Rotational Structure in Molecular Infrared Spectra

Rotational Structure in Molecular Infrared Spectra
Copyright
Contents
1 The Vibration-Rotation Problem
	1.1 Classical Kinetic Energy
		1.1.1 The Eckart Conditions
		1.1.2 Transformation to Normal Coordinates
		1.1.3 Kinetic Energy in Terms of Momenta
	1.2 The Quantum Mechanical Hamiltonian
		1.2.1 Linear Molecules
	References
2 Interaction of Matter and Light
	2.1 Time-Dependent Perturbations
	2.2 A Charge in an Electromagnetic Field
	2.3 A System of Charged Particles in a Radiation Field
		2.3.1 Electric Dipole Transitions
		2.3.2 A Higher Approximation: Magnetic Dipole and Electric Quadrupole Transitions
	2.4 More on Electric Dipole Transitions
		2.4.1 Radiation Density and Intensity
		2.4.2 Einstein Coefficients and Line Strengths
		2.4.3 The Integrated Absorption Coefficient
	2.5 Spontaneous Emission
	References
3 Molecular Symmetry and Spectroscopy
	3.1 Molecular Symmetry and Molecular Point Groups
	3.2 Rotational Energy and Rotational Hamiltonian of Rigid Rotors
	3.3 Rotational Symmetry and Rotational Groups
		3.3.1 Spherical Top Rotors
		3.3.2 Symmetric Top Rotors
		3.3.3 Linear Rotors
		3.3.4 Asymmetric Top Rotors
	3.4 Molecular Deformations and Molecular Symmetry Groups
	3.5 The Inversion Operation E* and Parity
	3.6 The Complete Nuclear Permutation and Permutation-Inversion Groups
	3.7 Feasible Operations and Molecular Symmetry Groups
	3.8 The Extension of Molecular Symmetry Groups
		3.8.1 Hydrogen Peroxide
		3.8.2 Ethane-Like Molecules
		3.8.3 Methanol and acetaldehyde
	3.9 Time Reversal
	3.10 A First Glance to Transition Selection Rules: Parity
	References
4 Symmetry of Wavefunctions in Vibration-Rotation Spectroscopy
	4.1 Rotational Coordinates
	4.2 Rotational Operators and Wavefunctions
		4.2.1 Effects of Time Reversal
	4.3 Molecular Vibrations
		4.3.1 Vibrational Modes and Vibrational States of Symmetric Tops
		4.3.2 Examples of overtones and combinations
		4.3.3 C3v Molecules
		4.3.4 D6h Molecules
	4.4 Vibration-Rotation Wavefunctions
	4.5 Linear Molecules
		4.5.1 Angular Momenta
		4.5.2 Symmetry Groups
	4.6 Asymmetric Top Molecules
		4.6.1 Rotational Symmetries
		4.6.2 Correlation With the Symmetric Top Limits
	4.7 Spherical Top Molecules
	References
5 Nuclear Spin Statistical Weights
	5.1 Symmetries of Nuclear Spin, Rovibronic, and Total Wavefunctions
		5.1.1 An Example: 12CH335Cl
		5.1.2 Another Example: 14NH3
		5.1.3 Hydrogen Peroxide: H216O2
	5.2 Linear Molecules
	5.3 Coupled and Uncoupled Nuclei
	5.4 Molecules with no Symmetry Elements
	Reference
6 Expansion and Transformations of the Vibration-Rotation Hamiltonian
	6.1 Expansion of the Vibration-Rotation Hamiltonian
		6.1.1 Dimensionless Normal Coordinates and Associated Momenta
		6.1.2 Expansion of Vn(q&e_020D7;)
		6.1.3 Expansion of the Inverse of the Inertia Tensor
	6.2 The Expanded Vibration-Rotation Hamiltonian
	6.3 An Isolated Vibrational State
		6.3.1 Effects of Interactions with Other Vibrational States
		6.3.2 Higher Order Coriolis Coefficients
	References
7 Effects of Centrifugal Distortions
	7.1 Linear Molecules
	7.2 Symmetric Top Molecules
	7.3 Spherical Top Molecules
	7.4 Asymmetric Top Molecules
		7.4.1 A and S Reductions
	References
8 SPECTRA OF SYMMETRIC TOP AND LINEAR MOLECULES
	8.1 Molecular Degrees of Freedom
	8.2 The Harmonic Oscillator-Rigid Rotor Approximation
	8.3 Semirigid Symmetric Top Molecules
		8.3.1 Nondegenerate Fundamental Vibrational States
		8.3.2 Degenerate Fundamental Vibrational States
	8.4 Overtones and Combinations
		8.4.1 Degenerate Overtones and Combinations
		8.4.2 Nondegenerate Overtones and Combinations
	8.5 Linear Molecules
	8.6 Vibration-Rotation Selection Rules: Line Intensities and Line Strengths
		8.6.1 Overall Selection Rules
		8.6.2 Vibrational and Rotational Selection Rules
		8.6.3 C3v, D3h, and D3d Molecules
		8.6.4 C6v and D6h Molecules
		8.6.5 D2d Molecules
	8.7 Parallel and Perpendicular Line Strengths
		8.7.1 Vibrational Transition Moments
	8.8 Line Strengths with Perturbed Upper States
	8.9 Line Shapes
	8.10 Main Spectral Features in Symmetric Tops and Linear Molecules
		8.10.1 Transitions Between Nondegenerate Vibrational States
		8.10.2 Transitions from Nondegenerate to Degenerate Vibrational States
