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Infrared Spectroscopy of Symmetric and Spherical Spindles for Space Observation 1


Infrared Spectroscopy of Symmetric and Spherical Spindles for Space Observation 1


1. Aufl.

von: Pierre-Richard Dahoo, Azzedine Lakhlifi

139,99 €

Verlag: Wiley
Format: EPUB
Veröffentl.: 23.04.2021
ISBN/EAN: 9781119824053
Sprache: englisch
Anzahl Seiten: 288

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Beschreibungen

This book is dedicated to the description and application of various different theoretical models to identify the near and mid-infrared spectra of symmetric and spherical top molecules in their gaseous form. <p>Theoretical models based on the use of group theory are applied to rigid and non-rigid molecules, characterized by the phenomenon of tunneling and large amplitude motions. The calculation of vibration-rotation energy levels and the analysis of infrared transitions are applied to molecules of ammonia (NH3) and methane (CH4). The applications show how interactions at the molecular scale modify the near and mid-infrared spectra of isolated molecules, under the influence of the pressure of a nano-cage (the substitution site of a rare gas matrix, clathrate, fullerene or zeolite) or a surface, and allow us to identify the characteristics of the perturbing environment. <p>This book provides valuable support for teachers and researchers but is also intended for engineering students, working research engineers and Master�s and doctorate students.
<p>Foreword ix<br /><i>Vincent BOUDON</i></p> <p>Preface xi</p> <p><b>Chapter 1. Group Theory in Infrared Spectroscopy </b><b>1</b></p> <p>1.1. Introduction 1</p> <p>1.2. The point-symmetry group of a molecule 2</p> <p>1.2.1. Symmetry operations and symmetry elements of a molecule 3</p> <p>1.2.2. Point symmetry group and laws of composition 6</p> <p>1.3. Representations by square matrices (general linear group of order <i>n </i>on <i>R </i>or <i>C</i>: GLn(R) or GLn(C)) 10</p> <p>1.3.1. Irreducible representations 10</p> <p>1.3.2. Equivalent representations 13</p> <p>1.4. Table of characters and fundamental theorems 14</p> <p>1.4.1. Tables of characters, classes and irreducible representations 14</p> <p>1.4.2. Irreducible representation of group <i>C<sub>3v</sub> </i>16</p> <p>1.4.3. Schur’s lemma 17</p> <p>1.4.4. Orthogonality and normalization theorem 18</p> <p>1.4.5. Orthogonality of lines 18</p> <p>1.4.6. Orthogonality of columns 20</p> <p>1.4.7. Decomposition of a reducible representation on an irreducible basis 20</p> <p>1.4.8. Projection operators for irreducible representations 21</p> <p>1.4.9. Characters of irreducible representations of the direct product of two groups 22</p> <p>1.5. Overall rotation group symmetry of a molecule 23</p> <p>1.6. Full symmetry group of the Hamiltonian of a molecule 26</p> <p>1.6.1. Permutation operations 27</p> <p>1.6.2. Permutation group <i>S<sub>n</sub> </i>28</p> <p>1.6.3. Complete nuclear permutation group (G<sup>CNP</sup>) of a molecule 30</p> <p>1.6.4. Inversion group ε and inversion operations <i>E<sup>*</sup> </i>and permutation-inversion operations <i>P<sup>*</sup> </i>30</p> <p>1.6.5. Permutation-inversion group G<sup>CNPI</sup> 31</p> <p>1.6.6. Group SO(3) isomorphic to permutation-inversion group G<sup>CNPI</sup> 32</p> <p>1.7. Correlation between the rotation group and a point-group symmetry of a molecule 34</p> <p>1.8. Example of group theory applications 39</p> <p>1.9. Conclusion 40</p> <p>1.10. Appendices: Groups and Lie algebra of SU(2) and SO(3) 40</p> <p>1.10.1. Appendix A: Groups SU(2) and SO(3) 