William W. Parson
Clemens Burda
Modern Optical
Spectroscopy
From Fundamentals to Applications in
Chemistry, Biochemistry and Biophysics
Third Edition
,Modern Optical Spectroscopy
,William W. Parson • Clemens Burda
Modern Optical
Spectroscopy
From Fundamentals to Applications in
Chemistry, Biochemistry and Biophysics
Third Edition
,William W. Parson Clemens Burda
Department of Biochemistry Department of Chemistry
University of Washington Case Western Reserve University
Seattle, WA, USA Cleveland, OH, USA
ISBN 978-3-031-17221-2 ISBN 978-3-031-17222-9 (eBook)
https://doi.org/10.1007/978-3-031-17222-9
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,Contents
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 The Beer-Lambert Law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.3 Regions of the Electromagnetic Spectrum . . . . . . . . . . . . . . . . 4
1.4 Absorption Spectra of Proteins and Nucleic Acids . . . . . . . . . . 6
1.5 Absorption Spectra of Mixtures . . . . . . . . . . . . . . . . . . . . . . . 8
1.6 The Photoelectric Effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
1.7 Techniques for Measuring Absorbance . . . . . . . . . . . . . . . . . . 11
1.8 Pump-Probe and Photon-Echo Experiments . . . . . . . . . . . . . . 15
1.9 Linear and Circular Dichroism . . . . . . . . . . . . . . . . . . . . . . . . 16
1.10 Distortions of Absorption Spectra by Light Scattering or
Nonuniform Distributions of the Absorbing Molecules . . . . . . 18
1.11 Fluorescence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
1.12 IR and Raman Spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . 25
1.13 Lasers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
1.14 Nomenclature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
1.15 Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
2 Basic Concepts of Quantum Mechanics . . . . . . . . . . . . . . . . . . . . . . 35
2.1 Wavefunctions, Operators and Expectation Values . . . . . . . . . 35
2.1.1 Wavefunctions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
2.1.2 Operators and Expectation Values . . . . . . . . . . . . . . . . 36
2.2 The Time-Dependent and Time-Independent Schrödinger
Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
2.2.1 Superposition States . . . . . . . . . . . . . . . . . . . . . . . . . . 47
2.3 Spatial Wavefunctions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
2.3.1 A Free Particle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
2.3.2 A Particle in a Box . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
2.3.3 The Harmonic Oscillator . . . . . . . . . . . . . . . . . . . . . . . 53
2.3.4 Atomic Orbitals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
2.3.5 Molecular Orbitals . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
2.3.6 Wavefunctions for Large Systems . . . . . . . . . . . . . . . . 66
v
,vi Contents
2.4 Spin Wavefunctions and Singlet and Triplet States . . . . . . . . . 69
2.5 Transitions Between States: Time-Dependent Perturbation
Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
2.6 Lifetimes of States and the Uncertainty Principle . . . . . . . . . . . 80
2.7 Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
3 Light . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
3.1 Electromagnetic Fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
3.1.1 Electrostatic Forces and Fields . . . . . . . . . . . . . . . . . . 87
3.1.2 Electrostatic Potentials . . . . . . . . . . . . . . . . . . . . . . . . 88
3.1.3 Electromagnetic Radiation . . . . . . . . . . . . . . . . . . . . . 91
3.1.4 Energy Density and Irradiance . . . . . . . . . . . . . . . . . . 98
3.1.5 Electromagnetic Momentum . . . . . . . . . . . . . . . . . . . . 101
3.2 The Black-Body Radiation Law . . . . . . . . . . . . . . . . . . . . . . . 103
3.3 Linear and Circular Polarization . . . . . . . . . . . . . . . . . . . . . . . 105
3.4 Quantum Theory of Electromagnetic Radiation . . . . . . . . . . . . 107
3.5 Superposition States and Interference Effects in Quantum
Optics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
3.6 Refraction, Evanescent Radiation, and Surface Plasmons . . . . . 115
3.7 The Classical Theory of Dielectric Dispersion . . . . . . . . . . . . . 118
3.8 Nonlinear Optics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
3.9 Birefringence and Electro-Optic Effects . . . . . . . . . . . . . . . . . 124
