Molecular aspects of symmetry:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York
Benjamin
1966
|
| Series: | The chemistry series.
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIII, 355 S. graph. Darst. |
Staff View
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Record in the Search Index
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| adam_text | Molecular Aspects
of Symmetry
Robin M Hochstrasser
University of Pennsylvania
WABKNJAMIN,INC
New York /I msterdam
Contents
Preface vii
1 The Utility of Symmetry in Chemistry 1
1 1 Transformation of Coordinates and Functions 4
1 2 Transformation of the Coulomb Potential 6
1 3 Transformation Properties of the Laplacian 9
1 4- The One-Dimensional Wave Ei/uation 13
1 5 Classification of Eigenfunctions 14
1 6 Definition of Symmetry Operations 15
1 7 Point Symmetry Operations 15
1 8 Frame of Reference for Rotations 15
1 9 Rotations About an Axis 17
1 10 Reflection Planes of Symmetry 19
1 11 Combinations of Rotations and Reflections 21
1 12 Center of Symmetry 22
1 13 Classes of Symmetry Operations 22
2 Some Mathematical Apparatus 27
2 1 Linear Transformations 27
2 2 The Reciprocal of a Matrix 30
ix
Contents
2 3 Further Properties of Matrires 37
2 4- Some Special Matrices 39
2 5 Vectors and Vector Spaces 41
2 6 The Hermitian Scalar Product 43
2 7 The Characteristic Equation of a Matrix 4-4
References 50
3 Point Symmetry Groups 51
3 1 The Cn Groups 62
3 2 The C„v Groups 52
3 3 The Groups Cnh 56
3 4 The Groups S„ 58
3 5 The Groups D„ 60
3 6 The Groups l)„d 62
3 7 The Groups Dnk 63
3 8 The Cubic Point Groups 66
3 9 Continuous Point Groups 70
3 10 Lie Groups 72
3 11 The ^Matrices for Infinite-fold Rotations 72
3 12 Ilomomorphism 74
3 13 Isomorphism 76
3 14- Subgroups 76
3 15 Invariant Subgroups 76
3 16 Left and Right Cosets 76
3 17 Factor Groups 77
References 83
4 Representations of Finite Groups 84
4-1 Unitary Representations 87
4-2 Schur s Lemma 87
4-3 Nonequivalence of Irreducible Representations 90
4-4• The Orthogonality Relations 91
4-5 The Characters of Representations 96
4-6 Characters and Classes 97
4-7 Reducible Representations of Groups 98
4-8 Reduction of Representations 101
References 103
5 Function Vectors, Linear Operators, Representations 104
5 1 Complete Sets of Functions 107
5 2 Linear Operators 107
x
Contents
5 3 Eigenfunctions as a Basis for Representations of Point Groups 112
54- General Case of n-fold Degenerate Solutions of the Schrddinger Equation 113
5 5 Some Important Concluding Remarks on Fxmctions, Conventions, and
Uniqueness of Representations 118
5 6 Direct Product Representations 122
References 124
6 Characters of the Irreducible Representations
of Finite Groups 125
6 1 The Groups Cn 1®6
6 2 The Groups C„„ 128
6 3 Direct Product Groups 131
6-4- The Groups S„ 131
6 5 The Groups Cn 132
6 6 The Groups Dn 132
6 7 The Groups Dnd 133
6 8 The Groups D„h 133
6 9 The Cubic Groups 133
6 10 The Group Td 136
6 11 The Group O 136
6 12 The Group Oh 136
6 13 Characters of Continuous Group*: The Two-DimensionalRotationGroup 136
6 14- The Group 137
6 15 The Group D amp;h 138
6 16 The Direct Products of Representations 138
6 17 The Correlation of Groups 141
6 18 Representations of Continuous Groups 143
6 19 Use of Infinitesimal Operators to Generate Reps of C(3) 148
References 152
7 Symmetry and Molecular Theory 153
7 1 Atomic Orbitals 154
7 2 Integrals Over Atomic Orbitals 161
7 3 The Symmetry of Operators in Quantum Mechanics 163
7 4- Angular Momentum 163
7 5 Linear Momentum 167
7 6 Angular Momentum in Molecules 167
7 7 Symmetric and Antisymmetric Direct Products 169
7 8 The Use of Symmetry in Molecular Orbital Theory 174
7 9 Configurations and States of M ulecules 186
7 10 Perturbation Theory ^ 196
xi
Contents
7 11 Simplification of Matrix Elements Using Symmetry 198
7 12 Some Further Aspects of Atomic Theory 205
7 13 Electron Spin 207
7 14- Energy Levels of Atoms 209
References 213
8 Selection Rules and Molecular Structure 215
8 1 Selection Rides for Magnetic Dipole Transitions 219
8 2 Electric Quadrupole Transition Moments 220
S S Electronic Transitions in Atoms 220
8-4- The Vibrational States of hfolecules 224
8 5 Selection Rules for Vibrational Spectra 229
8 6 Vibrational Electronic Coupling 229
8 7 The Equilibrium Nuclear Configurations of Molecules 236
S S The Noncrossing Rule and the Correlative Properties of Small Molecules 241
8 9 Hybrid Bond Orbitals 247
8 10 Hybridization in Intermediate Situations 250
References 253
9 Symmetry and Spin in Molecules 255
9 1 Permutation Groups 255
9 2 Permutation Symmetry of the Hamiltonian 256
9 3 The Symmetrization and Antisymmetrization of Many-Particle
Functions _ 257
9 4- The Two-Electron Problem 259
9 5 Probabilities of Singlet-Triplet Transitions 263
96A Perturbation Theory of Spin-Orbit Coupling in Molecides 265
9 7 First-Order Spin-Orbit Coupling 266
9 8 The Symmetry of the Vector (grad VXp) 267
