PREFACE ........................................................ xi
1 REVIEW OF TIME-INDEPENDENT QUANTUM MECHANICS
1.1 States, Operators, and Representations .................. 1
1.2 Eigenvalue Problems and the Schrцdinger Equation ........ 4
1.3 Expectation Values, Uncertainty Relations ............... 6
1.4 The Particle in a Box ................................... 7
1.5 Harmonic Oscillator ..................................... 9
1.6 The Hydrogen Atom and Angular Momentum ................. 12
1.7 Approximation Methods .................................. 15
1.8 Electron Spin .......................................... 18
1.9 The Born-Oppenheimer Approximation ..................... 22
1.10 Molecular Orbitals ..................................... 22
1.11 Energies and Time Scales; Separation of Motions ........ 25
Further Reading ............................................. 26
Problems .................................................... 27
2 ELECTROMAGNETIC RADIATION
2.1 Classical Description of Light ......................... 31
2.2 Quantum Mechanical Description of Light ................ 35
2.3 Fourier Transform Relationships Between Time and
Frequency .............................................. 38
2.1 Blackbody Radiation .................................... 40
2.5 Light Sources for Spectroscopy ......................... 42
References and Further Reading .............................. 44
Problems .................................................... 44
3 RADIATION-MATTER INTERACTIONS
3.1 The Time-Dependent Schrцdinger Equation ................ 47
3.2 Time-Dependent Perturbation Theory ..................... 50
3.3 Interaction of Matter with the Classical Radiation
Field .................................................. 54
3.4 Interaction of Matter with the Quantized Radiation
Field .................................................. 59
References and Further Reading .............................. 63
Problems .................................................... 64
4 ABSORPTION AND EMISSION OF LIGHT
4.1 Einstein Coefficients for Absorption and Emission ...... 67
4.2 Other Measures of Absorption Strength .................. 69
4.3 Radiative Lifetimes .................................... 72
4.4 Oscillator Strengths ................................... 73
4.5 Local Fields ........................................... 73
Further Reading ............................................. 74
Problems .................................................... 75
5 SYSTEM-BATH INTERACTIONS
5.1 Phenomenological Treatment of Relaxation and
Lineshapes ............................................. 79
5.2 The Density Matrix ..................................... 86
5.3 Density Matrix Methods in Spectroscopy ................. 90
5.4 Exact Density Matrix Solution for a Two-Level System ... 95
References and Further Reading .............................. 98
Problems .................................................... 98
6 SYMMETRY CONSIDERATIONS
6.1 Qualitative Aspects of Molecular Symmetry ............. 103
6.2 Introductory Group Theory ............................. 104
6.3 Finding the Symmetries of Vibrational Modes of
a Certain Type ........................................ 109
6.4 Finding the Symmetries of All Vibrational Modes ....... 111
Further Reading ............................................ 113
Problems ................................................... 113
7 MOLECULAR VIBRATIONS AND INFRARED SPECTROSCOPY
7.1 Vibrational Transitions ............................... 115
7.2 Diatomic Vibrations ................................... 117
7.3 Anharmonicity ......................................... 118
7.4 Polyatomic Molecular Vibrations: Normal Modes ......... 121
7.5 Symmetry Considerations ............................... 127
7.6 Isotopic Shifts ....................................... 130
7.7 Solvent Effects on Vibrational Spectra ................ 130
References and Further Reading ............................. 135
Problems ................................................... 135
8 ELECTRONIC SPECTROSCOPY
8.1 Electronic Transitions ................................ 139
8.2 Spin and Orbital Selection Rules ...................... 141
8.3 Spin-Orbit Coupling ................................... 143
8.4 Vibronic Structure .................................... 143
8.5 Vibronic Coupling ..................................... 148
8.6 The Jahn-Teller Effect ................................ 151
8.7 Considerations in Large Molecules ..................... 152
8.8 Solvent Effects on Electronic Spectra ................. 154
Further Reading ............................................ 159
