.3 Motions of Atomic Nuclei: Translations, Rotations and Vibrations 97
8.4.4 Transition Probabilities for the Absorption of Light 99
8.4.5 Transition Probabilities in Raman Spectra 101
8.4.6 Group Theory and Quantum Chemistry 103
8.4.7 Orbital and State Correlations 104
Chapter 9 Automorphism Groups 108
9.1 Automorphism of a Graph 108
9.2 The Automorphism Group A(G,) 109
9.3 Cycle Structure of Permutations 111
9.4 Isomorphism of Graphs and of Automorphism Groups 112.
9.5 Notation of some Permutation Groups 113
9.6 Direct Product and Wreath Product 114
9.7 The Representation of Automorphism Groups as Group Products .... 115
Chapter 10 Some Interrelations between Symmetry and Automorphism Groups 117
10.1 The Idea of Rigid Molecules 117
10.2 Local Symmetries 117
10.3 Non Rigid Molecules 118
10.4 What Determines the Respective Orders of the Symmetry and the Auto¬
morphism Group of a Given Molecule? 120
Part D Special Topics 121
Chapter 11 Topological Indices 123
11.1 Indices Based on the Distance Matrix 124
11.1.1 The Wiener Number and Related Quantities 124
11.1.2 Applications of the Wiener Number 127
11.2 Hosoya s Topological Index 127
11.2.1 Definition and Chemical Applications of Hosoya s Index. ... 128
11.2.2 Mathematical Properties of Hosoya s Index 129
11.2.3 Example: Hosoya s Index of the Path and the Cycle 131
11.2.4 Some Inequalities for Hosoya s Index 132
Chapter 12 Thermodynamic Stability of Conjugated Molecules 135
12.1 Total 7r Electron Energy and Thermodynamic Stability of Conjugated
Molecules 135
12.2 Total ^ Electron Energy and Molecular Topology 136
12.3 The Energy of a Graph 137
12.4 The Coulson Integral Formula 139
12.5 Some Further Applications of the Coulson Integral Formula 143
12.6 Bounds for Total rc Electron Energy 147
12.7 More on the McClelland Formula 149
12.8 Conclusion: Factors Determining the Total re Electron Energy 151
12.9 Use of Total 7r Electron Energy in Chemistry 151
X Contents
Chapter 13 Topological Effect on Molecular Orbitals 155
13.1 Topologically Related Isomers 155
13.2 Interlacing Rule 157
13.3 PE Spectra of Topomers 162
13.4 TEMO and (r Electron Systems 164
13.5 TEMO and Symmetry 166
Appendices 169
Appendix 1 Matrices 171
Appendix 2 Determinants 176
Appendix 3 Eigenvalues and Eigenvectors . . 179
Appendix 4 Polynomials 182
Appendix 5 Characters of Irreducible Representations of Symmetry Groups 184
Appendix 6 The Symbols Used 200
Literature 203
Bibliography 203
References 205
Subject Index 209
|
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| discipline | Chemie / Pharmazie Mathematik |
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| indexdate | 2024-07-09T15:17:17Z |
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| isbn | 3540162356 0387162356 |
| language | English |
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| physical | X, 212 S. Ill. |
| publishDate | 1986 |
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| publisher | Springer |
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| spelling | Gutman, Ivan Verfasser aut Mathematical concepts in organic chemistry Ivan Gutman ; Oskar E. Polansky Berlin u.a. Springer 1986 X, 212 S. Ill. txt rdacontent n rdamedia nc rdacarrier Topologie (DE-588)4060425-1 gnd rswk-swf Theoretische organische Chemie (DE-588)4185101-8 gnd rswk-swf Mathematik (DE-588)4037944-9 gnd rswk-swf Organische Chemie (DE-588)4043793-0 gnd rswk-swf Gruppentheorie (DE-588)4072157-7 gnd rswk-swf Organische Chemie (DE-588)4043793-0 s Mathematik (DE-588)4037944-9 s DE-604 Theoretische organische Chemie (DE-588)4185101-8 s 1\p DE-604 Topologie (DE-588)4060425-1 s 2\p DE-604 Gruppentheorie (DE-588)4072157-7 s 3\p DE-604 Polansky, Oskar E. 1919-1989 Verfasser (DE-588)1162846356 aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000408462&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Gutman, Ivan Polansky, Oskar E. 1919-1989 Mathematical concepts in organic chemistry Topologie (DE-588)4060425-1 gnd Theoretische organische Chemie (DE-588)4185101-8 gnd Mathematik (DE-588)4037944-9 gnd Organische Chemie (DE-588)4043793-0 gnd Gruppentheorie (DE-588)4072157-7 gnd |
| subject_GND | (DE-588)4060425-1 (DE-588)4185101-8 (DE-588)4037944-9 (DE-588)4043793-0 (DE-588)4072157-7 |
| title | Mathematical concepts in organic chemistry |
| title_auth | Mathematical concepts in organic chemistry |
| title_exact_search | Mathematical concepts in organic chemistry |
| title_full | Mathematical concepts in organic chemistry Ivan Gutman ; Oskar E. Polansky |
| title_fullStr | Mathematical concepts in organic chemistry Ivan Gutman ; Oskar E. Polansky |
| title_full_unstemmed | Mathematical concepts in organic chemistry Ivan Gutman ; Oskar E. Polansky |
| title_short | Mathematical concepts in organic chemistry |
| title_sort | mathematical concepts in organic chemistry |
| topic | Topologie (DE-588)4060425-1 gnd Theoretische organische Chemie (DE-588)4185101-8 gnd Mathematik (DE-588)4037944-9 gnd Organische Chemie (DE-588)4043793-0 gnd Gruppentheorie (DE-588)4072157-7 gnd |
| topic_facet | Topologie Theoretische organische Chemie Mathematik Organische Chemie Gruppentheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000408462&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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