Rotational Spectra and Molecular Structure (eBook)

Front Cover 1
Rotational Spectra and Molecular Structure 4
Copyright Page 5
Table of Contents 10
Dedication 6
PREFACE 8
ACKNOWLEDGMENTS 9
Chapter 1. Rotational Spectra 18
1-1. Energy Levels and Rotational Transitions 18
1-2. Information Contained in Rotational Spectra 21
Chapter 2. Rigid Rotor 24
2-1. Introduction 24
2-2. Molecular Parameters 24
2-3. Classes of Molecules 30
2-4a. Rigid Linear Molecules 30
2-4b. Spectrum and Selection Rules 31
2-5a. Rigid Symmetric-Top Molecules 32
2-5b. Spectrum and Selection Rules 35
2-6a. Rigid Asymmetric-Top Molecules 36
2-6b. Matrix Elements of E(k) 39
2-6c. Asymmetric Rotor Functions 41
2-6d. Selection Rules 44
2-6e. K Doubling in an Asymmetric Rotor 48
2-6f. Graphical Methods for Determining k and (A — C)/2 49
2-7. Rotational Transition Intensities 50
2-8. Statistical Weights 52
2-9. Nuclear Spin Statistics for Linear Molecules 54
2-10a. Nuclear Spin Statistics for Symmetric Tops 54
2-10b. Rotational Wave Functions 55
2-10c. Spin Wave Functions 55
2-11a. Nuclear Spin Statistics for Asymmetric Tops 57
2-11b. Rotational Wave Functions 57
2-11c. Spin Wave Functions 58
2-12a. Dipole Matrix Elements 59
2-12b. Dipole Matrix Elements for a Linear Molecule 61
2-12c. Dipole Matrix Elements for a Symmetric Rotor 62
2-12d. Dipole Matrix Elements for an Asymmetric Rotor 64
2-13. Transition Strengths and Approximate Wave Functions for Near Symmetric Tops 66
Chapter 3. Centrifugal Distortion, Coriolis Coupling, and Fermi Resonance 68
3-1. Introduction 68
3-2. Classical Appearance of Centrifugal and Coriolis Forces 69
3-3. Centrifugal Distortion in a Linear Molecule 71
3-4. Centrifugal Distortion in Symmetric Top Molecules 74
3-5. The Coriolis Coupling Constant 77
3-6a. /-Type Doubling in Linear Molecules 78
3-6b. Direct /-Type Transitions 82
3-7a. Degenerate Coriolis Splitting 83
3-7b. /-Type Doubling in Symmetric Top Molecules 86
3-7c. Energy Levels and Effects of Centrifugal Distortion 87
3-8. Dipole Matrix Elements and Selection Rules for /-Doubling 89
3-9. Fermi Resonance in Linear Molecules 90
3-10a. Nonrigid Effects in Asymmetric Rotors 92
3-10b. Perturbation Treatment of Vibration-Rotation Hamiltonian 93
3-10c. Interactions for Near Degeneracies 95
3-11. Coriolis Coupling Effects on Rotational Constants 97
3-12. Centrifugal Distortion in Asymmetric Tops 98
3-13. Fermi Resonance in Nonlinear Molecules 104
Chapter 4. Molecular Structure 105
4-1. Internuclear Distances and Moments of Inertia 105
4-2. ro Structure 107
4-3. rs Structure 109
4-4a. Linear Molecules 110
4-4b. Comparison of ro and rs Structures for Linear Molecules 111
4-5. Off-Axis Substitution in a Symmetric Top 114
4-6a. Planar Asymmetric Tops 115
4-6b. Nonplanar Asymmetric Tops 116
4-7. Structure Determinations When All Atoms Are Not Isotopically Substituted 117
4-8a. Determination of Coordinates near Principal Axes : Linear Molecules 119
4-8b. Near Axis Coordinates in Asymmetric Tops 120
4-8c. Coordinates of Atoms near the COM in an Asymmetric Top with a Plane of Symmetry 121
4-9a. The Inertia Defect 122
4-9b. Planar Molecules 124
