Infrared Spectroscopy of Diatomics for Space Observation

ISBN-13: 9781786301161 / Angielski / Twarda / 2018 / 240 str.

Pierre Richard Dahoo; Azzedine Lakhlifi

Opis

This book presents theoretical models for the calculation of the absorption spectrum in the infrared region of a diatomic molecule in the gas phase and isolated in the condensed phase in a nano-cage. The spectrum is the result of transitions between energy levels of vibration-rotation of the molecule.

Spis treści

Foreword ix

Preface xi

Chapter 1. Generalities on Diatomic Molecules  1

1.1. Generalities on detecting diatomic molecules 2

1.1.1. Radiation matter interaction for detection 2

1.1.2. Diatomic molecules: observation, analysis and interpretation  5

1.2. Hamiltonian of a diatomic molecule  9

1.3. Symmetry properties of a diatomic molecule 14

1.3.1. Group of symmetry  14

1.3.2. Symmetry of the electronic states  19

1.3.3. Symmetry of the total wave functions 22

1.4. Example of the diatomic molecule with two electrons H2, HD, D2  29

1.4.1. Hamiltonian of the isotopologues  29

1.4.2. BO approximation  32

1.4.3. Adiabatic representation  35

1.4.4. Diabatic representation  35

1.5. Conclusion  36

1.6. Appendix  37

Chapter 2. Energy Levels of a Diatomic Molecule in Gaseous Phase  41

2.1. Introduction  42

2.2. Pure vibration movement of a diatomic molecule  43

2.2.1. Harmonic oscillator: classical processing 44

2.2.2. Harmonic oscillator: quantum aspect 47

2.2.3. Transitions between two vibrational levels: selection rules  51

2.2.4. Creation and annihilation operators 54

2.2.5. Anharmonic oscillator  56

2.2.6. Contact transformation method  60

2.3. Rotation movement of a rigid diatomic molecule  67

2.3.1. Free rigid rotor: classical processing 67

2.3.2. Free rigid rotor: quantum aspect  68

2.3.3. Transitions between rotational levels: selection rules 72

2.4. Vibration rotation coupling of a free diatomic molecule 73

2.4.1. Non–rigid rotor  73

2.4.2. Rovibrational transitions: selection rules 74

2.5. Appendix  76

2.5.1. The commutators  76

2.5.2. Expressions of pn and qn in terms of the operators a and a   76

2.5.3. Matrix elements of pn and qn  77

2.5.4. Matrix of rotation and rotational transitions  80

Chapter 3. Profile and Shape of Spectral Lines  83

3.1. Introduction  84

3.2. Semiclassical model of calculating the broadening parameters of spectral lines 85

3.2.1. General description of the interacting physical system 85

3.2.2. General expression of the profile of a spectral line 86

3.2.3. Consequences of the invariance of the Zwanzig relaxation operator under rotation 91

3.2.4. Semiclassical context for calculating the relaxation matrix  93

3.2.5. Broadening parameter according to the diffusion operator  97

3.2.6. Calculation of the differential cross–section S(b, v) 98

3.2.7. Interaction potential energy 102

3.2.8. Relative trajectory of the molecules  107

3.2.9. Expression of S(b,v) in terms of resonance functions 112

3.3. True shape, profile and intensity of an absorption line 115

3.4. Line profile  116

3.4.1. Lorentz profile  117

3.4.2. Gauss profile. 118

3.4.3. Voigt profile 119

3.4.4. Galatry, Nelkin Ghatak and Rautian Sobelmann profiles  120

3.5. Conclusion  121

3.6. Appendix  122

3.6.1. Liouville formalism  122

3.6.2. The Clebsch Gordan coefficients and the Wigner 3j symbols  123

3.6.3. The terms of the differential cross–section expansion S(b,v)  124

Chapter 4. Energy Levels and Spectral Profile of a Diatomic Molecule in Condensed Phase  127

4.1. Introduction  127

4.2. Inclusion model 129

4.2.1. Binary interaction energy  130

4.2.2. Lakhlifi Dahoo inclusion model  137

4.3. Rare gas nanocage 138

4.3.1. The rare gases in the solid state.  138

4.3.2. Dynamics of the perfect fcc lattice (Bravais lattice) 141

4.3.3. Green function of the perfect monoatomic crystal 144

4.4. Inclusion of a molecule in a rare gas matrix 145

4.4.1. Deformation method  145

4.4.2. Equilibrium of the doped crystal  148

4.5. General Hamiltonian and separation of the movements 150

4.5.1. Hamiltonian of the system  150

4.5.2. Separation of the optical system s movements and the bath in the rigid matrix approximation  152

4.5.3. Vibrational mode  153

4.5.4. Orientational modes  155

4.5.5. Active optical system  163

4.5.6. Translational modes  163

4.5.7. Optical modes bath coupling  166

4.6. Infrared absorption coefficient 167

4.6.1. General expression  167

4.6.2. Heisenberg representation  168

4.6.3. Averages and correlation functions  172

4.6.4. Bar spectrum or Dirac spectrum  174

4.6.5. Spectral profile  175

4.7. Conclusion  176

4.8. Appendix  177

4.8.1. Expression of the dispersion repulsion contribution of the energy of truncated binary interaction in the fourth order  177

4.8.2. Rotation matrix  178

4.8.3. Eigenvalues correction of the orientation Hamiltonian 178

4.8.4. Eigenvalues correction of the orientation Hamiltonian 178

Chapter 5. Applications to HCl, CO, O2 and N2 179

5.1. The HCl heteronuclear molecule isolated and trapped in a matrix  179

5.1.1. Molecule in the gaseous phase  179

5.1.2. Molecule trapped in rare gas matrix  181

5.2. Lidar probing of terrestrial homonuclear molecules N2 and O2  183

5.3. The heteronuclear molecule CO trapped in a matrix and absorbed on graphite substrate (1000) at a low temperature 187

5.3.1. Molecule trapped in a rare gas matrix 187

5.3.2. Molecule adsorbed on the graphite substrate  189

5.3.3. Molecule graphite interaction energy 191

5.3.4. Adsorption observables at a low temperature  192

5.4. Conclusion  196

Bibliography 197

Index  207

O autorze

Pierre Richard Dahoo, University of Versailles St Quentin (UVSQ), France   Azzedine Lakhlifi, University of Franche–Comté, France