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This book presents a comprehensive theoretical basis of symmetry representations of molecular vibrations, matrix representation of symmetries, and the elements of group theory that are relevant to other symmetry elements/operations, crystallographic and molecular point groups. The book helps understand the reducible and irreducible representations of symmetry matrices and then derive the normal modes of vibration of different molecules by using suitable techniques independently. Targeted to graduate students and researchers, this book aims not only to derive the normal modes of vibration of any given molecule themselves but also compares and verifies them with the experimentally found modes by using IR and Raman-related techniques. For the first time in the crystallographic history, this book presents the group multiplication tables of all 32 point groups in both international and Schoenflies notations.
Preface
The Electromagnetic Spectrum
About the Author
Molecular and Crystal Symmetries
Introduction
Symmetry Elements
Symmetry Operations
Molecular Symmetries
Elements of Matrices
Matrix Representation of Symmetry Operations
Molecular Point Groups
Determination of Molecular Point Groups
Crystallographic Point Groups
Point Group Notations
Summary
Elements of Group Theory and Multiplication Tables
Introduction
Elements of Group Theory
Classifications of Crystallographic Point Groups
Construction of Group Multiplication Tables of Point Groups
Summary
Appendix
Group Multiplication Tables of Point Groups
Orthogonality Theorem and Character Tables
Introduction
Representations
Orthogonality Theorem
Properties of Irreducible Representation
Parts of a Character Table
Characters of Representations in Point Groups
Construction of Character Tables
Mulliken Symbols
Transformation Properties
Summary
Appendix: Character Tables
Character Tables for Some Important Point Groups using Schoenflies Notation
Character Tables for Linear Molecules
Normal Modes of Molecular Vibrations
Introduction
Molecular Motions
Relationship Between Reducible and Irreducible Representations
Characters of Matrices of Some Fundamental Symmetry Operations
Determination of Overall Reducible Representation of Nonlinear Molecules
Representations of Vibrational Modes of Nonlinear Molecules
Vibrational Modes in Some Nonlinear Molecules
Vibrational Modes in Some Linear Molecules
Summary
Vibrational Spectroscopy of Molecules
Introduction
Some Useful Observations Concerning Molecular Vibrations
General Survey of Vibrational Spectroscopy
Infrared (IR) Spectral Region
Theory of IR Absorption
Infrared (IR) Spectrometer
Fourier Transform Infrared (FTIR) Spectroscopy
Role of Functional Groups in Vibrational Spectroscopy
Nomenclature of Internal Modes of Vibration
Theory of Raman Scattering
Raman Spectrometer
Fourier Transform (FT) Raman Spectrometer
Symmetry Based on Some Useful General Conclusions
Determination of Molecular Structures Using IR and Raman Results
Correlation Between Super Group-Subgroup Species
Summary
Bibliography
Index
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