9 9 First-Order Spin-Orbit Coupling Selection Rules 270
9 10 First-Order Spin-Vibronic Interaction 272
9 11 An Alternative Approach to Spin-Orbit Coupling Selection Rules 274
9 12 Second-Order Contributions to the Spin-Orbit Coupling 277
9 13 The Possible Appearance of u Vibrations in a Spatially Allowed
Singlet (g) — Triplet (u) Transition 278
References 284
10 Applications of Symmetry to Organic
Molecular Crystals and Aggregates 285
10 1 Introduction to Space Groups 285
10 2 Representations of Space Groups 288
xii
Contents
10 3 Organic Crystals 296
104 Screw Axes and Glide Planes 299
10 5 Factor Group Character Tables 306
10 6 The Energies of Crystal States 307
10 7 The Intensities of k=0 Factor Group States in Molecular Crystals SI 2
10 8 Vibrational Electronic Coupling in Molecular Crystals 314
10 9 Strong Coupling 314
10 10 Weak Coupling 316
b 10 11
X 10 12
Second-Order Effects in Exciton Spectra 319 b 10 11
X 10 12 The Electronic Spectra of Organic Dimers 321
10 13 Other Comtnon Organic Space Groups 325
10 14 Triplet States in Molecular Crystals 327
References 330
Appendix Group Character Tables 333
Index 349
xiii
|
| any_adam_object | 1 |
| author | Hochstrasser, Robin M. |
| author_facet | Hochstrasser, Robin M. |
| author_role | aut |
| author_sort | Hochstrasser, Robin M. |
| author_variant | r m h rm rmh |
| building | Verbundindex |
| bvnumber | BV002284716 |
| callnumber-first | Q - Science |
| callnumber-label | QD461H62M 1966 |
| callnumber-raw | QD461H62M 1966 |
| callnumber-search | QD461H62M 1966 |
| callnumber-sort | QD 3461 H62 M 41966 |
| callnumber-subject | QD - Chemistry |
| classification_rvk | UQ 1300 VE 5700 |
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| ctrlnum | (OCoLC)421442534 (DE-599)BVBBV002284716 |
| dewey-full | 541.22 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 541 - Physical chemistry |
| dewey-raw | 541.22 |
| dewey-search | 541.22 |
| dewey-sort | 3541.22 |
| dewey-tens | 540 - Chemistry and allied sciences |
| discipline | Chemie / Pharmazie Physik Chemie |
| format | Book |
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| institution | BVB |
| language | English |
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| series2 | The chemistry series. |
| spelling | Hochstrasser, Robin M. Verfasser aut Molecular aspects of symmetry New York Benjamin 1966 XIII, 355 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier The chemistry series. Groupes, Théorie des - Symétriques ram Structure moléculaire ram Symétrie (Physique) Symétrie (physique) ram Symétrie moléculaire ram Théorie des groupes Théorie moléculaire Molekülsymmetrie (DE-588)4170385-6 gnd rswk-swf Quantenchemie (DE-588)4047979-1 gnd rswk-swf Gruppentheorie (DE-588)4072157-7 gnd rswk-swf Kristallsymmetrie (DE-588)4136175-1 gnd rswk-swf Chemie (DE-588)4009816-3 gnd rswk-swf Symmetrie (DE-588)4058724-1 gnd rswk-swf Kristallsymmetrie (DE-588)4136175-1 s DE-604 Molekülsymmetrie (DE-588)4170385-6 s Gruppentheorie (DE-588)4072157-7 s Chemie (DE-588)4009816-3 s Symmetrie (DE-588)4058724-1 s Quantenchemie (DE-588)4047979-1 s HEBIS Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001501518&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Hochstrasser, Robin M. Molecular aspects of symmetry Groupes, Théorie des - Symétriques ram Structure moléculaire ram Symétrie (Physique) Symétrie (physique) ram Symétrie moléculaire ram Théorie des groupes Théorie moléculaire Molekülsymmetrie (DE-588)4170385-6 gnd Quantenchemie (DE-588)4047979-1 gnd Gruppentheorie (DE-588)4072157-7 gnd Kristallsymmetrie (DE-588)4136175-1 gnd Chemie (DE-588)4009816-3 gnd Symmetrie (DE-588)4058724-1 gnd |
| subject_GND | (DE-588)4170385-6 (DE-588)4047979-1 (DE-588)4072157-7 (DE-588)4136175-1 (DE-588)4009816-3 (DE-588)4058724-1 |
| title | Molecular aspects of symmetry |
| title_auth | Molecular aspects of symmetry |
| title_exact_search | Molecular aspects of symmetry |
| title_full | Molecular aspects of symmetry |
| title_fullStr | Molecular aspects of symmetry |
| title_full_unstemmed | Molecular aspects of symmetry |
| title_short | Molecular aspects of symmetry |
| title_sort | molecular aspects of symmetry |
| topic | Groupes, Théorie des - Symétriques ram Structure moléculaire ram Symétrie (Physique) Symétrie (physique) ram Symétrie moléculaire ram Théorie des groupes Théorie moléculaire Molekülsymmetrie (DE-588)4170385-6 gnd Quantenchemie (DE-588)4047979-1 gnd Gruppentheorie (DE-588)4072157-7 gnd Kristallsymmetrie (DE-588)4136175-1 gnd Chemie (DE-588)4009816-3 gnd Symmetrie (DE-588)4058724-1 gnd |
| topic_facet | Groupes, Théorie des - Symétriques Structure moléculaire Symétrie (Physique) Symétrie (physique) Symétrie moléculaire Théorie des groupes Théorie moléculaire Molekülsymmetrie Quantenchemie Gruppentheorie Kristallsymmetrie Chemie Symmetrie |
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