4-9c. Inertia Defect and Molecular Structure of Planar Molecules 124
4-9d. Inertia Defect in Nonplanar Molecules 125
4-10. Variation of Bond Length with Isotopic Substitution 127
4-11. Values and Limitations of the Average Structure 129
Chapter 5. Nuclear Quadrupole Coupling 131
5-1. Quadrupole Nuclei in Molecules 131
5-2. Origin of the Quadrupole Interaction 132
5-3. Matrix Elements of HQ 138
5-4. First-Order Quadrupole Energy 139
5-5. Second-Order Quadrupole Energy 148
5-6. Molecules with Two Quadrupole Nuclei 150
5-7. Molecules with Three Quadrupole Nuclei 154
5-8. Quadrupole Hyperfine Structure in Excited Vibrational States 157
5-9. Relative Intensities of Quadrupole Components 159
Chapter 6. Internal Rotation 162
6-la. Introduction 162
6-lb. Physical Models 162
6-lc. Potential Energy and Hindered Rotation 163
6-2. High Potential Barriers 167
6-3a. Energy Levels, Selection Rules, and Intensities for a High Barrier 168
6-3b. A Single Internal Rotor 168
6-3c. Two Equivalent Internal Rotors 171
6-4. The PAM for a Symmetric Top Molecule 175
6-5. The IAM for a Symmetric Top Molecule 180
6-6. PAM for Asymmetric Molecules with Symmetric Internal Rotors 184
6-7. IAM for Asymmetric Top Molecules 189
6-8. Low Barriers 195
6-9. Completely Asymmetric Molecules 200
6-10. Internal Rotation Barriers from Intensities 201
6-11. Internal Barriers from Vibration-Rotation Interactions 201
6-12. Excited Torsional States 202
6-13a. Coriolis Interactions and Internal Rotation in Symmetric Top Molecules 203
6-13b. Coriolis Interactions in Excited Torsional States.of Asymmetric Rotors 205
6-14. V6 Contributions to the Torsional Barrier 207
6-15. Internal Rotation and Nuclear Quadrupole Coupling 209
6-16a. Molecules with Two Equivalent Methyl Groups 211
6-16b. Kinetic Energy 211
6-17. Symmetric Tops with Three Methyl Groups 216
6-18. Rotational Isomerism 218
6-19. Barriers Determined from Rotational Spectra 219
Chapter 7. Inversion 220
7-1. Characteristics of the Inversion Motion 220
7-2. Properties of the Inversion Wave Functions 222
7-3. Inversion in Symmetric Top Molecules 224
7-4a. Some Potential Functions for the Twofold Inversion Barrier 225
7-4b. Morse-Stuckelberg Potential 226
7-4c. Dennison-Uhlenbeck Potential 226
7-4d. Rosen-Morse Potential 228
7-4e. Manning Potential 230
7-4f. Wall-Glocker Potential 231
7-4g. Newton-Thomas Potential 233
7-4h. Sutherland-Costain Potential 233
7-4i. Harmonic Oscillator Perturbed by a Gaussian Barrier 234
7-4j. Quartic Oscillator 238
7-4k. Mixed Harmonic-Quartic Potential 239
7-5. Inversion-Vibration Interactions 239
7-6. Reduced Mass for NH3-like Symmetric Tops 240
7-7. Rotational Dependence of Inversion Splittings in Symmetric Tops 241
7-8. /K/ = 3 Inversion Transitions in Ammonia 242
7-9a. Inversion in Asymmetric Tops 243
7-9b. Selection Rules for Asymmetric Tops 244
7-9c. Types of Barriers 245
7-9d. Application of Symmetric Top Potential Functions to Asymmetric Tops 246
7-9e. Reduced Mass for Inversion in an Asymmetric Top 246
7-9f. Rotational Dependence of the Inversion Splittings in an Asymmetric Rotor 249
7-10. Inversion-Inversion Coupling 249
