Spectra of Atoms and Molecules

by Bernath, Peter F.

• ISBN13: 9780195075984
• ISBN10: 0195075986
• Format: Hardcover
• Copyright: 1995-03-23
• Publisher: Oxford University Press

Summary

Spectra of Atoms and Molecules is a very thorough and pedagogically organized textbook. It emphasizes the fundamental principles of spectroscopy with its primary goal being to teach students how to interpret spectra. The book reviews the basic skills needed to understand the material, including a clear presentation of group theory. A large number of excellent problems, many stated in the language of matrices, are found at the end of each chapter. In keeping with the visual aspects of the course, the author provides a large number of diagrams and spectra specifically recorded for this book. The author discusses such topics as molecular symmetry, matrix representation of groups, quantum mechanics and group theory. Analyses are made of atomic, rotational, vibrational, and electronic spectra. The Raman effect is also discussed. Undergraduate senior and first-year graduate students studying molecular spectroscopy will find this text indispensable. It will also be of interest to professionals in chemistry, physics, astronomy, and engineering.

Author Biography

Peter F. Bernath is Professor of Chemistry at the University of Waterloo in Ontario, Canada

Table of Contents

Introduction	p. 3
Waves, Particles, and Units	p. 3
The Electromagnetic Spectrum	p. 5
Interaction of Radiation with Matter	p. 7
Blackbody Radiation	p. 7
Einstein A and B Coefficients	p. 8
Absorption and Emission of Radiation	p. 11
Beer's Law	p. 19
Lineshape Functions	p. 21
Natural Lifetime Broadening	p. 22
Pressure Broadening	p. 27
Doppler Broadening	p. 28
Transit-Time Broadening	p. 31
Power Broadening	p. 33
Molecular Symmetry	p. 41
Symmetry Operations	p. 41
Operator Algebra	p. 42
Symmetry Operator Algebra	p. 46
Groups	p. 48
Point Groups	p. 49
Classes	p. 50
Subgroups	p. 51
Notation for Point Groups	p. 52
Matrix Representation of Groups	p. 58
Vectors and Matrices	p. 58
Matrix Eigenvalue Problem	p. 63
Similarity Transformations	p. 65
Symmetry Operations and Position Vectors	p. 65
Reflection	p. 66
Rotation	p. 67
Inversion	p. 68
Rotation-Reflection	p. 68
Identity	p. 69
Symmetry Operators and Basis Vectors	p. 69
Symmetry Operators and Basis Functions	p. 72
Function Spaces	p. 72
Gram-Schmidt Procedure	p. 74
Transformation Operators	p. 74
Equivalent, Reducible, and Irreducible Representations	p. 77
Equivalent Representations	p. 77
Unitary Representations	p. 78
Reducible and Irreducible Representations	p. 78
Great Orthogonality Theorem	p. 79
Characters	p. 81
Character Tables	p. 83
Mulliken Notation	p. 84
Quantum Mechanics and Group Theory	p. 91
Matrix Representation of the Schrodinger Equation	p. 91
Born-Oppenheimer Approximation	p. 97
Symmetry of the Hamiltonian Operator	p. 99
Projection Operators	p. 100
Direct Product Representations	p. 103
Integrals and Selection Rules	p. 105
Atomic Spectroscopy	p. 109
Background	p. 109
Angular Momentum	p. 111
The Hydrogen Atom and One-Electron Spectra	p. 115
Vector Model	p. 118
Spin-Orbit Coupling	p. 120
Many-Electron Atoms	p. 124
Selection Rules	p. 134
Atomic Spectra	p. 137
Hyperfine Structure	p. 137
Hydrogen Atom	p. 138
