The theoretical models described in Volumes 1, 2 and 3 are used in this volume, applying the cumulant theorem in the mean-field theory framework to interpret the near and mid-infrared spectra of symmetric top molecules, such as ammonia (NH3) and spherical molecules, such as methane (CH4). These molecules can be isolated in their gaseous form or subjected to the environmental constraints of a nano-cage (a substitution site, clathrate, fullerene or zeolite) or surfaces.
These methods are not only valuable in the fields of environmental sciences, planetology and astrophysics, but also fit into the framework of data processing and the concept of Big Data.
Table of Contents
Foreword ix
Pierre DROSSART
Preface xi
Chapter 1. IR Spectra in Space Observation 1
1.1. Introduction 1
1.2. Fourier transform spectroscopy 7
1.2.1. Principle of IR spectrum acquisition by interferometry 9
1.2.2. Design and operation of a long path difference interferometer 11
1.2.3. FTIR absorption spectroscopy in matrices 14
1.2.4. LIF and DR IR-IR spectroscopies in matrices 21
1.3. Resonant cavity laser absorption spectroscopy 26
1.3.1. Intracavity laser absorption spectroscopy (ICLAS) 30
1.3.2. Cavity ring-down spectroscopy (CRDS) 33
1.3.3. Frequency comb spectroscopy (FCS) 38
1.4. Spectroscopy for space observation 43
1.4.1. Spectroscopic ellipsometry for space observation 43
1.4.2. Space-borne spectroscopy 56
1.4.3. LIDAR spectroscopy for space observation 60
1.5. Conclusion 64
1.6. Appendices 64
1.6.1. Appendix 1: Measurement distortion and data processing 64
Chapter 2. Interactions Between a Molecule and Its Solid Environment 71
2.1. Introduction 72
2.2. Active molecule - solid environment system 74
2.2.1. Binary interaction energy 74
2.2.2. Dispersion-repulsion contribution 76
2.2.3. Electrostatic contribution 76
2.2.4. Induction contribution 78
2.3. Two-center expansion of the term 79
2.4. Conclusion 81
2.5. Appendices 82
2.5.1. Appendix 1: Multipole moments and dipole polarizability of a molecule with respect to its fixed reference frame 82
2.5.2. Appendix 2: Elements of the rotational matrix 82
2.5.3. Appendix 3: Clebsch-Gordan coefficients 84
Chapter 3. Nanocage of Rare Gas Matrix 87
3.1. Introduction 87
3.2. Rare gases in solid state 88
3.3. Molecule inclusion and deformation of the doped crystal 90
3.3.1. Molecule inclusion 90
3.3.2. Deformation of the doped crystal 92
3.3.3. NH3 in an argon matrix 95
3.3.4. Renormalization of the system’s Hamiltonian 96
3.4. Motions of NH3 trapped in an argon matrix 97
3.4.1. Vibration-inversion mode ν2 98
3.4.2. Orientational motion 100
3.4.3. Translational motion 106
3.4.4. Orientational motion-heat bath coupling 107
3.5. Infrared spectra 108
3.5.1. Infrared absorption coefficient 108
3.5.2. Bar spectrum 109
3.5.3. Spectral profile 112
3.6. Appendices 116
3.6.1. Appendix 1: Normal modes of vibrations of a Bravais lattice with face centered cubic (fcc) symmetry 116
3.6.2. Appendix 2: Adjustment of the weakly perturbed rotational potential energy on the basis of the rotation matrix elements 120
3.6.3. Appendix 3: Expansion coefficients of the coupling between the orientation of the molecule and lattice vibrations (phonons) 121
Chapter 4. Nanocages of Hydrate Clathrates 123
4.1. Introduction 123
4.2. The extended substitution model 124
4.3. Clathrate structures 129
4.4. Inclusion of a CH4 or NH3 molecule in a clathrate nanocage 131
4.4.1. Inclusion model 131
4.4.2. Interaction potential energy - equilibrium configuration 133
4.5. System Hamiltonian and separation of movements 136
4.6. Translational motion 139
4.6.1. CH4 - nanocages of the sI structure 140
4.6.2. NH3 - nanocages of the sI structure 141
4.7. Vibrational motions 142
4.7.1. CH4 - nanocages of the sI structure 143
4.7.2. NH3 - nanocages of the sI structure 144
4.8. Orientational motion 145
4.8.1. CH4 - nanocages of the sI structure 145
4.8.2. NH3 - nanocages of the sI structure 149
4.9. Bar spectra 157
4.9.1. Far infrared 157
4.9.2. Near infrared 159
4.10. Appendices 162
4.10.1. Appendix 1: Expressions of the orientational transition elements in the harmonic librators approximation 162
4.10.2. Appendix 2: Dipole moment as a function of dimensionless normal coordinates 164
Chapter 5. Fullerene Nanocage 169
5.1. Introduction 170
5.2. Ammonia molecule trapped in a fullerene C60 nanocage 171
5.2.1. Structure of the fullerene C60 nanocage 171
5.2.2. Inclusion of NH3 in a fullerene C60 nanocage 172
5.2.3. Interaction potential energy - equilibrium configuration 174
5.3. Potential energy surfaces - inertial model 176
5.3.1. Orientation-translational motion 176
5.3.2. Translational motion 178
5.3.3. Vibration-inversion-translational motion 179
5.3.4. Kinetic Lagrangian 179
5.4. Quantum treatment 182
5.4.1. Vibrational modes - frequency shifts 182
5.4.2. Vibration-inversion mode 183
5.4.3. Orientational motions 185
5.5. Bar spectra 187
5.5.1. Far infrared and microwaves 188
5.5.2. Near infrared 188
5.6. Appendices 190
5.6.1. Appendix 1: FORTRAN program 190
5.6.2. Appendix 2: Expressions of the components of the dipole moment vector and its derivatives with respect to the normal vibrational coordinates 211
Chapter 6. Adsorption on a Graphite Substrate 213
6.1. Introduction 213
6.2. “NH3 molecule-substrate” system interaction energy 214
6.2.1. Description of the system 214
6.2.2. “NH3 molecule-graphite substrate” interaction energy 216
6.3. Equilibrium configuration and potential energy surfaces 218
6.3.1. Adsorption energy 221
6.4. Hamiltonian of the system 221
6.4.1. Separation of movements 223
6.4.2. Renormalized Hamiltonians 224
6.4.3. Translational motions 224
6.4.4. Vibrational motions 225
6.4.5. Orientational motion 230
6.4.6. Orientational motion - heat bath dynamic coupling 235
6.5. Infrared spectra of the NH3 molecule adsorbed on the graphite substrate 235
6.5.1. Far-infrared spectrum 237
6.5.2. Near-infrared spectrum 240
6.6. Conclusion 246
6.7. Appendices 246
6.7.1. Appendix 1: FORTRAN program 246
6.7.2. Appendix 2: Expressions of the molecule orientation - heat bath phonons coupling terms 259
6.7.3. Appendix 3: Expressions of the components of the dipole moment vector and its derivatives with respect to the normal vibration coordinates 259
References 261
Index 293
