List of Figures ................................................. x
List of Tables ................................................. xv
Preface ...................................................... xvii
Acknowledgements .............................................. xix
List of Abbreviations ......................................... xxi
1 Fundamentals of Spectroscopy ................................. 1
1.1 Introduction ............................................ 1
1.2 Some Properties of Waves ................................ 2
1.2.1 Travelling waves ................................. 5
1.3 Electromagnetic Radiation ............................... 6
1.3.1 Wave nature of light ............................. 6
1.3.2 Particulate nature of radiation .................. 8
1.4 Electromagnetic Spectrum ............................... 12
1.5 Вlackbody Radiation .................................... 13
1.6 Boltzmann's Population Distribution .................... 15
1.7 Einstein's Coefficients ................................ 18
1.7.1 Lasers .......................................... 22
1.8 Line Broadening ........................................ 24
1.8.1 Natural line broadening ......................... 24
1.8.2 Pressure or collisional broadening .............. 32
1.8.3 Doppler broadening .............................. 32
1.9 Lambert-Beer's Law ..................................... 38
1.9.1 Power or saturation broadening .................. 41
1.10 Fourier Transform Spectroscopy ......................... 42
1.11 Summary ................................................ 46
1.12 Exercises .............................................. 47
2 Theoretical Principles ...................................... 51
2.1 Introduction ........................................... 51
2.2 The Postulates of Quantum Mechanics Explained .......... 52
2.3 Time-Dependent Perturbation ............................ 57
2.3.1 The interaction of electromagnetic radiation
with a molecular system ......................... 60
2.4 Einstein's Coefficient of Induced Absorption ........... 65
2.4.1 Comparison with experimental quantities ......... 68
2.5 Einstein's Coefficients of Induced and Spontaneous
Emission ............................................... 70
2.6 The Basis of Selection Rules ........................... 72
2.7 Overview of Selection Rules ............................ 74
2.8 Summary ................................................ 77
2.9 Exercises .............................................. 77
3 Atomic Spectroscopy ......................................... 79
3.1 Introduction ........................................... 79
3.2 The Bohr Theory of the Hydrogen Atom ................... 79
3.3 Hydrogen and Hydrogen-like Ion Spectra ................. 83
3.3.1 Transition probabilities ........................ 86
3.4 Multi-Electron Atoms ................................... 89
3.4.1 Alkali metal spectra ............................ 90
3.4.2 Two-electron systems ............................ 92
3.4.3 Ground state terms ............................. 102
3.4.4 Quantitative treatment of the coupling of
orbital and spin angular momenta for multi-
electron atoms ................................. 103
3.4.5 Intermediate coupling .......................... 109
3.4.6 Interaction with external fields ............... 109
3.5 Photoelectron Spectroscopy ............................ 115
3.6 Summary ............................................... 117
3.7 Exercises ............................................. 118
4 Pure Rotational Spectroscopy ............................... 124
4.1 Overview of Molecular Spectra ......................... 124
4.2 The Rigid Diatomic Molecule (The Rigid Rotor) ......... 127
4.2.1 Interaction of radiation with a rotating
molecule ....................................... 134
4.2.2 Rotational spectra and bond lengths of
diatomic molecules ............................. 137
4.2.3 The effect of isotopic substitution ............ 139
4.2.4 Rotational energy level populations:
Intensities of spectral lines .................. 141
4.2.5 Centrifugal distortion ......................... 147
4.3 Rotation of Polyatomic Molecules: Classification of
Molecules ............................................. 149
4.3.1 Linear molecules ............................... 152
4.3.2 Spherical tops ................................. 156
4.3.3 Symmetric tops ................................. 156
4.3.4 Asymmetric top molecules ....................... 165
4.4 The Effect of Electric Fields: The Stark Effect ....... 169
4.4.1 Effect on the energy levels of a symmetric top . 169
4.4.2 Stark effect for linear molecules ............... 172
4.5 Applications of Microwave Spectroscopy ................ 172
4.6 Summary ............................................... 173
4.7 Exercises ............................................. 174
5 Vibrational Spectroscopy of Diatomics ...................... 182
5.1 Introduction .......................................... 182
5.2 Oscillations of Systems with One Degree of Freedom .... 182
5.3 The Diatomic Molecule ................................. 185
5.3.1 Lagrange's equations of motion ................. 187
5.3.2 Normal coordinates and linear transformations .. 188
5.3.3 Simultaneous diagonalization ................... 189
5.3.4 Heteronuclear diatomic molecules ............... 191
5.3.5 Mass-weighted coordinates ...................... 192
5.4 Quantum Mechanical Treatment .......................... 196
5.4.1 Mechanism of infrared radiation absorption:
qualitative ideas .............................. 201
5.4.2 Quantitative treatment of selection rules ...... 202