Intensity of Atomic Lines	p. 140
Zeeman Effect	p. 147
Paschen-Back Effect	p. 152
Stark Effect	p. 153
Rotational Spectroscopy	p. 161
Rotation of Rigid Bodies	p. 161
Diatomic and Linear Molecules	p. 169
Selection Rules	p. 171
Centrifugal Distortion	p. 174
Vibrational Angular Momentum	p. 177
Line Intensities for Diatomic and Linear Molecules	p. 182
Symmetric Tops	p. 185
Molecule and Space-Fixed Angular Momenta	p. 185
Rotational Spectra	p. 190
Centrifugal Distortion	p. 190
Line Intensity	p. 192
Asymmetric Tops	p. 193
Selection Rules	p. 195
Line Intensity	p. 198
Structure Determination	p. 198
Vibrational Spectroscopy	p. 208
Diatomic Molecules	p. 208
Wavefunctions for Harmonic and Anharmonic Oscillators	p. 215
Vibrational Selection Rules for Diatomics	p. 216
Dissociation Energies from Spectroscopic Data	p. 220
Vibration-Rotation Transitions of Diatomics	p. 223
Combination Differences	p. 224
Vibrational Motion of Polyatomic Molecules	p. 226
Classical Mechanical Description	p. 226
Quantum Mechanical Description	p. 231
Internal Coordinates	p. 232
Symmetry Coordinates	p. 233
Symmetry of Normal Modes	p. 238
Selection Rules for Vibrational Transitions	p. 245
Vibration-Rotation Transitions of Linear Molecules	p. 247
Nuclear Spin Statistics	p. 253
Excited Vibrational States of Linear Molecules	p. 256
Vibrational Spectra of Symmetric Tops	p. 259
Coriolis Interactions in Molecules	p. 260
Infrared Transitions of Spherical Tops	p. 266
Vibrational Spectra of Asymmetric Tops	p. 270
Vibration-Rotation Line Intensities	p. 272
Line Intensity Calculations	p. 275
Fermi and Coriolis Perturbations	p. 278
Inversion Doubling and Fluxional Behavior	p. 280
Light Scattering and the Raman Effect	p. 293
Background	p. 293
Classical Model	p. 293
Quantum Model	p. 298
Polarization	p. 305
Rotational Raman Effect	p. 307
Diatomic Molecules	p. 309
Vibration-Rotation Raman Spectroscopy	p. 309
Diatomic Molecules	p. 309
Rayleigh and Raman Intensities	p. 310
Classical Theory	p. 310
Vibrational Intensity Calculations	p. 315
Conclusions	p. 317
Electronic Spectroscopy of Diatomics	p. 321
Orbitals and States	p. 321
Vibrational Structure	p. 326
Rotational Structure of Diatomic Molecules	p. 332
Singlet-Singlet Transitions	p. 332
Nonsinglet Transitions	p. 337
The Symmetry of Diatomic Energy Levels: Parity	p. 346
Total (+/-) Parity	p. 347
Rotationless (e/f) Parity	p. 349
Gerade/Ungerade (g/u) Parity	p. 351
Symmetric/Antisymmetric (s/a) Parity	p. 352
Rotational Line Intensities	p. 353
Dissociation, Photodissociation, and Predissociation	p. 359
Electronic Spectroscopy of Polyatomics	p. 367
Orbitals and States	p. 367
Walsh's Rules: Qualitative Molecular Orbital Theory	p. 368
Huckel Molecular Orbital Theory	p. 372
Vibrational Structure of Electronic Transitions	p. 379
Vibronic Coupling: The Herzberg-Teller Effect	p. 382
Jahn-Teller Effect	p. 385
Renner-Teller Effect	p. 386
Nonradiative Transitions: Jablonski Diagram	p. 388
Photoelectron Spectroscopy	p. 390
Rotational Structure: H[subscript 2]CO and HCN	p. 391
Intensity of Transitions	p. 398
Units, Conversions, and Physical Constants	p. 406
Character Tables	p. 408
Direct Product Tables	p. 420
Introductory Textbooks	p. 424
Figure Acknowledgments	p. 427
Index	p. 431
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