Pierre Richard Dahoo is Professor at the University of Versailles St Quentin (UVSQ), researcher at LATMOS, UMR 8190 CNRS, Manager of the University Institute of Technology of Mantes-en-Yvelines and Program Manager of the Chair "Materials Simulation and Engineering" of the UVSQ in Versailles, France.Azzedine Lakhlifi is Lecturer at the University of Franche-Comté, and researcher at the UTINAM Institute, UMR 6213 CNRS, Observatory of Besançon, France.

• Foreword ixPreface xiChapter 1. Generalities on Diatomic Molecules 11.1. Generalities on detecting diatomic molecules 21.1.1. Radiation–matter interaction for detection 21.1.2. Diatomic molecules: observation, analysis and interpretation 51.2. Hamiltonian of a diatomic molecule 91.3. Symmetry properties of a diatomic molecule 141.3.1. Group of symmetry 141.3.2. Symmetry of the electronic states 191.3.3. Symmetry of the total wave functions 221.4. Example of the diatomic molecule with two electrons H2, HD, D2 291.4.1. Hamiltonian of the isotopologues 291.4.2. BO approximation 321.4.3. Adiabatic representation 351.4.4. Diabatic representation 351.5. Conclusion 361.6. Appendix 37Chapter 2. Energy Levels of a Diatomic Molecule in Gaseous Phase 412.1. Introduction 422.2. Pure vibration movement of a diatomic molecule 432.2.1. Harmonic oscillator: classical processing 442.2.2. Harmonic oscillator: quantum aspect 472.2.3. Transitions between two vibrational levels: selection rules 512.2.4. “Creation” and “annihilation” operators 542.2.5. Anharmonic oscillator 562.2.6. Contact transformation method 602.3. Rotation movement of a rigid diatomic molecule 672.3.1. Free rigid rotor: classical processing 672.3.2. Free rigid rotor: quantum aspect 682.3.3. Transitions between rotational levels: selection rules 722.4. Vibration–rotation coupling of a free diatomic molecule 732.4.1. Non-rigid rotor 732.4.2. Rovibrational transitions: selection rules 742.5. Appendix 762.5.1. The commutators 762.5.2. Expressions of pn and qn in terms of the operators a and a† 762.5.3. Matrix elements of pn and qn 772.5.4. Matrix of rotation and rotational transitions 80Chapter 3. Profile and Shape of Spectral Lines 833.1. Introduction 843.2. Semiclassical model of calculating the broadening parameters of spectral lines 853.2.1. General description of the interacting physical system 853.2.2. General expression of the profile of a spectral line 863.2.3. Consequences of the invariance of the Zwanzig relaxation operator under rotation 913.2.4. Semiclassical context for calculating the relaxation matrix 933.2.5. Broadening parameter according to the diffusion operator 973.2.6. Calculation of the differential cross-section S(b, v) 983.2.7. Interaction potential energy 1023.2.8. Relative trajectory of the molecules 1073.2.9. Expression of S(b,v) in terms of resonance functions 1123.3. True shape, profile and intensity of an absorption line 1153.4. Line profile 1163.4.1. Lorentz profile 1173.4.2. Gauss profile 1183.4.3. Voigt profile 1193.4.4. Galatry, Nelkin–Ghatak and Rautian–Sobelmann profiles 1203.5. Conclusion 1213.6. Appendix 1223.6.1. Liouville formalism 1223.6.2. The Clebsch–Gordan coefficients and the Wigner 3j symbols 1233.6.3. The terms of the differential cross-section expansion S(b,v) 124Chapter 4. Energy Levels and Spectral Profile of a Diatomic Molecule in Condensed Phase 1274.1. Introduction 1274.2. Inclusion model 1294.2.1. Binary interaction energy 1304.2.2. Lakhlifi–Dahoo inclusion model 1374.3. Rare gas nanocage 1384.3.1. The rare gases in the solid state1384.3.2. Dynamics