Rotational Spectra and Molecular Structure (eBook)

Physical Chemistry: A Series of Monographs

James E. Wollrab (Autor)

Ernest M. Loebl (Herausgeber)

eBook Download: PDF

2013 | 1. Auflage
484 Seiten
Elsevier Science (Verlag)
978-1-4831-9485-1 (ISBN)

Infos

Physical Chemistry, A Series of Monographs: Rotational Spectra and Molecular Structure covers the energy levels and rotational transitions. This book is divided into nine chapters that evaluate the rigid asymmetric top molecules and the nuclear spin statistics for asymmetric tops. Some of the topics covered in the book are the asymmetric rotor functions; rotational transition intensities; classes of molecules; nuclear spin statistics for linear molecules and symmetric tops; and classical appearance of centrifugal and coriolis forces. Other chapters deal with the energy levels and effects of centrifugal distortion, as well as the internuclear distance and moments of inertia. The discussion then shifts to the coriolis coupling effects on rotational constants and the perturbation treatment of vibration-rotational Hamiltonian. The last chapter is devoted to the examination of origin of the quadrupole interaction. The book can provide useful information to chemists, physicists, electrical engineers, students, and researchers.

Inhalt

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

Produkt-Details

• Erscheint lt. Verlag: 22.10.2013
• Sprache: englisch
• Themenwelt: Naturwissenschaften ► Chemie ► Physikalische Chemie
• Themenwelt: Naturwissenschaften ► Physik / Astronomie ► Atom- / Kern- / Molekularphysik
• Themenwelt: Technik
• ISBN-10: 1-4831-9485-X / 148319485X
• ISBN-13: 978-1-4831-9485-1 / 9781483194851