5.5 The Potential Energy Function for a Chemical Bond ..... 208
5.5.1 Experimental accuracy of the Morse potential ... 214
5.5.2 Force constants ................................ 214
5.5.3 Isotopic substitution .......................... 216
5.5.4 Vibrational dependences of rotational
constants ...................................... 221
5.5.5 Combination differences ........................ 223
5.6 Summary ............................................... 224
5.7 Exercises ............................................. 225
6 Vibrational Spectroscopy of Polyatomic Molecules ........... 231
6.1 Introduction .......................................... 231
6.2 Normal Modes of Vibration of Carbon Dioxide ........... 231
6.2.1 Properties of normal modes ..................... 237
6.2.2 Selection rules for carbon dioxide ............. 238
6.2.3 Vibration-rotation spectra of symmetric top
molecules ...................................... 241
6.2.4 Symmetries of normal modes ..................... 242
6.2.5 Selection rales ................................ 250
6.2.6 Higher vibrational wave functions .............. 256
6.2.7 Combination bands .............................. 257
6.3 Summary ............................................... 260
6.4 Exercises ............................................. 260
7 The Raman Effect ........................................... 263
7.1 Introduction .......................................... 263
7.2 Classical Treatment of the Raman Effect ............... 264
7.2.1 Polarizability ................................. 264
7.2.2 Molecular rotations ............................ 265
7.2.3 Molecular vibrations ........................... 266
7.3 Quantum Theory ........................................ 267
7.3.1 Polarizability ellipsoid ....................... 267
7.3.2 Selection rules ................................ 270
7.4 Rule of Mutual Exclusion .............................. 277
7.5 Polarization of Raman Lines ........................... 279
7.6 Fermi Resonance ....................................... 282
7.7 Influence of Nuclear Spin ............................. 284
7.8 Structure Determination Using Combined Infrared and
Raman Data ............................................ 289
7.8.1 Examples of spectral assignments ............... 290
7.9 Group Frequencies ..................................... 297
7.10 Comparison of IR and Raman spectroscopies ............. 299
7.11 Advanced Raman Techniques ............................. 299
7.12 Summary ............................................... 300
7.13 Exercises ............................................. 300
8 Electronic Spectroscopy of Diatomic Molecules .............. 305
8.1 Introduction .......................................... 305
8.2 The Born-Oppenheimer Approximation .................... 305
8.3 Vibrational Coarse Structure .......................... 307
8.4 Franck-Condon Principle ............................... 308
8.5 Dissociation Energy ................................... 311
8.5.1 The Franck-Condon factor: Quantum mechanical
treatment ...................................... 314
8.6 Electronic Structure of Diatomic Molecules ............ 316
8.6.1 Homonuclear diatomic molecules ................. 322
8.6.2 Heteronuclear diatomic molecules ............... 324
8.7 Electronic Angular Momentum in Diatomic Molecules ..... 328
8.7.1 Completely fdled shells ........................ 328
8.7.2 Single unpaired electron ....................... 328
8.7.3 Two unpaired electrons ......................... 329
8.8 Selection Rules ....................................... 331
8.9 Rotational Fine Structure of Electronic-Vibrational
Transitions ........................................... 334
8.9.1 The Fortrat diagram ............................ 336
8.10 Photoelectron Spectroscopy (PES) ...................... 337
8.11 Summary ............................................... 342
8.12 Exercises ............................................. 342
9 Electronic Spectroscopy of Polyatomic Molecules ............ 346
9.1 Introduction .......................................... 346
9.2 Intensities of Electronic Transitions ................. 346
9.2.1 Calculation of oscillator strength ............. 347
9.3 Types of Electronic Transitions ....................... 349
9.3.1 Effect of conjugation .......................... 352
9.3.2 Effect of solvent .............................. 354
9.4 Theories of π → π* Transitions ........................ 355
9.4.1 Hьckel molecular orbital (HMO) theory .......... 356
9.5 Free Electron Model of Linear Polyenes ................ 365
9.5.1 Calculation of the wave functions .............. 366
9.5.2 Energy of the longest wavelength transition
in polyenes .................................... 366
9.5.3 Selection rules for particle-in-a-box wave
functions ...................................... 370
9.6 Change of Molecular Shape on Absorption ............... 372
9.6.1 AH2 molecules .................................. 372
9.6.2 The electronic structure of formaldehyde ....... 377
9.7 Vibronic Coupling ..................................... 380
9.8 Re-emission of Energy by an Excited Molecule .......... 381
9.9 Kinetics of Photochemistry ............................ 385
9.10 Summary ............................................... 389
9.11 Exercises ............................................. 389
Appendix 1 .................................................... 397
Appendix 2 .................................................... 399
Bibliography .................................................. 403
Index ......................................................... 405
| 