of the perfect fcc lattice (Bravais lattice) 1414.3.3. Green function of the perfect monoatomic crystal 1444.4. Inclusion of a molecule in a rare gas matrix 1454.4.1. Deformation method 1454.4.2. Equilibrium of the doped crystal 1484.5. General Hamiltonian and separation of the movements 1504.5.1. Hamiltonian of the system 1504.5.2. Separation of the optical system’s movements and the bath in the rigid matrix approximation 1524.5.3. Vibrational mode 1534.5.4. Orientational modes 1554.5.5. Active optical system 1634.5.6. Translational modes 1634.5.7. Optical modes – bath coupling 1664.6. Infrared absorption coefficient 1674.6.1. General expression 1674.6.2. Heisenberg representation 1684.6.3. Averages and correlation functions 1724.6.4. Bar spectrum or Dirac spectrum 1744.6.5. Spectral profile 1754.7. Conclusion 1764.8. Appendix 1774.8.1. Expression of the dispersion–repulsion contribution of the energy of truncated binary interaction in the fourth order 1774.8.2. Rotation matrix 1784.8.3. Eigenvalues correction of the orientation Hamiltonian 1784.8.4. Eigenvalues correction of the orientation Hamiltonian 178Chapter 5. Applications to HCl, CO, O2 and N2 1795.1. The HCl heteronuclear molecule isolated and trapped in a matrix 1795.1.1. Molecule in the gaseous phase 1795.1.2. Molecule trapped in rare gas matrix 1815.2. Lidar probing of terrestrial homonuclear molecules N2 and O2 1835.3. The heteronuclear molecule CO trapped in a matrix and absorbed on graphite substrate (1000) at a low temperature 1875.3.1. Molecule trapped in a rare gas matrix 1875.3.2. Molecule adsorbed on the graphite substrate 1895.3.3. Molecule–graphite interaction energy 1915.3.4. Adsorption observables at a low temperature 1925.4. Conclusion 196Bibliography 197Index 207

Pierre Richard Dahoo is Professor at the University of Versailles St Quentin (UVSQ), researcher at LATMOS, UMR 8190 CNRS, Manager of the University Institute of Technology of Mantes-en-Yvelines and Program Manager of the Chair "Materials Simulation and Engineering" of the UVSQ in Versailles, France.Azzedine Lakhlifi is Lecturer at the University of Franche-Comté, and researcher at the UTINAM Institute, UMR 6213 CNRS, Observatory of Besançon, France.

• Foreword ixPreface xiChapter 1. Generalities on Diatomic Molecules 11.1. Generalities on detecting diatomic molecules 21.1.1. Radiation–matter interaction for detection 21.1.2. Diatomic molecules: observation, analysis and interpretation 51.2. Hamiltonian of a diatomic molecule 91.3. Symmetry properties of a diatomic molecule 141.3.1. Group of symmetry 141.3.2. Symmetry of the electronic states 191.3.3. Symmetry of the total wave functions 221.4. Example of the diatomic molecule with two electrons H2, HD, D2 291.4.1. Hamiltonian of the isotopologues 291.4.2. BO approximation 321.4.3. Adiabatic representation 351.4.4. Diabatic representation 351.5. Conclusion 361.6. Appendix 37Chapter 2. Energy Levels of a Diatomic Molecule in Gaseous Phase 412.1. Introduction 422.2. Pure vibration movement of a diatomic molecule 432.2.1. Harmonic oscillator: classical processing 442.2.2. Harmonic oscillator: quantum aspect 472.2.3. Transitions between two vibrational levels: selection rules 512.2.4. “Creation” and “annihilation” operators 542.2.5. Anharmonic oscillator 562.2.6. Contact transformation method 602.3. Rotation movement of a rigid diatomic molecule 672.3.1. Free rigid rotor: classical processing 672.3.2. Free rigid rotor: quantum aspect 682.3.3. Transitions between rotational levels: selection rules 