3.10 Optical Wavepackets and Mode-Locked Lasers . . . . . . . . . . . . 127
3.11 Local-Field Correction Factors . . . . . . . . . . . . . . . . . . . . . . . . 130
3.12 Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
4 Electronic Absorption . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
4.1 Interactions of Electrons with Oscillating Electric Fields . . . . . 137
4.2 The Rates of Absorption and Stimulated Emission . . . . . . . . . . 142
4.3 Transition Dipoles and Dipole Strengths . . . . . . . . . . . . . . . . . 146
4.4 Calculating Transition Dipoles for π Molecular Orbitals . . . . . . 156
4.5 The Role of Molecular Symmetry in Electronic Transitions . . . 158
4.6 Using Group Theory to Determine Whether a Transition Is
Allowed by Symmetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164
4.7 Linear Dichroism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176
4.8 Configuration Interactions . . . . . . . . . . . . . . . . . . . . . . . . . . . 180
4.9 Calculating Electric Transition Dipoles with the Gradient
Operator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184
4.10 Transition Dipoles for Excitations to Singlet and Triplet
States . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193
4.11 The Born-Oppenheimer Approximation, Franck-Condon
Factors, and the Shapes of Electronic Absorption Bands . . . . . 195
4.12 Spectroscopic Hole Burning . . . . . . . . . . . . . . . . . . . . . . . . . . 204
,Contents vii
4.13 Effects of the Surroundings on Molecular Transition
Energies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207
4.14 The Electronic Stark Effect . . . . . . . . . . . . . . . . . . . . . . . . . . 216
4.15 Spectroscopy of Transition-Metal Complexes . . . . . . . . . . . . . 223
4.16 Thermodynamics of Photoexcitation . . . . . . . . . . . . . . . . . . . . 228
4.17 Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 236
5 Fluorescence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245
5.1 The Einstein Coefficients for Absorption and Emission . . . . . . 245
5.2 The Stokes Shift . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 248
5.3 The Mirror-image Law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 250
5.4 The Strickler-Berg Equation and Other Relationships Between
Absorption and Fluorescence . . . . . . . . . . . . . . . . . . . . . . . . . 253
5.5 Quantum Theory of Absorption and Emission . . . . . . . . . . . . . 259
5.6 Fluorescence Yields and Lifetimes . . . . . . . . . . . . . . . . . . . . . 264
5.7 Fluorescent Probes and Tags . . . . . . . . . . . . . . . . . . . . . . . . . 271
5.8 Quantum Dot Fluorescence . . . . . . . . . . . . . . . . . . . . . . . . . . 274
5.9 Photobleaching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 276
5.10 Fluorescence Anisotropy . . . . . . . . . . . . . . . . . . . . . . . . . . . . 277
5.11 Single-molecule Fluorescence and High-resolution
Fluorescence Microscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . 284
5.12 Fluorescence Correlation Spectroscopy . . . . . . . . . . . . . . . . . . 289
5.13 Intersystem Crossing, Phosphorescence, and Delayed
Fluorescence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 295
5.14 Electron Transfer from Excited Molecules . . . . . . . . . . . . . . . 298
5.15 Solar Cells and Light-emitting Diodes . . . . . . . . . . . . . . . . . . 306
5.16 Aggregation-induced Emission . . . . . . . . . . . . . . . . . . . . . . . . 309
5.17 Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 311
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 312
6 Vibrational Absorption . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 331
6.1 Vibrational Normal Modes and Wavefunctions . . . . . . . . . . . . 331
6.2 Vibrational Excitation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 340
6.3 Selection Rules and Effects of Anharmonicity . . . . . . . . . . . . . 342
6.4 Comparisons of IR and Raman Spectroscopy . . . . . . . . . . . . . 345
6.5 Effects of Molecular Symmetry in IR and Raman
Spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 348
6.6 Rotational Absorption and Fine Structure . . . . . . . . . . . . . . . . 353
6.7 Infrared Spectroscopy of Proteins and Nucleic Acids . . . . . . . . 357
6.8 Vibrational Stark Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . 362
6.9 IR Lasers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 364
