Symmetry through the eyes of a chemist

It is gratifying to launch the third edition of our book. Its coming to life testi?es about the task it has ful?lled in the service of the com- nity of chemical research and learning. As we noted in the Prefaces to the ?rst and second editions, our book surveys chemistry from the point of view of symmetry. We present many examples from ch- istry as well as from other ?elds to emphasize the unifying nature of the symmetry concept. Our aim has been to provide aesthetic pl- sure in addition to learning experience. In our ?rst Preface we paid tribute to two books in particular from which we learned a great deal; they have in?uenced signi?cantly our approach to the subject matter of our book. They are Weyl's classic, Symmetry, and Shubnikov and Koptsik's Symmetry in Science and Art. The structure of our book has not changed. Following the Int- duction (Chapter 1), Chapter 2 presents the simplest symmetries using chemical and non-chemical examples. Molecular geometry is discussed in Chapter3. The next four chapters present gro- theoretical methods (Chapter 4) and, based on them, discussions of molecular vibrations (Chapter 5), electronic structures (Chapter 6), and chemical reactions (Chapter 7). For the last two chapters we return to a qualitative treatment and introduce space-group sym- tries (Chapter 8), concluding with crystal structures (Chapter 9). For the third edition we have further revised and streamlined our text and renewed the illustrative material.

Author Notes

Magdolna Hargittai and Istvn Hargittai are PhDs (Eoumlet;tvoumlet;s University), DScs (Hungarian Academy of Sciences), and Dr.h.c.s (University of North Carolina). They are currently affiliated with the Department of Inorganic and Analytical Chemistry and Materials Structure and Modeling Research Group of the Hungarian Academy of Sciences at the Budapest University of Technology and Economics. They are members of the Hungarian Academy of Sciences and the Academia Europaea (London).

Reviews 1

Choice Review

Symmetry appears everywhere in science, and probably nowhere more than in chemistry. Molecules can have various kinds of symmetry (or none); molecular crystals can present a wide range of symmetrical appearances; and spectroscopists can use a substance's overall symmetry to analyze its molecular spectra. Most importantly, the elegant principles governing the conservation of molecular orbital symmetry are considered to be one of the major chemical discoveries of the 20th century. Yet to this reviewer's knowledge, this book (2nd ed., CH, Apr'96, 33-4511; 1st ed., 1987) is the first to include introductory chapters devoted to each of these manifestations of symmetry. Magdolna Hargittai and Istvan Hargittai (both, Budapest Univ. of Technology and Economics, Hungary) provide a variety of examples of symmetry in art and decoration, and use examples from these areas throughout the book to illustrate chemical concepts. This work is useful for academic and professional chemists, and could even be of interest and possible inspiration to designers and artists. Summing Up: Recommended. Upper-division undergraduates through professionals; general readers. A. Fry Wesleyan University