722.4. Vibration–rotation coupling of a free diatomic molecule 732.4.1. Non-rigid rotor 732.4.2. Rovibrational transitions: selection rules 742.5. Appendix 762.5.1. The commutators 762.5.2. Expressions of pn and qn in terms of the operators a and a† 762.5.3. Matrix elements of pn and qn 772.5.4. Matrix of rotation and rotational transitions 80Chapter 3. Profile and Shape of Spectral Lines 833.1. Introduction 843.2. Semiclassical model of calculating the broadening parameters of spectral lines 853.2.1. General description of the interacting physical system 853.2.2. General expression of the profile of a spectral line 863.2.3. Consequences of the invariance of the Zwanzig relaxation operator under rotation 913.2.4. Semiclassical context for calculating the relaxation matrix 933.2.5. Broadening parameter according to the diffusion operator 973.2.6. Calculation of the differential cross-section S(b, v) 983.2.7. Interaction potential energy 1023.2.8. Relative trajectory of the molecules 1073.2.9. Expression of S(b,v) in terms of resonance functions 1123.3. True shape, profile and intensity of an absorption line 1153.4. Line profile 1163.4.1. Lorentz profile 1173.4.2. Gauss profile 1183.4.3. Voigt profile 1193.4.4. Galatry, Nelkin–Ghatak and Rautian–Sobelmann profiles 1203.5. Conclusion 1213.6. Appendix 1223.6.1. Liouville formalism 1223.6.2. The Clebsch–Gordan coefficients and the Wigner 3j symbols 1233.6.3. The terms of the differential cross-section expansion S(b,v) 124Chapter 4. Energy Levels and Spectral Profile of a Diatomic Molecule in Condensed Phase 1274.1. Introduction 1274.2. Inclusion model 1294.2.1. Binary interaction energy 1304.2.2. Lakhlifi–Dahoo inclusion model 1374.3. Rare gas nanocage 1384.3.1. The rare gases in the solid state1384.3.2. Dynamics of the perfect fcc lattice (Bravais lattice) 1414.3.3. Green function of the perfect monoatomic crystal 1444.4. Inclusion of a molecule in a rare gas matrix 1454.4.1. Deformation method 1454.4.2. Equilibrium of the doped crystal 1484.5. General Hamiltonian and separation of the movements 1504.5.1. Hamiltonian of the system 1504.5.2. Separation of the optical system’s movements and the bath in the rigid matrix approximation 1524.5.3. Vibrational mode 1534.5.4. Orientational modes 1554.5.5. Active optical system 1634.5.6. Translational modes 1634.5.7. Optical modes – bath coupling 1664.6. Infrared absorption coefficient 1674.6.1. General expression 1674.6.2. Heisenberg representation 1684.6.3. Averages and correlation functions 1724.6.4. Bar spectrum or Dirac spectrum 1744.6.5. Spectral profile 1754.7. Conclusion 1764.8. Appendix 1774.8.1. Expression of the dispersion–repulsion contribution of the energy of truncated binary interaction in the fourth order 1774.8.2. Rotation matrix 1784.8.3. Eigenvalues correction of the orientation Hamiltonian 1784.8.4. Eigenvalues correction of the orientation Hamiltonian 178Chapter 5. Applications to HCl, CO, O2 and N2 1795.1. The HCl heteronuclear molecule isolated and trapped in a matrix 1795.1.1. Molecule in the gaseous phase 1795.1.2. Molecule trapped in rare gas matrix 1815.2. Lidar probing of terrestrial homonuclear molecules N2 and O2 1835.3. The heteronuclear molecule CO trapped in a matrix and absorbed on graphite substrate (1000) at a low temperature 1875.3.1. Molecule trapped in a rare gas matrix 1875.3.2. Molecule adsorbed on the graphite substrate 1895.3.3. Molecule–graphite interaction energy 1915.3.4. Adsorption observables at a low temperature 1925.4. Conclusion 196Bibliography 197Index 207