Symmetry through the Eyes of a Chemist / Edition 3

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It is gratifying to launch the third edition of our book. Its coming to life testifies about the task it has fulfilled in the service of the com- nity of chemical research and learning. As we noted in the Prefaces to the first 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 influenced significantly 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 Chapter 3. 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.

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Editorial Reviews

From the Publisher
Reviews of previous editions

“This has to be the most delightful book on symmetry ever written!” F.L. Pilar, Elementary Quantum Chemistry

“The book gives a fascinating overview of the rich variety of applications of symmetry, showing both its power and its aesthetic appeal.” Science

“Education by aesthetic appeal.” Nature

“The cosmopolitan eye… good-humored and clearly delighted by diversity, informs this entire book. The work offers a broad new perspective.” Scientific American

“In the refreshing style of scientists with an almost renaissance versatility.” New Scientist

“This beautiful book… looks at symmetry as a unifying theme in the nature of things.” Mathematical Reviews

“…gives the reader a broad perspective…” The Mathematical Intelligencer

“An outstanding book that succeeds admirably on a number of levels…” Bowker’s Good Reading

“I warmly recommend it to all chemists.” Journal of Chemical Education

“Succeeds not only in demonstrating how central [in] the study of all fields of chemistry symmetry consideration [is] but how these same concepts of symmetry can be traced through all our cultural traditions unifying and contrasting diverse endeavors in literature, music, and art.” Journal of the American Chemical Society

“The book…to which I shall return frequently and with considerable pleasure.” Chemistry and Industry

From the reviews of the third edition:

"This book … is the first to include introductory chapters devoted to each of these manifestations of symmetry. … Magdolna Hargittai and Istvin Hargittai … 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, Choice, Vol. 47 (1), September, 2009)

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Product Details

  • ISBN-13: 9789048136896
  • Publisher: Springer Netherlands
  • Publication date: 2/22/2010
  • Edition description: 3rd ed. 2009
  • Edition number: 3
  • Pages: 520
  • Product dimensions: 6.10 (w) x 9.10 (h) x 1.10 (d)

Meet the Author

Magdolna Hargittai and István Hargittai are PhD’s (Eötvös University), DSc’s (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 also members of the Hungarian Academy of Sciences and the Academia Europaea (London).

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Table of Contents

1 Introduction 1

References 20

2 Simple and Combined Symmetries 25

2.1 Bilateral Symmetry 25

2.2 Rotational Symmetry 33

2.3 Combined Symmetries 37

2.3.1 A Rotation Axis with Intersecting Symmetry Planes 37

2.3.2 Snowflakes 39

2.4 Inversion 53

2.5 Singular Point and Translational Symmetry 55

2.6 Polarity 57

2.7 Chirality 60

2.7.1 Asymmetry and Dissymmetry 66

2.7.2 Vital Importance 69

2.7.3 La coupe du roi 74

2.8 Polyhedra 76

References 91

3 Molecular Shape and Geometry 97

3.1 Isomers 98

3.2 Rotational Isomerism 100

3.3 Symmetry Notations 104

3.4 Establishing the Point Group 105

3.5 Examples 107

3.6 Consequences of Substitution 115

3.7 Polyhedral Molecular Geometries 119

3.7.1 Boron Hydride Cages 123

3.7.2 Polycyclic Hydrocarbons 125

3.7.3 Structures with Central Atom 133

3.7.4 Regularities in Nonbonded Distances 136

3.7.5 The VSEPR Model 139

3.7.6 Consequences of Intramolecular Motion 152

References 161

4 Helpful Mathematical Tools 169

4.1 Groups 169

4.2 Matrices 176

4.3 Representation of Groups 183

4.4 The Character of a Representation 189

4.5 Character Tables and Properties of Irreducible Representations 191

4.6 Antisymmetry 197

4.7 Shortcut to Determine a Representation 204

4.8 Reducing a Representation 206

4.9 Auxiliaries 208

4.9.1 Direct Product 209

4.9.2 Integrals of Product Functions 209

4.9.3 Projection Operator 211

4.10 Dynamic Properties 212

4.11 Where Is Group Theory Applied? 213

References 214

5 Molecular Vibrations 217

5.1 Normal Modes 217

5.1.1 Their Number 218

5.1.2 Their Symmetry 220

5.1.3 Their Types 224

5.2 Symmetry Coordinates 225

5.3 Selection Rules 227

5.4 Examples 229

References 237

6 Electronic Structure of Atoms and Molecules 239

6.1 One-Electron Wave Function 241

6.2 Many-Electron Atoms 249

6.3 Molecules 252

6.3.1 Constructing Molecular Orbitals 252

6.3.2 Electronic States 261

6.3.3 Examples of MO Construction 263

6.4 Quantum Chemical Calculations 287

6.5 Influence of Environmental Symmetry 290

6.6 Jahn-Teller Effect 294

References 308

7 Chemical Reactions 313

7.1 Potential Energy Surface 315

7.1.1 Transition State, Transition Structure 316

7.1.2 Reaction Coordinate 319

7.1.3 Symmetry Rules for the Reaction Coordinate 320

7.2 Electronic Structure 324

7.2.1 Changes During a Chemical Reaction 324

7.2.2 Frontier Orbitals: HOMO and LUMO 325

7.2.3 Conservation of Orbital Symmetry 326

7.2.4 Analysis in Maximum Symmetry 327

7.3 Examples 328

7.3.1 Cycloaddition 328

7.3.2 Intramolecular Cyclization 343

7.3.3 Generalized Woodward-Hoffmann Rules 350

7.4 Hückel-Möbius Concept 350

7.5 Isolobal Analogy 356

References 364

8 Space-Group Symmetries 371

8.1 Expanding to Infinity 371

8.2 One-Sided Bands 375

8.3 Two-Sided Bands 378

8.4 Rods, Spirals, and Similarity Symmetry 381

8.5 Two-Dimensional Space Groups 395

8.5.1 Simple Networks 401

8.5.2 Side-Effects of Decorations 406

8.5.3 Moirés 408

References 410

9 Crystals 413

9.1 Basic Laws 417

9.2 The 32 Crystal Groups 423

9.3 Restrictions 424

9.4 The 230 Space Groups 432

9.4.1 Rock Salt and Diamond 438

9.5 Dense Packing 440

9.5.1 Sphere Packing 442

9.5.2 Icosahedral Packing 446

9.5.3 Connected Polyhedra 449

9.5.4 Atomic Sizes 453

9.6 Molecular Crystals 456

9.6.1 Geometrical Model 457

9.6.2 Densest Molecular Packing 466

9.6.3 Energy Calculations and Structure Predictions 470

9.6.4 Hypersymmetry 474

9.6.5 Crystal Field Effects 476

9.7 Beyond the Perfect System 483

9.8 Quasicrystals 489

9.9 Returning to Shapes 494

References 496

Epilogue 505

Other Titles by the Authors 507

Index 509

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