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.
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1 Molecular and Crystal Symmetries |
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1 | (48) |
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1 | (1) |
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1 | (1) |
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2 | (7) |
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9 | (1) |
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10 | (12) |
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1.6 Matrix Representation of Symmetry Operations |
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22 | (14) |
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1.7 Molecular Point Groups |
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36 | (2) |
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1.8 Determination of Molecular Point Groups |
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38 | (2) |
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1.9 Crystallographic Point Groups |
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40 | (1) |
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1.10 Point Group Notations |
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41 | (6) |
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47 | (2) |
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2 Elements of Group Theory and Multiplication Tables |
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49 | (74) |
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49 | (1) |
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2.2 Elements of Group Theory |
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49 | (16) |
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2.3 Classifications of Crystallographic Point Groups |
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65 | (2) |
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2.4 Construction of Group Multiplication Tables of 32 Point Groups |
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67 | (8) |
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75 | (48) |
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76 | (47) |
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3 Orthogonality Theorem and Character Tables |
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123 | (68) |
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123 | (1) |
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123 | (2) |
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3.3 Orthogonality Theorem |
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125 | (1) |
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3.4 Properties of Irreducible Representation |
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126 | (8) |
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3.5 Parts of a Character Table |
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134 | (1) |
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3.6 Characters of Representations in Point Groups |
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135 | (3) |
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3.7 Construction of Character Tables |
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138 | (14) |
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152 | (1) |
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3.9 Transformation Properties |
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153 | (2) |
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155 | (36) |
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Appendix: Character Tables |
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156 | (35) |
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4 Normal Modes of Molecular Vibrations |
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191 | (60) |
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191 | (1) |
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191 | (12) |
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4.3 Relationship Between Reducible and Irreducible Representations |
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203 | (1) |
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4.4 Characters of Matrices of Some Fundamental Symmetry Operations |
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204 | (5) |
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4.5 Determination of Overall Reducible Representation of Nonlinear Molecules |
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209 | (4) |
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4.6 Representations of Vibrational Modes of Nonlinear Molecules |
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213 | (3) |
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4.7 Vibrational Modes in Some Nonlinear Molecules |
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216 | (21) |
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4.8 Vibrational Modes in Some Linear Molecules |
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237 | (11) |
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248 | (3) |
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5 Vibrational Spectroscopy of Molecules |
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251 | (34) |
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251 | (1) |
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5.2 Some Useful Observations Concerning Molecular Vibrations |
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251 | (2) |
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5.3 General Survey of Vibrational Spectroscopy |
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253 | (1) |
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5.4 Infrared (IR) Spectral Region |
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253 | (1) |
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5.5 Theory of IR Absorption |
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254 | (4) |
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5.6 Infrared (IR) Spectrometer |
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258 | (3) |
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5.7 Fourier Transform Infrared (FTIR) Spectroscopy |
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261 | (2) |
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5.8 Role of Functional Groups in Vibrational Spectroscopy |
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263 | (2) |
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5.9 Nomenclature of Internal Modes of Vibration |
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265 | (1) |
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5.10 Theory of Raman Scattering |
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266 | (4) |
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270 | (1) |
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5.12 Fourier Transform (FT) Raman Spectrometer |
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271 | (1) |
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5.13 Symmetry Based on Some Useful General Conclusions |
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272 | (2) |
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5.14 Determination of Molecular Structures Using IR and Raman Results |
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274 | (4) |
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5.15 Correlation Between Super Group-Subgroup Species |
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278 | (3) |
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281 | (4) |
| Bibliography |
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285 | (2) |
| Index |
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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.
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