6.10 Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 365
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 367
,viii Contents
7 Resonance Energy Transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 377
7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 377
7.2 The Förster Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 379
7.3 Using Energy Transfer to Study Fast Processes in Single
Protein Molecules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 394
7.4 Exchange Coupling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 396
7.5 Energy Transfer in Photosynthetic Antennas . . . . . . . . . . . . . . 398
7.6 Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 402
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 404
8 Exciton Interactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 409
8.1 Stationary States of Systems with Interacting Molecules . . . . . 409
8.2 Effects of Exciton Interactions on the Absorption Spectra of
Oligomers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 418
8.3 Transition-Monopole Treatments of Interaction Matrix
Elements and Mixing with Charge-Transfer Transitions . . . . . . 424
8.4 Exciton Absorption Band Shapes and Dynamic Localization
of Excitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 428
8.5 Exciton States in Photosynthetic Antenna Complexes . . . . . . . 431
8.6 Excimers and Exciplexes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 433
8.7 Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 436
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 439
9 Circular Dichroism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 445
9.1 Magnetic Transition Dipoles and n - π Transitions . . . . . . . . 445
9.2 The Origin of Circular Dichroism . . . . . . . . . . . . . . . . . . . . . . 456
9.3 Circular Dichroism of Dimers and Higher Oligomers . . . . . . . . 462
9.4 UV Circular Dichroism of Proteins and Nucleic Acids . . . . . . . 467
9.5 Vibrational Circular Dichroism . . . . . . . . . . . . . . . . . . . . . . . 470
9.6 Magnetic Circular Dichroism . . . . . . . . . . . . . . . . . . . . . . . . . 473
9.7 Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 476
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 478
10 Coherence and Dephasing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 483
10.1 Oscillations Between Quantum States of an Isolated
System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 483
10.2 The Density Matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 487
10.3 The Stochastic Liouville Equation . . . . . . . . . . . . . . . . . . . . . 493
10.4 Effects of Stochastic Relaxations on the Dynamics of
Quantum Transitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 495
10.5 A Density-Matrix Treatment of Absorption of Weak,
Continuous Light . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 501
10.6 The Relaxation Matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 504
10.7 More General Relaxation Functions and Spectral
Lineshapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 513
10.8 Anomalous Fluorescence Anisotropy . . . . . . . . . . . . . . . . . . . 519
,Contents ix
10.9 Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 525
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 526
11 Pump-Probe Spectroscopy, Photon Echoes, Two-Dimensional
Spectroscopy and Vibrational Wavepackets . . . . . . . . . . . . . . . . . . 529
11.1 First-Order Optical Polarization . . . . . . . . . . . . . . . . . . . . . . . 529
11.2 Third-Order Optical Polarization and Non-linear Response
Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 538
11.3 Pump-Probe Spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . 543
11.4 Photon Echoes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 547
11.5 Two-Dimensional Electronic and Vibrational Spectroscopy . . . 553
11.6 Transient Gratings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 558
11.7 Vibrational Wavepackets . . . . . . . . . . . . . . . . . . . . . . . . . . . . 561
11.8 Wavepacket Pictures of Spectroscopic Transitions . . . . . . . . . . 568
11.9 Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 572
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 573
12 Raman Scattering and Other Multi-photon Processes . . . . . . . . . . . 583
12.1 Types of Light Scattering . . . . . . . . . . . . . . . . . . . . . . . . . . . . 583
