Foreword ix
Jonathan TENNYSON
Introduction xiii
Iwona GULACZYK, Michaël REY and Ha TRAN Chapter 1. Automated Rovibrational Configuration Interaction Calculations 1
Subhasish DAS and Guntram RAUHUT
1.1. Introduction 1
1.2. The Hamiltonian 2
1.3. VSCF/VCI calculations 5
1.4. RVCI calculations 10
1.5. Infrared intensities 19
1.6. Conclusion and outlook 24
1.7. Acknowledgments 26
1.8. References 26
Chapter 2. Efficient Numerical and Group-Theoretical Methods for Computing Spectra 31
Michaël REY
2.1. Introduction 31
2.2. Exploiting symmetry in molecular spectroscopy 32
2.2.1. Group theory for rigid and nonrigid molecules 33
2.2.2. Symmetry-adapted functions and irreducible tensor operators 35
2.3. Variational calculation 42
2.3.1. Computation of ro-vibrational energy levels by pruning the basis 42
2.3.2. Nested tensor train contracted basis functions and symmetry 45
2.4. Hamiltonian for semirigid molecules 49
2.4.1. ITO formulation of the Eckart-Watson Hamiltonian 49
2.4.2. ITO formulation of Eckart-frame Hamiltonians in curvilinear coordinates 51
2.4.3. ITO formulation of ab initio effective Hamiltonians and dipole moment operators 53
2.5. Hybrid Hamiltonian for non-rigid molecules: ITO formulation of the Hougen-Bunker-Johns formalism 55
2.6. Calculation of rotation-vibration spectra 58
2.7. References 59
Chapter 3. Isolated Line Shape Theory 65
Ha TRAN, Ngoc Hoa NGO and Piotr WCISLO
3.1. Introduction 65
3.2. Doppler broadening and the Gauss profile 67
3.3. Collisional broadening and shift and the Lorentz and Voigt profiles 68
3.3.1. Collisional broadening and shift and the Lorentz profile 68
3.3.2. The usual Voigt profile 68
3.4. Refined collisional effects and line-shape profiles 71
3.4.1. Dicke narrowing effect 71
3.4.2. The speed dependence of line broadening and shift 75
3.4.3. The Hartmann-Tran profile 78
3.4.4. The modified Hartmann-Tran profile 82
3.5. Beyond the impact approximation 86
3.6. Conclusion 87
3.7. References 87
Chapter 4. Semi-Classical Line-shape Theory 95
Robert R. GAMACHE
4.1. Introduction 95
4.2. Semi-classical line-shape theory 97
4.2.1. From ATC theory to modern semi-classical theories 97
4.2.2. Collisional line broadening and shifting 98
4.2.3. Components contributing to the broadening and shifting 104
4.2.4. The physics of what is going on 106
4.2.5. What does an understanding of the collisional line broadening mechanism tell us? 109
4.3. The semi-classical CRBM theory 112
4.4. Components of the calculation to be considered 113
4.4.1. Trajectory models 114
4.4.2. Velocity integration versus mean-relative thermal velocity approximation 116
4.4.3. Effect of imaginary components on the pressure-broadened half-width 116
4.4.4. The atom-atom component of the intermolecular potential and the effects of its expansion 118
4.4.5. Adjusting the atom-atom potential 121
4.4.6. Line coupling 124
4.5. Temperature dependence of ¿ and ¿ 125
4.6. Comparison with measurement 130
4.7. Speed dependence of ¿ and ¿ 132
4.8. Vibrational effects 135
4.9. Predicting line-shape parameters 135
4.10. Conclusion 139
4.11. References 140
Chapter 5. Ab Initio Calculations of Line-Shape Parameters 153
Hubert JÓZWIAK and Piotr WCISLO
5.1. Formulation of the line-shape problem 153
5.1.1. Derivation of the generalized Waldmann-Snider equation 159
5.1.2. State multipoles 168
5.1.3. Spectral line shape within the Hess method 171
5.1.4. Relation to the phenomenological line-shape models 177
5.1.5. Generalizations and other approaches to the spectral line shape problem 180
5.2. Quantum scattering theory 181
5.3. Application of the fully ab initio approach to molecular systems 188
5.4. References 192
Chapter 6. Line Mixing Within and Beyond the Impact Approximation 199
Christian BOULET and Ha TRAN
6.1. Introduction 199
6.2. Collisional line mixing within the impact approximation 202
6.2.1. Some basic equations 202
6.2.2. The weak overlapping regime 204
6.2.3. Profile in the near wing of a cluster of lines 206
6.2.4. Profile in the near wing of a vibrational band 207
6.2.5. Building the impact relaxation matrix 209
6.3. Line mixing beyond the impact approximation 226
6.3.1. Introduction 226
6.3.2. Empirical models: the correcting ¿ factor 227
6.3.3. Far wings: the quasi-static approach of Rosenkranz 227
6.3.4. From resonance to the far wings: non-Markovian ECS model 231
6.3.5. Direct predictions from rCMDS (and CMDS) 234
6.4. Conclusion 235
6.5. References 235
Conclusion 243
Iwona GULACZYK, Michaël REY and Ha TRAN
List of Authors 245
Index 247
Summary of Volume 1A 251
