1  Cover

      2  Title Page

      3  Copyright

      4  Foreword

      5  Preface

      6  1 Group Theory in Infrared Spectroscopy 1.1. Introduction 1.2. The point-symmetry group of a molecule 1.3. Representations by square matrices (general linear group of order n on R or C: GLn(R) or GLn(C)) 1.4. Table of characters and fundamental theorems 1.5. Overall rotation group symmetry of a molecule 1.6. Full symmetry group of the Hamiltonian of a molecule 1.7. Correlation between the rotation group and a point-group symmetry of a molecule 1.8. Example of group theory applications 1.9. Conclusion 1.10. Appendices: Groups and Lie algebra of SU(2) and SO(3)

      7  2 Symmetry of Symmetric and Spherical Top Molecules 2.1. Introduction 2.2. Symmetry group of molecular Hamiltonian 2.3. Symmetry of the NH₃ molecule and its isotopologues ND₃, NHD₂ and NDH₂ 2.4. Symmetry of CH₄ and its isotopologues CD₄, CHD₃, CDH₃ and CH₂D₂ 2.5. Symmetry group of the complete CNPI group 2.6. Conclusion

      8  3 Line Profiles, Symmetries and Selection Rules According to Group Theory 3.1. Introduction 3.2. Symmetries of the eigenstates of the zeroth-order Hamiltonian 3.3. Intensity of the vibration–rotation lines and bar spectrum 3.4. Transition operator for the selection rules 3.5. Dipole moment operator and line profile 3.6. Irreducible representations of the vibrations of the molecules 3.7. Types of vibrations of irreducible representations 3.8. Rotation and spin Hamiltonian symmetries 3.9. Conclusion 3.10. Appendix: Absorption and emission of a molecule in the gas phase

      9  4 Energy Levels of Symmetric Tops in the Gas Phase 4.1. Introduction 4.2. Vibrational–rotational motions of an isolated symmetric top 4.3. Vibrational motions of an isolated pyramidal symmetric top 4.4. Rotational motion of an isolated rigid symmetric top molecule 4.5. Rovibrational energy levels of an isolated symmetric top and selection rules 4.6. Application to the ammonia NH₃ molecule 4.7. Appendices

      10  5 Spherical Top CH₄ 5.1. Introduction 5.2. Characteristics of the CH₄ molecule in gas phase 5.3. Tensor formalism for the CH₄ molecule 5.4. Application to the CH₄ molecule 5.5. Rotational structure in the degenerate vibrational levels 5.6. Conclusion 5.7. Appendices

      11  References

      12  Index

      13  End User License Agreement

      1 Chapter 1Figure 1.1. Symmetry operations and symmetry elements of a moleculeFigure 1.2. Equivalent symmetry operations of plane rotation and reflection over...Figure 1.3. Symmetry elements of the NH3 molecule and its reversed equilibrium c...Figure 1.4. Symmetry operations and flow diagram of point groups according to th...Figure 1.5. The operations equivalent to rotational symmetry (cyclic group of or...Figure 1.6. The effect of operation E* on a CH3D molecule. For a color version o...

      2 Chapter 2Figure 2.1. Mobile reference frame and the two equilibrium configurations of the...Figure 2.2. Potential with two minima depending on the distance h