7-11. Inversion and Internal Rotation—The Methyl Amines 251
7-12a. Inversion in Near-Planar Molecules 253
7-12b. Inertial Defect 254
7-12c. Satellites and Intensities 254
7-12d. Stark Effect 255
7-12e. Far Infrared Spectrum 256
7-12f. Variation of Rotational Constants with Vibrational State 256
7-13. Vibration-Rotation Interactions 258
Chapter 8. Stark Effect 261
8-1. Introduction 261
8-2. General Properties of the Stark Effect 262
8-3. Matrix Elements of He 263
8-4. First-Order Stark Effect 264
8-5. Second-Order Stark Effect 264
8-6. High Field Stark Effect and Higher-Order Perturbation Terms 267
8-7. Stark Effect for Near Degeneracies 270
8-8a. Stark Effect and Quadrupole Hyperfine Structure 271
8-8b. Weak Field with a Single Quadrupole Nucleus (µe « eqQ) 273
8-8c. Strong Field with a Single Quadrupole Nucleus (µe » eqQ) 277
8-8d. Intermediate Case (µe ˜ eqQ) 278
8-8e. Near Degeneracies 279
8-9. Polarizability 279
8-10a. Stark Splittings and Relative Intensities 281
8-10b. .M = 0 Transitions 281
8-10c. .M = ±1 Transitions 283
8-1 Od. Intensities in the Presence of Hyperfine Structure 283
8-11a. Stark Effect in a Linear Molecule—OCS 284
8-11b. Stark Effect for an /-Type Doublet 286
8-11c. Stark Effect in a Symmetric Top Molecule—CH3F 288
8-11d. Stark Effect in an Asymmetric Rotor—CH3CHF2 290
8-11e. Stark Effect in a II Electronic State—NO 291
8-12. Stark Effect and Hindered Internal Motions 291
8-13. Dipole Moment Measurement Techniques 293
8-14. Stark Effects in Rapidly Varying Fields 296
8-15. Variation of µ with Isotopic Substitution and with Vibrational State 297
Chapter 9. Instrumentation 299
9-1. Spectroscopy in the Microwave Region 299
9-2. General Qualities of the Spectrometer 300
9-3a. Characteristics of Microwave Spectrometers 305
9-3b. Radiation Sources 306
9-3c. Source Stabilization 308
9-3d. Waveguide Stark Cell 311
9-3e. Modulation, Detection, and Display 312
9-3f. Frequency Measurements 317
9-3g. Millimeter and Submillimeter Techniques 318
9-4. Relative Intensity and Line Width Measurement 322
9-5. Parallel Plate Spectrometers 326
9-6. High Temperature and Molecular Beam Spectroscopy 327
9-7. Applications of Double-Resonance and Beam-Maser Spectrometers 329
9-8. Study of Free Radicals and Unstable Species 331
9-9. Zeeman Effect Spectrometers 332
Appendix 1: References 335
Appendix 2: Short Table of Physical Constants, Conversion Factors, and Waveguide Nomenclature 409
Appendix 3: Evaluation of E(k) 410
Appendix 4: Derivation of the Hamiltonian for Treating the Vibration-Rotation Interaction Problem 416
Appendix 5: Derivation of the Inertial Defect 423
Appendix 6: Coupling of Angular Momentum Vectors 426
Appendix 7: The Van Vleck Transformation 428
Appendix 8: Internal Rotation Splittings for the IAM 431
Appendix 9: Barriers to Internal Rotation Determined by Microwave Spectroscopy 433
Appendix 10: Vanishing of Odd-Order Nondegenerate Stark Corrections 439
Appendix 11: Mathieu's Equation 440
Appendix 12: Perturbation Coefficients for the Internal Rotation Problem 444
Appendix 13: Molecular Zeeman Effect 457
Appendix 14: Stark Corrections for a Linear Molecule 464
AUTHOR INDEX 466
SUBJECT INDEX 481