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.

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.

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.

Pierre-Richard Dahoo 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.

Azzedine Lakhlifi 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.

Klappentext

This book is dedicated to the description and application of variousdifferent theoretical models to identify the near and mid-infrared spectraof symmetric and spherical top molecules in their gaseous form.

Theoretical models based on the use of group theory are applied to rigidand non-rigid molecules, characterized by the phenomenon of tunnelingand large amplitude motions. The calculation of vibration-rotationenergy levels and the analysis of infrared transitions are applied tomolecules of ammonia (NH3) and methane (CH4).The applications show how interactions at the molecular scale modifythe near and mid-infrared spectra of isolated molecules, under theinfluence of the pressure of a nano-cage (the substitution site of a raregas matrix, clathrate, fullerene or zeolite) or a surface, and allow us toidentify the characteristics of the perturbing environment.

This book provides valuable support for teachers and researchers but isalso intended for engineering students, working research engineers andMaster s and doctorate students.

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.

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.

Inhalt

Foreword ix
Vincent BOUDON

Preface xi

Chapter 1. Group Theory in Infrared Spectroscopy 1

1.1. Introduction 1

1.2. The point-symmetry group of a molecule 2

1.2.1. Symmetry operations and symmetry elements of a molecule 3

1.2.2. Point symmetry group and laws of composition 6

1.3. Representations by square matrices (general linear group of order n on R or C: GLn(R) or GLn(C)) 10

1.3.1. Irreducible representations 10

1.3.2. Equivalent representations 13

1.4. Table of characters and fundamental theorems 14

1.4.1. Tables of characters, classes and irreducible representations 14

1.4.2. Irreducible representation of group C_3v 16

1.4.3. Schur's lemma 17

1.4.4. Orthogonality and normalization theorem 18

1.4.5. Orthogonality of lines 18

1.4.6. Orthogonality of columns 20

1.4.7. Decomposition of a reducible representation on an irreducible basis 20

1.4.8. Projection operators for irreducible representations 21

1.4.9. Characters of irreducible representations of the direct product of two groups 22

1.5. Overall rotation group symmetry of a molecule 23

1.6. Full symmetry group of the Hamiltonian of a molecule 26

1.6.1. Permutation operations 27

1.6.2. Permutation group S_n 28

1.6.3. Complete nuclear permutation group (G^CNP) of a molecule 30

1.6.4. Inversion group and inversion operations E^* and permutation-inversion operations P^* 30

1.6.5. Permutation-inversion group G^CNPI 31

1.6.6. Group SO(3) isomorphic to permutation-inversion group G^CNPI 32

1.7. Correlation between the rotation group and a point-group symmetry of a molecule 34

1.8. Example of group theory applications 39

1.9. Conclusion 40

1.10. Appendices: Groups and Lie algebra of SU(2) and SO(3) 40

1.10.1. Appendix A: Groups SU(2) and SO(3) 40

1.10.2. Appendix B: Lie algebra and SO(3) 42

Chapter 2. Symmetry of Symmetric and Spherical Top Molecules 45

2.1. Introduction 46

2.2. Symmetry group of molecular Hamiltonian 47

2.3. Symmetry of the NH₃ molecule and its isotopologues ND₃, NHD₂ and NDH₂ 54

2.3.1. Symmetry group of the symmetric molecular tops NH₃ and ND₃ 54

2.3.2. Symmetry group of asymmetric molecular tops NHD₂ and NDH₂ 56

2.3.3. Symmetry group of the complete group taking into account the inversion 57

2.4. Symmetry of CH₄ and its isotopologues CD₄, CHD₃, CDH₃ and CH₂D₂ 59

2.4.1. Symmetry group of spherical tops CH₄ and CD₄ 59

2.4.2. Symmetry group of symmetric tops CHD₃ and CDH₃ 61

2.4.3. Symmetry group of the asymmetric top CH₂D₂ 62

2.5. Symmetry group of the complete CNPI group 62

2.6. Conclusion 66

Chapter 3. Line Profiles, Symmetries and Selection Rules According to Group Theory 67

3.1. Introduction 68

3.2. Symmetries of the eigenstates of the zeroth-order Hamiltonian 70

3.3. Intensity of the vibrationrotation lines and bar spectrum 72

3.4. Transition operator for the selection rules 74

3.5. Dipole moment operator and line profile 77

3.6. Irreducible representations of the vibrations of the molecules 82

3.6.1. Procedure for the decomposition of the reducible representation 82

3.6.2. Case of symmetric tops XY₃ and...