1 Introduction	p. 1
References	p. 20
2 Simple and Combined Symmetries	p. 25
2.1 Bilateral Symmetry	p. 25
2.2 Rotational Symmetry	p. 33
2.3 Combined Symmetries	p. 37
2.3.1 A Rotation Axis with Intersecting Symmetry Planes	p. 37
2.3.2 Snowflakes	p. 39
2.4 Inversion	p. 53
2.5 Singular Point and Translational Symmetry	p. 55
2.6 Polarity	p. 57
2.7 Chirality	p. 60
2.7.1 Asymmetry and Dissymmetry	p. 66
2.7.2 Vital Importance	p. 69
2.7.3 La coupe du roi	p. 74
2.8 Polyhedra	p. 76
References	p. 91
3 Molecular Shape and Geometry	p. 97
3.1 Isomers	p. 98
3.2 Rotational Isomerism	p. 100
3.3 Symmetry Notations	p. 104
3.4 Establishing the Point Group	p. 105
3.5 Examples	p. 107
3.6 Consequences of Substitution	p. 115
3.7 Polyhedral Molecular Geometries	p. 119
3.7.1 Boron Hydride Cages	p. 123
3.7.2 Polycyclic Hydrocarbons	p. 125
3.7.3 Structures with Central Atom	p. 133
3.7.4 Regularities in Nonbonded Distances	p. 136
3.7.5 The Vsepr Model	p. 139
3.7.6 Consequences of Intramolecular Motion	p. 152
References	p. 161
4 Helpful Mathematical Tools	p. 169
4.1 Groups	p. 169
4.2 Matrices	p. 176
4.3 Representation of Groups	p. 183
4.4 The Character of a Representation	p. 189
4.5 Character Tables and Properties of Irreducible Representations	p. 191
4.6 Antisymmetry	p. 197
4.7 Shortcut to Determine a Representation	p. 204
4.8 Reducing a Representation	p. 206
4.9 Auxiliaries	p. 208
4.9.1 Direct Product	p. 209
4.9.2 Integrals of Product Functions	p. 209
4.9.3 Projection Operator	p. 211
4.10 Dynamic Properties	p. 212
4.11 Where Is Group Theory Applied?	p. 213
References	p. 214
5 Molecular Vibrations	p. 217
5.1 Normal Modes	p. 217
5.1.1 Their Number	p. 218
5.1.2 Their Symmetry	p. 220
5.1.3 Their Types	p. 224
5.2 Symmetry Coordinates	p. 225
5.3 Selection Rules	p. 227
5.4 Examples	p. 229
References	p. 237
6 Electronic Structure of Atoms and Molecules	p. 239
6.1 One-Electron Wave Function	p. 241
6.2 Many-Electron Atoms	p. 249
6.3 Molecules	p. 252
6.3.1 Constructing Molecular Orbitals	p. 252
6.3.2 Electronic States	p. 261
6.3.3 Examples of MO Construction	p. 263
6.4 Quantum Chemical Calculations	p. 287
6.5 Influence of Environmental Symmetry	p. 290
6.6 Jahn-Teller Effect	p. 294
References	p. 308
7 Chemical Reactions	p. 313
7.1 Potential Energy Surface	p. 315
7.1.1 Transition State, Transition Structure	p. 316
7.1.2 Reaction Coordinate	p. 319
7.1.3 Symmetry Rules for the Reaction Coordinate	p. 320
7.2 Electronic Structure	p. 324
7.2.1 Changes During a Chemical Reaction	p. 324
7.2.2 Frontier Orbitals: Homo and Lumo	p. 325
7.2.3 Conservation of Orbital Symmetry	p. 326
7.2.4 Analysis in Maximum Symmetry	p. 327
7.3 Examples	p. 328
7.3.1 Cycloaddition	p. 328
7.3.2 Intramolecular Cyclization	p. 343
7.3.3 Generalized Woodward-Hoffmann Rules	p. 350
7.4 Hückel-Möbius Concept	p. 350
7.5 Isolobal Analogy	p. 356
References	p. 364
8 Space-Group Symmetries	p. 371
8.1 Expanding to Infinity	p. 371
8.2 One-Sided Bands	p. 375
8.3 Two-Sided Bands	p. 378
8.4 Rods, Spirals, and Similarity Symmetry	p. 381
8.5 Two-Dimensional Space Groups	p. 395
8.5.1 Simple Networks	p. 401
8.5.2 Side-Effects of Decorations	p. 406
8.5.3 Moirés	p. 408
References	p. 410
9 Crystals	p. 413
9.1 Basic Laws	p. 417
9.2 The 32 Crystal Groups	p. 423
9.3 Restrictions	p. 424
9.4 The 230 Space Groups	p. 432
9.4.1 Rock Salt and Diamond	p. 438
9.5 Dense Packing	p. 440
9.5.1 Sphere Packing	p. 442
9.5.2 Icosahedral Packing	p. 446
9.5.3 Connected Polyhedra	p. 449
9.5.4 Atomic Sizes	p. 453
9.6 Molecular Crystals	p. 456
9.6.1 Geometrical Model	p. 457
9.6.2 Densest Molecular Packing	p. 466
9.6.3 Energy Calculations and Structure Predictions	p. 470
9.6.4 Hypersymmetry	p. 474
9.6.5 Crystal Field Effects	p. 476
9.7 Beyond the Perfect System	p. 483
9.8 Quasicrystals	p. 489
9.9 Returning to Shapes	p. 494
References	p. 496
Epilogue	p. 505
Other Titles by the Authors	p. 507
Index	p. 509

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