| Preface | 4 |
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| Acknowledgments | 6 |
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| Contents | 7 |
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| to 1Introduction | 11 |
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| to 2Simple and Combined Symmetries | 34 |
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| Bilateral Symmetry | 34 |
| Rotational Symmetry | 42 |
| Combined Symmetries | 46 |
| A Rotation Axis with Intersecting Symmetry Planes | 46 |
| Snowflakes | 48 |
| Inversion | 62 |
| Singular Point and Translational Symmetry | 64 |
| Polarity | 66 |
| Chirality | 69 |
| Asymmetry and Dissymmetry | 75 |
| Vital Importance | 78 |
| La coupe du roi | 83 |
| Polyhedra | 85 |
| to 3Molecular Shape and Geometry | 105 |
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| Isomers | 106 |
| Rotational Isomerism | 108 |
| Symmetry Notations | 112 |
| Establishing the Point Group | 113 |
| Examples | 115 |
| Consequences of Substitution | 123 |
| Polyhedral Molecular Geometries | 127 |
| Boron Hydride Cages | 131 |
| Polycyclic Hydrocarbons | 133 |
| Structures with Central Atom | 141 |
| Regularities in Nonbonded Distances | 144 |
| The VSEPR Model | 147 |
| Analogies | 150 |
| Molecular Shapes | 151 |
| Historical Remarks | 159 |
| Consequences of Intramolecular Motion | 160 |
| to 4Helpful Mathematical Tools | 176 |
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| Groups | 176 |
| Matrices | 183 |
| Representation of Groups | 190 |
| The Character of a Representation | 196 |
| Character Tables and Properties of Irreducible Representations | 198 |
| Antisymmetry | 204 |
| Shortcut to Determine a Representation | 211 |
| Reducing a Representation | 213 |
| Auxiliaries | 215 |
| Direct Product | 216 |
| Integrals of Product Functions | 216 |
| Projection Operator | 218 |
| Dynamic Properties | 219 |
| Where Is Group Theory Applied? | 220 |
| to 5Molecular Vibrations | 223 |
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| Normal Modes | 223 |
| Their Number | 224 |
| Their Symmetry | 226 |
| Their Types | 230 |
| Symmetry Coordinates | 231 |
| Selection Rules | 233 |
| Examples | 235 |
| to 6Electronic Structure of Atoms and Molecules | 244 |
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| One-Electron Wave Function | 246 |
| Many-Electron Atoms | 254 |
| Molecules | 257 |
| Constructing Molecular Orbitals | 257 |
| Electronic States | 266 |
| Examples of MO Construction | 268 |
| Homonuclear Diatomics | 268 |
| Polyatomic Molecules | 271 |
| Short Summary of MO Construction | 291 |
| Quantum Chemical Calculations | 292 |
| Influence of Environmental Symmetry | 295 |
| Jahn--Teller Effect | 299 |
| to 7Chemical Reactions | 318 |
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| Potential Energy Surface | 320 |
| Transition State, Transition Structure | 321 |
| Reaction Coordinate | 324 |
| Symmetry Rules for the Reaction Coordinate | 325 |
| Electronic Structure | 329 |
| Changes During a Chemical Reaction | 329 |
| Frontier Orbitals: HOMO and LUMO | 330 |
| Conservation of Orbital Symmetry | 331 |
| Analysis in Maximum Symmetry | 332 |
| Examples | 333 |
| Cycloaddition | 333 |
| Ethylene Dimerization | 333 |
| Diels--Alder Reaction | 345 |
| Intramolecular Cyclization | 348 |
| Generalized Woodward--Hoffmann Rules | 355 |
| HöckelöMöbius Concept | 355 |
| Isolobal Analogy | 361 |
| to 8Space-Group Symmetries | 376 |
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| Expanding to Infinity | 376 |
| One-Sided Bands | 380 |
| Two-Sided Bands | 383 |
| Rods, Spirals, and Similarity Symmetry | 386 |
| Two-Dimensional Space Groups | 400 |
| Simple Networks | 406 |
| Side-Effects of Decorations | 411 |
| Moirés | 413 |
| to 9Crystals | 418 |
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| Basic Laws | 422 |
| The 32 Crystal Groups | 428 |
| Restrictions | 429 |
| The 230 Space Groups | 437 |
| Rock Salt and Diamond | 443 |
| Dense Packing | 445 |
| Sphere Packing | 447 |
| Icosahedral Packing | 451 |
| Connected Polyhedra | 454 |
| Atomic Sizes | 458 |
| Molecular Crystals | 461 |
| Geometrical Model | 462 |
| Densest Molecular Packing | 471 |
| Energy Calculations and Structure Predictions | 475 |
| Hypersymmetry | 479 |
| Crystal Field Effects | 481 |
| Structure Differences in Free and Crystalline Molecules | 482 |
| Conformational Polymorphism | 486 |
| Beyond the Perfect System | 488 |
| Quasicrystals | 494 |
| Returning to Shapes | 499 |
| Epilogue | 510 |
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| Other Titles by the Authors | 512 |
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| Index | 514 |
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