40</p> <p>1.10.2. Appendix B: Lie algebra and SO(3) 42</p> <p><b>Chapter 2. Symmetry of Symmetric and Spherical Top Molecules </b><b>45</b></p> <p>2.1. Introduction 46</p> <p>2.2. Symmetry group of molecular Hamiltonian 47</p> <p>2.3. Symmetry of the NH<sub>3</sub> molecule and its isotopologues ND<sub>3</sub>, NHD<sub>2</sub> and NDH<sub>2</sub> 54</p> <p>2.3.1. Symmetry group of the symmetric molecular tops NH<sub>3</sub> and ND<sub>3</sub> 54</p> <p>2.3.2. Symmetry group of asymmetric molecular tops NHD<sub>2</sub> and NDH<sub>2</sub> 56</p> <p>2.3.3. Symmetry group of the complete group taking into account the inversion 57</p> <p>2.4. Symmetry of CH<sub>4</sub> and its isotopologues CD<sub>4</sub>, CHD<sub>3</sub>, CDH<sub>3</sub> and CH<sub>2</sub>D<sub>2</sub> 59</p> <p>2.4.1. Symmetry group of spherical tops CH<sub>4</sub> and CD<sub>4</sub> 59</p> <p>2.4.2. Symmetry group of symmetric tops CHD<sub>3</sub> and CDH<sub>3</sub> 61</p> <p>2.4.3. Symmetry group of the asymmetric top CH<sub>2</sub>D<sub>2</sub> 62</p> <p>2.5. Symmetry group of the complete CNPI group 62</p> <p>2.6. Conclusion 66</p> <p><b>Chapter 3. Line Profiles, Symmetries and Selection Rules According to Group Theory </b><b>67</b></p> <p>3.1. Introduction 68</p> <p>3.2. Symmetries of the eigenstates of the zeroth-order Hamiltonian 70</p> <p>3.3. Intensity of the vibration–rotation lines and bar spectrum 72</p> <p>3.4. Transition operator for the selection rules 74</p> <p>3.5. Dipole moment operator and line profile 77</p> <p>3.6. Irreducible representations of the vibrations of the molecules 82</p> <p>3.6.1. Procedure for the decomposition of the reducible representation 82</p> <p>3.6.2. Case of symmetric tops XY<sub>3</sub> and XZY<sub>3</sub> (NH<sub>3</sub>, ND<sub>3</sub>, CDH<sub>3</sub>, CHD<sub>3</sub>) 84</p> <p>3.6.3. Case of spherical top XY<sub>4</sub> (CH<sub>4</sub>, CD<sub>4</sub>) 88</p> <p>3.6.4. Case of the asymmetric top XY<sub>2</sub>Z<sub>2</sub> (CH<sub>2</sub>D<sub>2</sub>) 90</p> <p>3.6.5. Case of the asymmetric top XY<sub>2</sub>Z (NDH<sub>2</sub> or NHD<sub>2</sub>) 92</p> <p>3.6.6. Case of inversion for NH<sub>3</sub>, ND<sub>3</sub>, NDH<sub>2</sub> and NHD<sub>2</sub> 93</p> <p>3.7. Types of vibrations of irreducible representations 93</p> <p>3.7.1. Case of symmetric tops XY<sub>3</sub> and XZY<sub>3</sub> (NH<sub>3</sub>, ND<sub>3</sub>, CDH<sub>3</sub>, CHD<sub>3</sub>) 93</p> <p>3.7.2. Case of spherical top XY<sub>4</sub> (CH<sub>4</sub>, CD<sub>4</sub>) 100</p> <p>3.7.3. Case of the asymmetric top XY<sub>2</sub>Z<sub>2</sub> (CD<sub>2</sub>H<sub>2</sub>) 105</p> <p>3.7.4. Case of the asymmetric top XY<sub>2</sub>Z (NDH<sub>2</sub> or NHD<sub>2</sub>) 108</p> <p>3.8. Rotation and spin Hamiltonian symmetries 111</p> <p>3.8.1. Vibronic degrees of freedom of NH<sub>3</sub> and CH<sub>4</sub> 111</p> <p>3.8.2. Rovibronic degrees of freedom 114</p> <p>3.8.3. Rotational degrees of freedom 116</p> <p>3.8.4. Spin degrees of freedom 123</p> <p>3.8.5. IR and Raman selection rules for the rotational levels 133</p> <p>3.9. Conclusion 134</p> <p>3.10. Appendix: Absorption and emission of a molecule in the gas phase 134</p> <p><b>Chapter 4. Energy Levels of Symmetric Tops in the Gas Phase </b><b>139</b></p> <p>4.1. Introduction 140</p> <p>4.2. Vibrational–rotational motions of an isolated symmetric top 141</p> <p>4.3. Vibrational motions of an isolated pyramidal symmetric top 146</p> <p>4.3.1. Kinetic and potential energy functions 146</p> <p>4.3.2. Harmonic oscillators – classical approach 147</p> <p>4.3.3. Separation of vibrational modes 160</p> <p>4.3.4. Harmonic oscillators – quantum approach 161</p> <p>4.3.5. Molecular vibrations beyond the harmonic approximation 165</p> <p>4.3.6. Intrinsic inversion phenomenon of certain pyramidal molecules of type XY<sub>3</sub> 166</p> <p>4.3.7. Transitions between two vibrational levels: selection rules 169</p> <p>4.4. Rotational motion of an isolated rigid symmetric top molecule 171</p> <p>4.4.1. Rotational kinetic Hamiltonian and energy level scheme 171</p> <p>4.4.2. Transitions between two rotational levels: selection rules 173</p> <p>4.5. Rovibrational energy levels of an isolated symmetric top and selection rules 175</p> <p>4.6. Application to the ammonia NH<sub>3</sub> molecule 177</p> <p>4.6.1. Geometric, rotational and vibrational characteristics 177</p> <p>4.6.2. Vibrational motions in the harmonic approximation 178</p> <p>4.6.3. Vibrational motions beyond the harmonic approximation 181</p> <p>4.6.4. Vibration-inversion mode 182</p> <p>4.6.5. Dipole moment as a function of normal coordinates 184</p> <p>4.7. Appendices 184</p> <p>4.7.1. Appendix A: Rotation matrix 184</p> <p>4.7.2. Appendix B: Expressions of force constants 185</p> <p>4.7.3. Appendix C: Rotational moments of transition 189</p> <p>4.7.4. Appendix D: Values of non-zero anharmonic vibrational force constants and corrected eigenvectors 192</p> <p><b>Chapter 5. Spherical Top CH<sub>4</sub> </b><b>195</b></p> <p>5.1. Introduction 195</p> <p>5.2. Characteristics of the CH<sub>4</sub> molecule in gas phase 199</p> <p>5.3. Tensor formalism for the CH<sub>4</sub> molecule 202</p> <p>5.3.1. Orientation of SO(3) in <i>T<sub>d</sub> </i>204</p> <p>5.3.2. Vibrational tensor operators 207</p> <p>5.3.3. Rotational tensor operators 215</p> <p>5.3.4. Rovibrational tensor operators 218</p> <p>5.3.5. Expression of the rovibrational Hamiltonian 218</p> <p>5.3.6. Expression of the vibration wave functions 219</p> <p>5.3.7. Expression of rotational wave functions 219</p> <p>5.3.8. Expression of rovibrational wave functions 221</p> <p>5.4. Application to the CH<sub>4</sub> molecule 221</p> <p>5.4.1. Electric dipole transition moment 222</p> <p>5.4.2. Polarizability 225</p> <p>5.5. Rotational structure in the degenerate vibrational levels 228</p> <p>5.5.1. The degenerate vibrational level <i>v<sub>2</sub> </i>= 1 229</p> <p>5.5.2. The degenerate vibrational level <i>v<sub>s</sub> </i>= 1 (<i>s </i>= 3 or 4) 230</p> <p>5.5.3. Vibration–rotation Coriolis interaction 233</p> <p>5.6. Conclusion 236</p> <p>5.7. Appendices 236</p> <p>5.7.1. Appendix A: Quantum mechanics review 236</p> <p>5.7.2. Appendix B: Creation and annihilation operators 239</p> <p>5.7.3. Appendix C: Clebsch–Gordan coefficients and Wigner <i>3j</i>-symbols 241</p> <p>5.7.4. Appendix D: Tensor operators and the Wigner–Eckart theorem 242</p> <p>5.7.5. Appendix E: Hamiltonian as a function of dimensionless normal coordinates up to fourth order 243</p> <p>5.7.6. Appendix F: Hamiltonian transformed using the contact method 245</p> <p>References 249</p> <p>Index 259</p>
<p><b>Pierre-Richard Dahoo</b> is Professor and Holder of the Chair Materials Simulation and Engineering at the University of Versailles Saint-Quentin in France. He is Director of Institut des Sciences et Techniques des Yvelines and a specialist in modeling and spectroscopy at the LATMOS laboratory of CNRS. <p><b>Azzedine Lakhlifi</b> is Senior Lecturer at the University of Franche-Comte and a researcher, specializing in modeling and spectroscopy at UTINAM Institute, UMR 6213 CNRS, OSU THETA Franche-Comte Bourgogne, University Bourgogne Franche-Comte, Besancon, France.

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