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.
Author(s): M. A. Wahab
Series: Springer Series in Chemical Physics, 126
Publisher: Springer
Year: 2022
Language: English
Pages: 299
City: Singapore
Preface
The Electromagnetic Spectrum
Contents
About the Author
1 Molecular and Crystal Symmetries
1.1 Introduction
1.2 Symmetry Elements
1.3 Symmetry Operations
1.4 Molecular Symmetries
1.5 Elements of Matrices
1.6 Matrix Representation of Symmetry Operations
1.7 Molecular Point Groups
1.8 Determination of Molecular Point Groups
1.9 Crystallographic Point Groups
1.10 Point Group Notations
1.11 Summary
2 Elements of Group Theory and Multiplication Tables
2.1 Introduction
2.2 Elements of Group Theory
2.3 Classifications of Crystallographic Point Groups
2.4 Construction of Group Multiplication Tables of 32 Point Groups
2.5 Summary
Appendix
Group Multiplication Tables of 32 Point Groups
3 Orthogonality Theorem and Character Tables
3.1 Introduction
3.2 Representations
3.3 Orthogonality Theorem
3.4 Properties of Irreducible Representation
3.5 Parts of a Character Table
3.6 Characters of Representations in Point Groups
3.7 Construction of Character Tables
3.8 Mulliken Symbols
3.9 Transformation Properties
3.10 Summary
Appendix: Character Tables
Character Tables for Some Important Point Groups using Schoenflies Notation
Character Tables for Linear Molecules
4 Normal Modes of Molecular Vibrations
4.1 Introduction
4.2 Molecular Motions
4.3 Relationship Between Reducible and Irreducible Representations
4.4 Characters of Matrices of Some Fundamental Symmetry Operations
4.5 Determination of Overall Reducible Representation of Nonlinear Molecules
4.6 Representations of Vibrational Modes of Nonlinear Molecules
4.7 Vibrational Modes in Some Nonlinear Molecules
4.8 Vibrational Modes in Some Linear Molecules
4.9 Summary
5 Vibrational Spectroscopy of Molecules
5.1 Introduction
5.2 Some Useful Observations Concerning Molecular Vibrations
5.3 General Survey of Vibrational Spectroscopy
5.4 Infrared (IR) Spectral Region
5.5 Theory of IR Absorption
5.6 Infrared (IR) Spectrometer
5.7 Fourier Transform Infrared (FTIR) Spectroscopy
5.8 Role of Functional Groups in Vibrational Spectroscopy
5.9 Nomenclature of Internal Modes of Vibration
5.10 Theory of Raman Scattering
5.11 Raman Spectrometer
5.12 Fourier Transform (FT) Raman Spectrometer
5.13 Symmetry Based on Some Useful General Conclusions
5.14 Determination of Molecular Structures Using IR and Raman Results
5.15 Correlation Between Super Group-Subgroup Species
5.16 Summary
Bibliography
Index
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