Symmetry through the eyes of a chemist

1. Introduction

References

2. Simple and Combined Symmetries

2.1. Bilateral Symmetry

2.2. Rotational Symmetry

2.3. Combined Symmetries

2.3.1. A Rotation Axis with Intersecting Symmetry Planes

2.3.2. Snowflakes

2.4. Inversion

2.5. Singular Point and Translational Symmetry

2.6. Polarity

2.7. Chirality

2.7.1. Asymmetry and Dissymmetry

2.7.2. Vital Importance

2.7.3. La coupe du roi

2.8. Polyhedra

References

3. Molecular Shape and Geometry

3.1. Isomers

3.2. Rotational Isomerism

3.3. Symmetry Notations

3.4. Establishing the Point Group

3.5. Examples

3.6. Consequences of Substitution

3.7. Polyhedral Molecular Geometries

3.7.1. Boron Hydride Cages

3.7.2. Polycyclic Hydrocarbons

3.7.3. Structures with Central Atom

3.7.4. Regularities in Nonbonded Distances

3.7.5. The Vsepr Model

3.7.6. Consequences of Intramolecular Motion

References

4. Helpful Mathematical Tools

4.1. Groups

4.2. Matrices

4.3. Representation of Groups

4.4. The Character of a Representation

4.5. Character Tables and Properties of Irreducible Representations

4.6. Antisymmetry

4.7. Shortcut to Determine a Representation

4.8. Reducing a Representation

4.9. Auxiliaries

4.9.1. Direct Product

4.9.2. Integrals of Product Functions

4.9.3. Projection Operator

4.10. Dynamic Properties

4.11. Where Is Group Theory Applied?

References

5. Molecular Vibrations

5.1. Normal Modes

5.1.1. Their Number

5.1.2. Their Symmetry

5.1.3. Their Types

5.2. Symmetry Coordinates

5.3. Selection Rules

5.4. Examples

References

6. Electronic Structure of Atoms and Molecules

6.1. One-Electron Wave Function

6.2. Many-Electron Atoms

6.3. Molecules

6.3.1. Constructing Molecular Orbitals

6.3.2. Electronic States

6.3.3. Examples of MO Construction

6.4. Quantum Chemical Calculations

6.5. Influence of Environmental Symmetry

6.6. Jahn-Teller Effect

References

7. Chemical Reactions

7.1. Potential Energy Surface

7.1.1. Transition State, Transition Structure

7.1.2. Reaction Coordinate

7.1.3. Symmetry Rules for the Reaction Coordinate

7.2. Electronic Structure

7.2.1. Changes During a Chemical Reaction

7.2.2. Frontier Orbitals: Homo and Lumo

7.2.3. Conservation of Orbital Symmetry

7.2.4. Analysis in Maximum Symmetry

7.3. Examples

7.3.1. Cycloaddition

7.3.2. Intramolecular Cyclization

7.3.3. Generalized Woodward-Hoffmann Rules

7.4. Hüet;ckel-Möet;bius Concept

7.5. Isolobal Analogy

References

8. Space-Group Symmetries

8.1. Expanding to Infinity

8.2. One-Sided Bands

8.3. Two-Sided Bands

8.4. Rods, Spirals, and Similarity Symmetry

8.5. Two-Dimensional Space Groups

8.5.1. Simple Networks

8.5.2. Side-Effects of Decorations

8.5.3. Moirés

References

9. Crystals

9.1. Basic Laws

9.2. The 32 Crystal Groups

9.3. Restrictions

9.4. The 230 Space Groups

9.4.1. Rock Salt and Diamond

9.5. Dense Packing

9.5.1. Sphere Packing

9.5.2. Icosahedral Packing

9.5.3. Connected Polyhedra

9.5.4. Atomic Sizes

9.6. Molecular Crystals

9.6.1. Geometrical Model

9.6.2. Densest Molecular Packing

9.6.3. Energy Calculations and Structure Predictions

9.6.4. Hypersymmetry

9.6.5. Crystal Field Effects

9.7. Beyond the Perfect System

9.8. Quasicrystals

9.9. Returning to Shapes

References

Epilogue

Other Titles by the Authors

Index