Symmetry and Structure: Readable Group Theory for Chemists, Third Edition

Symmetry and Structure: Readable Group Theory for Chemists......Page 5
Contents......Page 7
Preface to Third Edition......Page 11
1.2 The Ammonia Molecule......Page 13
1.2.1 The Atomic Orbital Model......Page 14
1.2.2 The Hybrid Orbital Model......Page 15
1.2.3 The Electron-Repulsion Model......Page 16
1.2.4 The Electron-Spin-Repulsion Model......Page 18
1.2.5 Accurate Calculations......Page 19
2.1 Symmetry Operations and Symmetry Elements......Page 23
2.2 Multipliers Associated with Symmetry Operations......Page 31
2.3 Group Multiplication Tables......Page 48
2.4 Character Tables......Page 52
2.5 Summary......Page 55
3.1 The Orthonormal Properties of Irreducible Representations......Page 57
3.2 The Transformation Properties of Atomic Orbitals in the Water Molecule......Page 59
3.3 A Reducible Representation......Page 63
3.4 Symmetry-Adapted Combinations......Page 66
3.5 The Bonding Interactions in H2O and their Angular Dependence......Page 71
3.6 The Molecular Orbital Energy Level Diagram for H2O......Page 77
3.7 Comparison with Experiment......Page 79
3.8 The Walsh Diagram for Triatomic Dihydrides......Page 80
3.9 Simple Models for the Bonding in H2O......Page 82
3.10 A Rapprochement between Simple and Symmetry Models......Page 85
3.11 Summary......Page 86
4 Vibrational Spectra of the Water Molecule......Page 87
4.1 Vibrations of the Water Molecule: Part 1 (easy)......Page 88
4.2 Vibrations of the Water Molecule: Part 2 (less easy!)......Page 92
4.3 Product Functions......Page 104
4.4 Direct Products and Quantum Mechanical Integrals......Page 108
4.5 Spectroscopic Selection Rules......Page 111
4.6 The Vibrational Spectroscopy of the Water Molecule......Page 115
4.7 Optical Activity......Page 119
4.8 Summary......Page 120
5.1 The Symmetry of the Ethene Molecule......Page 121
5.2 The Character and Multiplication Tables of the D2h Group......Page 124
5.3 Direct Products of Groups......Page 126
5.4 Nodal Patterns of the Irreducible Representations of the D2h Group......Page 129
5.5 The Symmetries of the Carbon Atomic Orbitals in Ethene......Page 133
5.6 The Symmetries of the Hydrogen 1s Orbitals in Ethene......Page 140
5.7 The Projection Operator Method......Page 141
5.8 Bonding in the Ethene Molecule......Page 146
5.9 Bonding in the Diborane Molecule......Page 148
5.10 Comparison with Other Models......Page 153
5.11 Summary......Page 156
6 The Electronic Structure of Bromine Pentafluoride, BrF5......Page 157
6.1 Symmetry Operations of the C4v Group......Page 159
6.2 Problems in Using the C4v Group......Page 162
6.3 Orthonormality Relationships......Page 164
6.4 The Derivation of the C4v Character Table Using the Orthonormality Theorems......Page 167
6.5 Nodal Patterns of the Irreducible Representations of C4v......Page 172
6.6 The Bonding in the BrF5 Molecule......Page 174
6.7 Summary......Page 183
7.1 The Symmetry of the Ammonia Molecule......Page 185
7.2 Nodal Patterns of the Irreducible Representations of C3v......Page 190
7.3 The Bonding in the Ammonia Molecule......Page 192
7.4 Summary......Page 199
8 The Electronic Structures of some Octahedral Molecules......Page 201
8.1 The Symmetry Operations of the Octahedron......Page 202
8.2 Nodal Patterns of the Irreducible Representations of the Oh Group......Page 211
8.3 The Bonding in the SF6 Molecule......Page 216
8.4 Octahedral Transition Metal Complexes......Page 230
8.5 Summary......Page 241
9.1 The Determination of the Point Group of a Molecule......Page 243
9.2 The Relationships between Point Groups......Page 247
9.3 Correlation Tables......Page 252
9.4 Summary......Page 256
10.1 An Overview......Page 257
10.2 The Tetrahedron......Page 259
10.3 The Icosahedron......Page 263
10.4 Spherical Symmetry......Page 266
10.5 Linear Molecules......Page 273
10.6 Summary......Page 274
11.1 Square Cyclobutadiene and the C4 Point Group......Page 275
11.2 Working with Complex Characters......Page 280
11.3 The  Orbitals of Cyclobutadiene......Page 281
11.4 The Energies of the Orbitals of Cyclobutadiene in the Huckel Approximation......Page 283
11.5 Symmetry and Chemical Reactions......Page 288
11.6 Summary......Page 292
12.1 The Problem of Electron Spin......Page 293
12.2 More about the Symmetry of Product Functions......Page 300
12.3 Configurations and Terms......Page 301
12.4 The Inclusion of Electron Spin......Page 306
12.5 Summary......Page 309
13.1 The Crystal Systems......Page 311
13.2 The Bravais Lattices......Page 320
13.3 The Crystallographic Point Groups......Page 323
13.4 The Symmorphic Space Groups......Page 329
13.5 The Non-Symmorphic Space Groups......Page 334
13.6 Unit Cells......Page 337
13.7 Wigner–Seitz Unit Cells......Page 339
13.8 Summary......Page 342
14.1 Translational Invariance......Page 343
14.2 The Factor Group and Unit Cell Group Models......Page 345
14.3.1 The (CO) Spectra of Crystalline (C6H6)Cr(CO)3......Page 348
14.3.2 The Vibrational Spectrum of a M(C≡O)3 Species Crystallizing in the C2/c (C2h6) Space Group Using the Unit Cell Model......Page 352
14.4 Summary......Page 356
A1.1 Groups......Page 357
A1.2 Some Examples of Groups......Page 359
A1.3 The Classes of a Group......Page 361
A1.4 Class Algebra......Page 364
A2.1 Matrix Algebra and Symmetry Operations......Page 367
A2.2 Direct Products......Page 375
Appendix 3 Character Tables of the More Important Point Groups......Page 381
Appendix 4 The Fluorine Group Orbitals of Symmetry in SF6......Page 405
A4.1 Ligand Group Orbitals of Complex Ions......Page 411
Appendix 5 The Hermann–Mauguin Notation......Page 419
Appendix 6 Non-Symmorphic Relatives of the Point Group D2......Page 423
A6.1 The Space Group P21/c (C52h)......Page 432
Index......Page 435