		8.10.3 Transitions from Gv=0 to Gv=±1
		8.10.4 Transitions from Gv=n/2 to Gv=n/2±1
		8.10.5 Transitions Between Degenerate Vibrational States
	8.11 Lower and Upper State Combination Differences
	8.12 Hot and Difference Bands
		8.12.1 A Special Application of Hot Bands: Determination of the K-Structure Parameters of the Vibrational Ground State
	8.13 Phase Conventions
	8.14 Anharmonic Interactions
		8.14.1 Vibrational l-Doubling
	8.15 Coriolis Interactions
		8.15.1 z-Axis Coriolis Operators
		8.15.2 x,y-Axis Coriolis Operators
		8.15.3 Nonvanishing Coriolis Coefficients
		8.15.4 x,y-Coriolis Coupling and Intensity Perturbations
		8.15.5 x,y-Coriolis Coupling and Perturbation-Induced Transitions
		8.15.6 Transitions with K=0 and ΔK=0
	8.16 l-Type Interactions and Doublings
		8.16.1 Interactions and Doublings of the type l-(±2,±2)
		8.16.2 Interactions and Doublings of the type l-(±2, ∓ 2)
		8.16.3 Interactions and Doublings of the type l-(±2, ∓1)
		8.16.4 l-Doubling in Linear Molecules
		8.16.5 l-Perturbations in Overtones and Combinations
	8.17 Higher Order Perturbations
	8.18 Isolated Vibrational Levels and Polyads
	References
9 Spectra of Asymmetric Top Molecules
	9.1 Rotational Energy
	9.2 Orthorhombic Molecules
	9.3 Vibration–Rotation Transitions
		9.3.1 A-Type Transitions
		9.3.2 C-Type Transitions
		9.3.3 B-Type Transitions
	9.4 Hybrid Bands
	9.5 Near-Symmetric Tops
	9.6 Anharmonic and Coriolis Interactions
		9.6.1 Anharmonic Interactions
		9.6.2 Coriolis Interactions
	9.7 Intensity Calculation
	References
10 Spectra of Spherical Top Molecules
	10.1 General Considerations
	10.2 Fundamental Vibrational States
	10.3 Overtones and Combinations of F-Modes
	10.4 Coriolis Coupling in Overtones and Combinations of F-Modes
	10.5 Selection Rules and Intensities
		10.5.1 Selection Rules
		10.5.2 Intensities of Fundamental Transitions
	10.6 Effects of Anharmonicity
		10.6.1 Level Shifts and Spherical Splitting
		10.6.2 Molecular Symmetry Splitting
	10.7 Centrifugal Distortion Effects
	10.8 Remarks
	10.9 Cubic Symmetry
	References
11 Floppy Molecules
	11.1 Molecular Inversion
	11.2 Internal Rotation
		11.2.1 Torsional Splitting
		11.2.2 Internal Rotation in Symmetric Top Molecules
	11.3 Effects of Torsional Coriolis Coupling
	11.4 Perturbation Approach for the Degenerate Modes of Ethane-Like Molecules
	References
12 Hyperfine Structure and the Interaction of Molecular Rotation With Nuclear Electric Quadrupoles
	12.1 Reduced Matrix Elements of Q(2) and V(2)
	12.2 A Simpler Alternative Method
	12.3 Matrix Elements
	12.4 Selection Rules for Electric Dipole Transitions
	12.5 Hyperfine Structure in an Infrared Spectrum
	References
Appendix A1 Phases of Wavefunctions
Appendix A2 Eigenfunctions of Commuting Operators
	A2.1 Angular Momenta
	Reference
Appendix A3 Coupling of Angular Momenta
	A3.1 Internal and Rotational Angular Momenta
	A3.2 Separation of Rotation and Vibration
	A3.3 Coupling of J with the Nuclear Spin
	A3.4 Projection Theorem and the Coupling of Molecular Rotation with a Nuclear Spin
	A3.5 Phases and Clebsch–Gordan Coefficients
	References
Appendix A4 Angular Momentum Matrix Elements
	A4.1 Rotational Angular Momenta in a Molecule-Fixed Frame
Appendix A5 The Full Rotation Group and Irreducible Spherical Tensors
	A5.1 The Wigner–Eckart Theorem
		A5.1.1 Phases in the Wigner–Eckart Theorem
	A5.2 Reduced Matrix Elements in Uncoupled and Coupled Representations
	A5.3 Products of Tensor Operators
	A5.4 Contraction of Tensor Operators
	A5.5 The Full Rotation-Reflection Group
	References
Appendix A6 Direction Cosine Operators
	A6.1 Direction Cosine Operators as Spherical Tensors
	A6.2 Second-Rank Direction Cosine Tensor Operators
	References
Appendix A7 Harmonic Oscillators
	A7.1 Mono-Dimensional Harmonic Oscillator
	A7.2 Two-Dimensional Isotropic Harmonic Oscillator
	A7.3 Three-Dimensional Isotropic Harmonic Oscillator
	References
Appendix A8 Vibrational Normal Modes and Coriolis Coefficients
	A8.1 Vibrational Normal Modes
		A8.1.1 Internal and symmetrized vibrational coordinates
	A8.2 Coriolis coefficients
	References
Appendix A9 Contact Transformation and Perturbation Methods
	A9.1 Contact Transformations
		A9.1.1 Illustration of the Method
	A9.2 Van Vleck Perturbation Method
	References
Index