Chemical Applications of Group Theory

by Cotton, F. Albert

• ISBN13: 9780471510949
• ISBN10: 0471510947
• Edition: 3rd
• Format: Hardcover
• Copyright: 1991-01-16
• Publisher: Wiley-Interscience
• More Book Details

Summary

Retains the easy-to-read format and informal flavor of the previous editions, and includes new material on the symmetric properties of extended arrays (crystals), projection operators, LCAO molecular orbitals, and electron counting rules. Also contains many new exercises and illustrations.

Author Biography

F. ALBERT COTTON, PhD, is a professor in the Department of Chemistry at Texas A&M University.

Table of Contents

Part I. Principles
Introduction	3	(14)
Definitions and Theorems of Group Theory
The Defining Properties of a Group	6	(2)
Some Examples of Groups	8	(4)
Subgroups	12	(1)
Classes	13	(4)
Exercises	16	(1)
Molecular Symmetry and the Symmetry Groups	17	(51)
General Remarks	17	(1)
Symmetry Elements and Operations	18	(1)
Symmetry Planes and Reflections	18	(4)
The Inversion Center	22	(1)
Proper Axes and Proper Rotations	22	(5)
Improper Axes and Improper Rotations	27	(2)
Products of Symmetry Operations	29	(3)
Equivalent Symmetry Elements and Equivalent Atoms	32	(1)
General Relations Among Symmetry Elements and Operations	33	(1)
Symmetry Elements and Optical Isomerism	34	(5)
The Symmetry Point Groups	39	(5)
Symmetries with Multiple High-Order Axes	44	(6)
Classes of Symmetry Operations	50	(4)
A Systematic Procedure for Symmetry Classification of Molecules	54	(2)
Illustrative Examples	56	(12)
Exercises	61	(7)
Representations of Groups	68	(32)
Prefactory Comments on Matrices and Vectors	68	(10)
Representations of Groups	78	(3)
The ``Great Orthogonality Theorem'' and Its Consequences	81	(9)
Character Tables	90	(5)
Representations for Cyclic Groups	95	(5)
Exercises	99	(1)
Group Theory and Quantum Mechanics	100	(14)
Wave Functions as Bases for Irreducible Representations	100	(5)
The Direct Product	105	(4)
Identifying Nonzero Matrix Elements	109	(5)
Exercises	113	(1)
Symmetry-Adapted Linear Combinations	114	(19)
Introductory Remarks	114	(1)
Derivation of Projection Operators	115	(4)
Using Projection Operators to Construct SALCs	119	(14)
Exercises	129	(4)
Part II. Applications
Molecular Orbital Theory and Its Applications in Organic Chemistry	133	(71)
General Principles	133	(7)
Symmetry Factoring of Secular Equations	140	(2)
Carbocyclic Systems	142	(17)
More General Cases of LCAO--MO π Bonding	159	(13)
A Worked Example: Naphthalene	172	(4)
Electronic Excitations of Naphthalene: Selection Rules and Configuration Interaction	176	(4)
Three-Center Bonding	180	(8)
Symmetry-Based ``Selection Rules'' for Cyclization Reactions	188	(16)
Exercises	201	(3)
Molecular Orbital Theory for Inorganic and Organometallic Compounds	204	(49)
Introduction	204	(1)
Transformation Properties of Atomic Orbitals	205	(4)
Molecular Orbitals for σ Bonding in ABn Molecules: The Tetrahedral AB4 Case	209	(5)
Molecular Orbitals for σ Bonding in Other ABn Molecules	214	(8)
Hybrid Orbitals	222	(5)
Molecular Orbitals for π Bonding in ABn Molecules	227	(3)
Cage and Cluster Compounds	230	(10)
Molecular Orbitals for Metal Sandwich Compounds	240	(13)
Exercises	251	(2)
Ligand Field Theory	253	(51)
Introductory Remarks	253	(1)
Electronic Structures of Free Atoms and Ions	254	(6)
Splitting of Levels and Terms in a Chemical Environment	260	(5)
Construction of Energy Level Diagrams	265	(16)
Estimation of Orbital Energies	281	(8)
Selection Rules and Polarizations	289	(8)
Double Groups	297	(7)
Exercises	302	(2)
Molecular Vibrations	304	(44)
Introductory Remarks	304	(1)
The Symmetry of Normal Vibrations	305	(4)
Determining the Symmetry Types of the Normal Modes	309	(6)
Contributions of Particular Internal Coordinates to Normal Modes	315	(2)
How to Calculate Force Constants: The F and G Matrix Method	317	(7)
Selection Rules for Fundamental Vibrational Transitions	324	(4)
Illustrative Examples	328	(10)
Some Important Special Effects	338	(10)
Exercises	346	(2)
Crystallographic Symmetry	348	(109)
Introduction	348	(2)
The Concept of a Lattice---In Two Dimensions	350	(8)
Two-Dimensional Space Symmetries	358	(10)
Three-Dimensional Lattices and Their Symmetries	368	(7)
Crystal Symmetry: The 32 Crystallographic Point Groups	375	(5)
Interrelating Lattice Symmetry, Crystal Symmetry, and Diffraction Symmetry	380	(4)
Additional Symmetry Elements and Operations: Glide Planes and Screw Axes	384	(4)
The 230 Three-Dimensional Space Groups	388	(12)
Space Groups and X-Ray Crystallography	400	(17)
Exercises	410	(7)
Part III. Appendices
I. Matrix Algebra	417	(9)
IIA. Character Tables for Chemically Important Symmetry Groups	426	(11)
IIB. Correlation Table for Group Oh	437	(1)
III. Some Remarks About the Resonance Integral β	438	(3)
IV. The Shapes of f Orbitals	441	(2)
V. Character Tables for Some Double Groups	443	(1)
VI. Elements of The g Matrix	444	(4)
VII. Stereographic Projections for the 32 Crystallographic Point Groups	448	(2)
VIII. The 230 Space Groups	450	(2)
IX. Reading List	452	(5)
Index	457