1Introduction to Group Theory
1408.5 Stereoisomerism in Organic Compounds
21.1 Definition and Importance of Group Theory
141Configurational Isomerism:
31.2 Basic Concepts: Groups, Subgroups, and Group Operations
1421. Geometrical Isomerism (Cis-Trans Isomerism):
4Subgroups:: Group Operations:
1432. Optical Isomerism (Enantiomers and Diastereomers):: Conformational Isomerism:
51.3 Historical Development of Group Theory: Example 1: The Group of Integers under Addition
1448.6 Stereochemistry in Inorganic Compounds
61.4 Applications of Group Theory in Chemistry
145Coordination Compounds:
71. Molecular Symmetry and Point Groups:
146Stereochemistry in Organometallic Compounds:
82. Molecular Orbital Theory:
147Stereochemical Considerations in Catalysis:
93. Spectroscopy:
148Practice Problem 4 Solution:
104. Crystallography:
149Practice Problem 5 Solution:: Practice Problem 6 Solution:
115. Reaction Mechanisms:
150Conclusion
126. Vibrational Analysis:: 7. Quantum Chemistry:
151Reaction Mechanisms and Symmetry
131.5 Mathematical Prerequisites
1529.1 Introduction to Reaction Mechanisms
141. Matrix Algebra:
153Reaction Intermediates and Transition States:
152. Linear Algebra:
154Energy Diagrams:
163. Calculus:
155Kinetic and Thermodynamic Considerations:: Practice Problem 1:
174. Complex Numbers:
1569.2 Woodward-Hoffmann Rules
185. Set Theory:
157Pericyclic Reactions:
196. Combinatorics:: Example 2: Symmetry Operations and Point Groups
158Frontier Molecular Orbitals:
20Conclusion
159Symmetry Conservation:: Practice Problem 2:
21Symmetry Operations and Point Groups
1609.3 Frontier Molecular Orbital Theory
222.1 Definition of Symmetry Operations
161Frontier Molecular Orbitals:
232.2 Proper and Improper Rotations
162HOMO-LUMO Interactions:
24Proper Rotations:
163Perturbation Theory:
25Principal Axis (Cₙ):
164Applications of FMO Theory:
26Dihedral Axis (Sₙ):
165Computational Methods:
27Improper Rotations:
166Practice Problem 3:
28Reflections (σ):
167Solutions to Practice Problems:
29Inversions (i):
168Solution to Practice Problem 2:: Solution to Practice Problem 3:
30Improper Rotation Axes (Sₙ):
1699.4 Symmetry-Allowed and Symmetry-Forbidden Reactions
312.3 Reflection Operations
170Symmetry-Allowed Reactions:
32Vertical Reflection Planes (σᵥ):
171Symmetry-Forbidden Reactions:
33Horizontal Reflection Planes (σₕ):: Dihedral Reflection Planes (σᵈ):
172Importance of Symmetry Considerations:: Practice Problem 1:
342.4 Inversion Operations
1739.5 Electrocyclic Reactions
352.5 Determination of Point Groups
174Thermal and Photochemical Electrocyclic Reactions:
361. Visual Inspection:
175Stereochemistry of Electrocyclic Reactions:
372. Systematic Procedure:
176Reverse reactions and equilibria:
383. Character Tables:: 4. Computational Methods:
177Applications of Electrocyclic Reactions:: Practice Problem 2:
392.6 Examples of Point Groups in Molecules
1789.6 Cycloaddition Reactions
40Conclusion
179Types of Cycloaddition Reactions:
41Matrix Representations of Groups
180Diels-Alder Reactions:
423.1 Introduction to Matrix Representations: Importance of Matrix Representations:
181Stereochemistry of Diels-Alder Reactions:
433.2 Reducible and Irreducible Representations
182Endo and Exo Selectivity:
44Reducible Representations:
183Frontier Molecular Orbital (FMO) Theory and Regioselectivity:
45Irreducible Representations:: Importance of Irreducible Representations:
184Other Cycloaddition Reactions:
463.3 Great Orthogonality Theorem
185Applications of Cycloaddition Reactions:
47Statement of the Great Orthogonality Theorem:
186Practice Problem 3:
481. Column Orthogonality:
187Solutions to Practice Problems:
492. Row Orthogonality:: Importance of the Great Orthogonality Theorem:
188Solution to Practice Problem 1:
503.4 Character Tables: Properties of Character Tables:
189Solution to Practice Problem 2:: Solution to Practice Problem 3:
513.5 Construction of Character Tables