Problems ................................................... 160
9 PHOTOPHYSICAL PROCESSES
9.1 Jablonski Diagrams .................................... 163
9.2 Quantum Yields and Lifetimes .......................... 166
9.3 Fermi's Golden Rule for Radiationless Transitions ..... 167
9.4 Internal Conversion and Intersystem Crossing .......... 167
9.5 Intramolecular Vibrational Redistribution ............. 173
9.6 Energy Transfer ....................................... 179
9.7 Polarization and Molecular Reorientation in Solution .. 182
References and Further Reading ............................. 186
Problems ................................................... 186
10 LIGHT SCATTERING
10.1 Rayleigh Scattering from Particles .................... 191
10.2 Classical Treatment of Molecular Raman and Rayleigh
Scattering ............................................ 193
10.1 Quantum Mechanical Treatment of Molecular Raman and
Rayleigh Scattering ................................... 195
10.4 Nonresonant Raman Scattering .......................... 204
10.5 Symmetry Considerations and Depolarization Ratios in
Raman Scattering ...................................... 206
10.6 Resonance Raman Spectroscopy .......................... 207
References and Further Reading ............................. 211
Problems ................................................... 211
11 NONLINEAR AND PUMP-PROBE SPECTROSCOPIES
11.1 Linear and Nonlinear Susceptibilities ................. 215
11.2 Multiphoton Absorption ................................ 216
11.3 Pump-Probe Spectroscopy: Transient Absorption and
Stimulated Emission ................................... 219
11.4 Vibrational Oscillations and Impulsive Stimulated
Scattering ............................................ 225
11.5 Second Harmonic and Sum Frequency Generation .......... 227
11.6 Four-Wave Mixing ...................................... 232
11.7 Photon Echoes ......................................... 232
References and Further Reading ............................. 234
Problems ................................................... 234
12 ELECTRON TRANSFER PROCESSES
12.1 Charge-Transfer Transitions ........................... 239
12.2 Marcus Theory ......................................... 243
12.3 Spectroscopy of Anions and Cations .................... 247
References and Further Reading ............................. 248
Problems ................................................... 248
13 COLLECTIONS OF MOLECULES
13.1 Van der Waals Molecules ............................... 251
13.2 Dimers and Aggregates ................................. 252
13.3 Localized and Delocalized Excited States .............. 253
13.4 Conjugated Polymers ................................... 256
References ................................................. 259
Problems ................................................... 259
14 METALS AND PLASMONS
14.1 Dielectric Function of a Metal ........................ 263
14.2 Plasmons .............................................. 266
14.3 Spectroscopy of Metal Nanoparticles ................... 268
14.4 Surface-Enhanced Raman and Fluorescence ............... 270
References and Further Reading ............................. 274
Problems ................................................... 275
15 CRYSTALS
15.1 Crystal Lattices ...................................... 277
15.2 Phonons in Crystals ................................... 281
15.3 Infrared and Raman Spectra ............................ 284
15.4 Phonons in Nanocrystals ............................... 286
References and Further Reading ............................. 287
Problems ................................................... 287
16 ELECTRONIC SPECTROSCOPY OF SEMICONDUCTORS
16.1 Band Structure ........................................ 291
16.2 Direct and Indirect Transitions ....................... 296
16.3 Excitons .............................................. 296
16.4 Defects ............................................... 298
16.5 Semiconductor Nanocrystals ............................ 298
Further Reading ............................................ 302
Problems ................................................... 302
APPENDICES
A PHYSICAL CONSTANTS, UNIT SYSTEMS, AND CONVERSION FACTORS ... 305
В MISCELLANEOUS MATHEMATICS REVIEW ........................... 309
С MATRICES AND DETERMINANTS .................................. 313
D CHARACTER TABLES FOR SOME COMMON POINT GROUPS .............. 317
E FOURIER TRANSFORMS ......................................... 321
INDEX ......................................................... 323
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