12.2 The Kramers-Heisenberg-Dirac Theory . . . . . . . . . . . . . . . . . . 587
12.3 The Wavepacket Picture of resonance Raman Scattering . . . . . 596
12.4 Selection Rules for Raman Scattering . . . . . . . . . . . . . . . . . . . 598
12.5 Surface-enhanced Raman Scattering . . . . . . . . . . . . . . . . . . . . 601
12.6 Applications of Raman Spectroscopy . . . . . . . . . . . . . . . . . . . 601
12.7 Coherent (Stimulated) Raman Scattering . . . . . . . . . . . . . . . . . 603
12.8 Multi-photon Absorption . . . . . . . . . . . . . . . . . . . . . . . . . . . . 605
12.9 Quasielastic (Dynamic) Light Scattering (Photon Correlation
Spectroscopy) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 608
12.10 Mie scattering by Larger Particles . . . . . . . . . . . . . . . . . . . . . 612
12.11 Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 614
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 615
Appendix A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 623
Vectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 623
Matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 625
Fourier Transforms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 627
Phase Shift and Modulation Amplitude in Frequency-Domain
Spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 631
CGS and SI Units and Abbreviations . . . . . . . . . . . . . . . . . . . . . . . . . 633
Harmonic-Oscillator Wavefunction Integrals . . . . . . . . . . . . . . . . . . . . 634
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 637
Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 639
, List of Boxes
Box 2.1 Operators for Observable Properties Must Be Hermitian . . . . . .. . . . 38
Box 2.2 Commutators and Formulations of the Position, Momentum
and Hamiltonian Operators . . .. .. . .. .. . .. .. . .. . .. .. . .. .. . .. .. . .. .. . .. . 39
Box 2.3 The Origin of the Time-Dependent Schrödinger Equation . . . . . . . . 43
Box 2.4 Linear Momentum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
Box 2.5 Hermite Polynomials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
Box 2.6 Boltzmann, Fermi-Dirac and Bose-Einstein Statistics . . . . . . . . . . . . . 74
Box 3.1 Maxwell’s Equations and the Vector Potential . . . . . . . . . . . . . . . . . . . . . 93
Box 4.1 Energy of a Dipole in an External Electric Field . . . . . . . . . . . . . . . . . . . 138
Box 4.2 Multipole Expansion of the Energy of a Set of Charges in a
Variable External Field . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
Box 4.3 The Behavior of the Function [exp(iy)-1]/y as y goes to 0 . . . . . . . . 143
Box 4.4 The Function sin2x/x2 and Its Integral . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
Box 4.5 The Oscillating Electric Dipole of a Superposition State . . . . . . . . . . 147
Box 4.6 The Mean-Squared Energy of Interaction of an External Field
with Dipoles in an Isotropic System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151
Box 4.7 Physical Constants and Conversion Factors for Absorption of
Light . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
Box 4.8 Evaluating Configuration-Interaction Coefficients . . . . . . . . . . . . . . . . . 181
Box 4.9 The Relationship between Matrix Elements of the Electric
Dipole and Gradient Operators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185
Box 4.10 Matrix Elements of the Gradient Operator for Atomic 2p
Orbitals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188
Box 4.11 Selection Rules for Electric-Dipole Excitations of Linear
Polyenes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192
Box 4.12 Recursion Formulas for Vibrational Overlap Integrals . . . . . . . . . . . . 199
Box 4.13 Thermally Weighted Franck-Condon Factors . . . . . . . . . . . . . . . . . . . . . . 201
Box 4.14 Electronic Stark Spectroscopy of Immobilized Molecules . . . . . . . . 220
Box 5.1 The ν3 Factor in the Strickler-Berg Equation . . . . . . . . . . . . . . . . . . . . . . . 256
Box 5.2 Creation and Annihilation Operators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263
Box 5.3 Binomial, Poisson and Gaussian Distributions . . . . . . . . . . . . . . . . . . . . . 291
Box 6.1 Normal Coordinates and Molecular-dynamics Simulations . . . . . . . 332
Box 7.1 Dipole-dipole Interactions . . . . .. . . . . .. . . . .. . . . . .. . . . . .. . . . . .. . . . . .. . . . 383
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