190Conclusion
523.6 Applications of Character Tables
191Crystallography and Space Groups
531. Determining the symmetry species of molecular orbitals:
19210.1 Introduction to Crystallography
542. Predicting the number and types of normal modes of vibration:
193Crystals and Crystalline Solids:
553. Identifying allowed and forbidden transitions in spectroscopy:
194Importance of Crystallography:: Practice Problem 1:
564. Constructing symmetry-adapted linear combinations (SALCs) of atomic orbitals:
19510.2 Crystal Systems and Bravais Lattices
575. Studying chemical reactions and reaction pathways:: 6. Investigating the degeneracy of energy levels:
196Crystal Systems:
58Conclusion
197Bravais Lattices:
59Molecular Orbital Theory and Symmetry
198Crystal Symmetry:: Practice Problem 2:
604.1 Atomic Orbitals and Symmetry
19910.3 Space Groups and Symmetry Operations
61Symmetry Properties of Atomic Orbitals:
200Space Groups:
621. s orbitals (l = 0):
201Symmetry Operations:
632. p orbitals (l = 1):
202Importance of Space Groups:
643. d orbitals (l = 2):: 4. f orbitals (l = 3):
203Practice Problem 3:
654.2 Linear Combination of Atomic Orbitals (LCAO): Symmetry Considerations in LCAO:
204Solutions to Practice Problems:
664.3 Sigma and Pi Molecular Orbitals
205Solution to Practice Problem 1:: Solution to Practice Problem 2:
67Sigma (σ) Molecular Orbitals:: Pi (π) Molecular Orbitals:
20610.4 International Tables for Crystallography
684.4 Symmetry Adapted Linear Combinations (SALCs)
207Structure and Content of the International Tables:
694.5 Molecular Orbital Diagrams
208Importance and Applications:: Practice Problem 1:
70Components of a Molecular Orbital Diagram:: Construction of Molecular Orbital Diagrams:
20910.5 X-Ray Diffraction and Structure Determination
714.6 Homonuclear and Heteronuclear Diatomic Molecules
210X-Ray Diffraction:
72Homonuclear Diatomic Molecules:
211Bragg’s Law:
73Heteronuclear Diatomic Molecules:
212Structure Determination Techniques:: Practice Problem 2:
74Bonding Molecular Orbitals:: Antibonding Molecular Orbitals:
21310.6 Applications in Solid-State Chemistry
75Conclusion
214Practice Problem 3:
76Hybridization and Molecular Geometry
215Solutions to Practice Problems:
775.1 Valence Bond Theory and Hybridization
216Solution to Practice Problem 1:
78Example:
217Solution to Practice Problem 2:: Solution to Practice Problem 3:
79Solved Problem:: Practice Problem:
218Conclusion
805.2 sp Hybridization
219Molecular Spectroscopy and High-Resolution Techniques
81Solved Problem:: Practice Problem:
22011.1 Introduction to High-Resolution Spectroscopy
825.3 sp2 Hybridization
22111.2 Microwave Spectroscopy
83Solved Problem:
22211.2.1 Principles of Microwave Spectroscopy
84Practice Problem:
22311.2.2 Experimental Methods and Instrumentation
85Solution to Practice Problem from Section 5.1:: Solution to Practice Problem from Section 5.2:
22411.2.3 Data Analysis and Group Theory Applications: Solved Examples and Practice Problems:
865.4 sp3 Hybridization
22511.3 Infrared Spectroscopy
87Solved Problem:: Practice Problem:
22611.3.1 Principles of Infrared Spectroscopy
885.5 Hypervalent Molecules
22711.3.2 Experimental Methods and Instrumentation
89Solved Problem:: Practice Problem:
22811.3.3 Data Analysis and Group Theory Applications
905.6 Molecular Geometry and VSEPR Theory
229Solved Examples and Practice Problems:
91The main postulates of the VSEPR theory are:
230Combination bands:: Overtones:
92Solved Problem:
23111.4 Nuclear Magnetic Resonance (NMR) Spectroscopy
93Practice Problem:
23211.4.1 Principles of NMR Spectroscopy
94Here are the solutions to the practice problems from the previous sections:
23311.4.2 Experimental Methods and Instrumentation
95Solution to Practice Problem from Section 5.4 (sp3 Hybridization):
23411.4.3 Data Analysis and Group Theory Applications: Solved Examples and Practice Problems:
