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Chemical Applications of Group Theory, An Indian Adaptation

F. Albert Cotton

ISBN: 9788194726364

484 pages

INR 699


Chemical Applications of Group Theory is a well-established textbook that explains the principles of molecular and crystallographic symmetry and their immense significance. It aims to teach the use of symmetry arguments to the typical experimental chemist in a meaningful and useful manner and serves as the first introduction for students intending to pursue theoretical work in the field. It 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.

Part I. Principle


1. Introduction to Symmetry

1.1 Molecular Symmetry in Everyday Life

1.2 Symmetry and Chemistry

1.3 Symmetry in Crystallography

1.4 Conclusions


2. Definitions and Theorems of Group Theory

2.1 The Defining Properties of a Group

2.2 Some Examples of Groups

2.3 Subgroups

2.4 Classes


3. Molecular Symmetry and the Symmetry Groups

3.1 General Remarks

3.2 Symmetry Elements and Operations

3.3 Symmetry Planes and Reflections

3.4 The Inversion Center

3.5 Proper Axes and Proper Rotations

3.6 Improper Axes and Improper Rotations

3.7 Products of Symmetry Operations

3.8 Equivalent Symmetry Elements and Equivalent Atoms

3.9 General Relations Among Symmetry Elements and Operations

3.10 Symmetry Elements and Optical Isomerism

3.11 The Symmetry Point Groups

3.12 Symmetries with Multiple High-Order Axes

3.13 Classes of Symmetry Operations

3.14 A Systematic Procedure for Symmetry Classification of Molecules

3.15 Illustrative Examples


4. Representations of Groups

4.1 Prefactory Comments on Matrices and Vectors

4.2 Representations of Groups

4.3 The “Great Orthogonality Theorem” and Its Consequences

4.4 Character Tables

4.5 Representations for Cyclic Groups


5. Role of Quantum Mechanics in Group Theory

5.1 Wave Functions as Bases for Irreducible Representations

5.2 The Direct Product

5.3 Identifying Nonzero Matrix Elements

5.4 Symmetry-Adapted Linear Combinations

5.5 Derivation of Projection Operators

5.6 Using Projection Operators to Construct SALCs



6. Molecular Orbital Theory and its Applications in Organic Chemistry

6.1 General Principles

6.2 Symmetry Factoring of Secular Equations

6.3 Carbocyclic Systems

6.4 More General Cases of LCAO-MO π Bonding

6.5 A Worked Example: Naphthalene

6.6 Electronic Excitations of Naphthalene: Selection Rules and Configuration Interaction

6.7 Three-Center Bonding

6.8 Symmetry-Based “Selection Rules” for Cyclization Reactions


7. Molecular Orbital Theory for Inorganic and Organometallic Compounds

7.1 Introduction

7.2 Transformation Properties of Atomic Orbitals

7.3 Molecular Orbitals For σ Bonding in ABn Molecules: The Tetrahedral AB4 Case

7.4 Molecular Orbitals for σ Bonding in Other ABn Molecules

7.5 Hybrid Orbitals

7.6 Molecular Orbitals for π Bonding in ABn Molecules

7.7 Cage and Cluster Compounds

7.8 Molecular Orbitals for Metal Sandwich Compounds


8. Ligand Field Theory

8.1 Introductory Remarks

8.2 Electronic Structures of Free Atoms and Ions

8.3 Splitting of Levels and Terms in a Chemical Environment

8.4 Construction of Energy Level Diagrams

8.5 Estimation of Orbital Energies

8.6 Selection Rules and Polarizations

8.7 Double Groups


9. Molecular Vibrations

9.1 Introductory Remarks

9.2 The Symmetry of Normal Vibrations

9.3 Determining the Symmetry Types of the Normal Modes

9.4 Contributions of Particular Internal Coordinates to Normal Modes

9.5 How to Calculate Force Constants: The F and G Matrix Method

9.6 Selection Rules for Fundamental Vibrational Transitions

9.7 Applications of Group Theory in Raman and Infrared Spectroscopy

9.8 Some Important Special Effects


10. Crystallographic Symmetry

10.1 Introduction

10.2 The Concept of A Lattice—In Two Dimensions

10.3 Two-Dimensional Space Symmetries

10.4 Three-Dimensional Lattices and Their Symmetries

10.5 Crystal Symmetry: The 32 Crystallographic Point Groups

10.6 Interrelating Lattice Symmetry, Crystal Symmetry, and Diffraction Symmetry

10.7 Additional Symmetry Elements and Operations: Glide Planes and Screw Axes

10.8 Representation of Three-Dimensional Space Groups

10.9 Elements of X-Ray Diffraction

10.10 Determination of Space Groups and Applications in X-Ray Crystallography



I. Matrix Algebra

IIA. Character Tables for Chemically Important Symmetry Groups

IIB. Correlation Table for Group Oh

III. Some Remarks about the Resonance Integral β

IV. The Shapes of f-Orbitals

V. Character Tables for some Double Groups

VI. Elements of the g Matrix

VII. Stereographic Projections for the 32 Crystallographic Point Groups

VIII. The 230 Space Groups

IX. Reading List