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El. knyga: Symmetry Representations of Molecular Vibrations

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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.

1 Molecular and Crystal Symmetries
1(48)
1.1 Introduction
1(1)
1.2 Symmetry Elements
1(1)
1.3 Symmetry Operations
2(7)
1.4 Molecular Symmetries
9(1)
1.5 Elements of Matrices
10(12)
1.6 Matrix Representation of Symmetry Operations
22(14)
1.7 Molecular Point Groups
36(2)
1.8 Determination of Molecular Point Groups
38(2)
1.9 Crystallographic Point Groups
40(1)
1.10 Point Group Notations
41(6)
1.11 Summary
47(2)
2 Elements of Group Theory and Multiplication Tables
49(74)
2.1 Introduction
49(1)
2.2 Elements of Group Theory
49(16)
2.3 Classifications of Crystallographic Point Groups
65(2)
2.4 Construction of Group Multiplication Tables of 32 Point Groups
67(8)
2.5 Summary
75(48)
Appendix
76(47)
3 Orthogonality Theorem and Character Tables
123(68)
3.1 Introduction
123(1)
3.2 Representations
123(2)
3.3 Orthogonality Theorem
125(1)
3.4 Properties of Irreducible Representation
126(8)
3.5 Parts of a Character Table
134(1)
3.6 Characters of Representations in Point Groups
135(3)
3.7 Construction of Character Tables
138(14)
3.8 Mulliken Symbols
152(1)
3.9 Transformation Properties
153(2)
3.10 Summary
155(36)
Appendix: Character Tables
156(35)
4 Normal Modes of Molecular Vibrations
191(60)
4.1 Introduction
191(1)
4.2 Molecular Motions
191(12)
4.3 Relationship Between Reducible and Irreducible Representations
203(1)
4.4 Characters of Matrices of Some Fundamental Symmetry Operations
204(5)
4.5 Determination of Overall Reducible Representation of Nonlinear Molecules
209(4)
4.6 Representations of Vibrational Modes of Nonlinear Molecules
213(3)
4.7 Vibrational Modes in Some Nonlinear Molecules
216(21)
4.8 Vibrational Modes in Some Linear Molecules
237(11)
4.9 Summary
248(3)
5 Vibrational Spectroscopy of Molecules
251(34)
5.1 Introduction
251(1)
5.2 Some Useful Observations Concerning Molecular Vibrations
251(2)
5.3 General Survey of Vibrational Spectroscopy
253(1)
5.4 Infrared (IR) Spectral Region
253(1)
5.5 Theory of IR Absorption
254(4)
5.6 Infrared (IR) Spectrometer
258(3)
5.7 Fourier Transform Infrared (FTIR) Spectroscopy
261(2)
5.8 Role of Functional Groups in Vibrational Spectroscopy
263(2)
5.9 Nomenclature of Internal Modes of Vibration
265(1)
5.10 Theory of Raman Scattering
266(4)
5.11 Raman Spectrometer
270(1)
5.12 Fourier Transform (FT) Raman Spectrometer
271(1)
5.13 Symmetry Based on Some Useful General Conclusions
272(2)
5.14 Determination of Molecular Structures Using IR and Raman Results
274(4)
5.15 Correlation Between Super Group-Subgroup Species
278(3)
5.16 Summary
281(4)
Bibliography 285(2)
Index 287
M. A. WAHAB is Former Professor and Head of the Department of Physics, Jamia Millia Islamia, New Delhi, India. He completed his Ph.D. (Physics) from the University of Delhi, India, and M.Sc. (Physics) from Aligarh Muslim University, India. Earlier, he served as a lecturer at the P. G. Department of Physics and Electronics, University of Jammu, Jammu and Kashmir, India, from 1981, and later, at the P. G. Department of Physics, Jamia Millia Islamia, from 1985. During these years, he taught electrodynamics, statistical mechanics, theory of relativity, advance solid state physics, crystallography, physics of materials, growth and imperfections of materials, and general solid state physics. He has authored 4 books: Solid State Physics, Essentials of Crystallography, and Numerical Problems in Solid State Physics, and Numerical problems in Crystallography (from Springer Nature). He has also published over 100 research papers in national and international journals of repute and supervised 15 Ph.D. theses during his career at Jamia Millia Islamia. Professor Wahab has published the discovery of hexagonal close packing (HCP) and rhombohedral close packing (RCP) as the two new space lattices, along with his son (Mr. Khurram Mujtaba Wahab), as their first joint paper after his retirement.