96Solution to Practice Problem from Section 5.5 (Hypervalent Molecules):: Solution to Practice Problem from Section 5.6 (Molecular Geometry and VSEPR Theory):
23511.5 Electron Spin Resonance (ESR) Spectroscopy
97Conclusion
23611.5.1 Principles of ESR Spectroscopy
98Vibrational Spectroscopy and Symmetry
23711.5.2 Experimental Methods and Instrumentation
996.1 Introduction to Vibrational Spectroscopy
23811.5.3 Data Analysis and Group Theory Applications: Solved Examples and Practice Problems:
100Infrared (IR) Spectroscopy:
23911.6 Applications in Structure Determination
101Raman Spectroscopy:
24011.6.1 Structure Determination of Small Molecules
102Solved Problem:: Practice Problem:
24111.6.2 Structure Determination of Biomolecules
1036.2 Normal Modes of Vibration
24211.6.3 Structure Determination of Solid-State Materials
104Solved Problem:: Practice Problem:
243Solved Examples and Practice Problems:
1056.3 Symmetry of Normal Modes
244Here are the solutions to all the practice problems:
106Solved Problem:
245Practice Problem 1 (Section 11.3 Infrared Spectroscopy):
107Practice Problem:
246Practice Problem 2 (Section 11.5 Electron Spin Resonance (ESR) Spectroscopy):: Practice Problem 1 (Section 11.4 Nuclear Magnetic Resonance (NMR) Spectroscopy):
108Solution to Practice Problem from Section 6.1:
247Conclusion
109Solution to Practice Problem from Section 6.2:: Solution to Practice Problem from Section 6.3:
248Photochemistry and Symmetry
1106.4 Selection Rules for Infrared Spectroscopy
24912.1 Introduction to Photochemistry: Practice Problem 1:
111Solved Problem:: Practice Problem:
25012.2 Jablonski Diagrams
1126.5 Selection Rules for Raman Spectroscopy
25112.3 Excited State Dynamics
113Solved Problem:: Practice Problem:
252Radiative Processes:
1146.6 Mutual Exclusion Principle
253Non-Radiative Processes:
115Solved Problem:
254Practice Problem 3:: Practice Problem 4:
116Practice Problem:
25512.4 Photochemical Reactions: Practice Problem 1:
117Solution to Practice Problem from Section 6.4:
25612.5 Photoisomerization
118Solution to Practice Problem from Section 6.5:: Solution to Practice Problem from Section 6.6:
257Practice Problem 2:
119Conclusion
25812.6 Applications in Photochemical Synthesis: Practice Problem 3:
120Electronic Spectroscopy and Symmetry
259Conclusion
1217.1 Introduction to Electronic Spectroscopy
260Solid-State Chemistry and Group Theory
1227.2 Atomic Term Symbols
26113.1 Introduction to Solid-State Chemistry: Practice Problem 1:
1237.3 Molecular Term Symbols
26213.2 Crystal Field Theory: Practice Problem 2:
124Practice Problem 1 Solution:
26313.3 Ligand Field Theory: Practice Problem 3:
125Practice Problem 2 Solution:: Practice Problem 3 Solution:
26413.4 Molecular Magnetism: Practice Problem 1:
1267.4 Selection Rules for Electronic Transitions
26513.5 Superconductivity
1277.5 Laporte Selection Rule
266The BCS Theory of Superconductivity:
1287.6 Applications in UV-Vis Spectroscopy
267Group Theory and Superconductivity:
129Practice Problem 4 Solution:
2681. Symmetry of the Superconducting Order Parameter:
130Practice Problem 5 Solution:: Practice Problem 6 Solution:
2692. Electronic Structure and Fermi Surface:: Practice Problem 2:
131Conclusion
27013.6 Applications in Materials Science
132Stereochemistry and Chirality
2711. Crystal Structure Analysis:
1338.1 Introduction to Stereochemistry
2722. Electronic Structure and Band Theory:
1348.2 Chirality and Enantiomerism
2733. Spectroscopy and Vibrational Analysis:
1358.3 Point Groups and Chirality
2744. Magnetic Materials and Spin Systems:
136Practice Problem 1 Solution:
2755. Design and Development of Functional Materials:: Practice Problem 3:
137Practice Problem 2 Solution:: Practice Problem 3 Solution:
276Conclusion
1388.4 Stereochemical Descriptors (R/S, D/L)
277Glossary
139R/S System (Cahn-Ingold-Prelog System):: D/L System (Fischer Projection System):
278Index
