Modern Optical Spectroscopy: From Fundamentals to Applications in Chemistry, Biochemistry and Biophysics

653 Pages·2023·18.19 MB·English

by  William W. Parson, Clemens Burda

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 (cid:129) Clemens Burda
Modern Optical
Spectroscopy
From Fundamentals to Applications in
Chemistry, Biochemistry and Biophysics
Third Edition
WilliamW.Parson ClemensBurda
DepartmentofBiochemistry DepartmentofChemistry
UniversityofWashington CaseWesternReserveUniversity
Seattle,WA,USA Cleveland,OH,USA
ISBN978-3-031-17221-2 ISBN978-3-031-17222-9 (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 TheBeer-LambertLaw. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.3 RegionsoftheElectromagneticSpectrum. . . . . . . . . . . . . . . . 4
1.4 AbsorptionSpectraofProteinsandNucleicAcids. . . . . . . . . . 6
1.5 AbsorptionSpectraofMixtures. . . . . . . . . . . . . . . . . . . . . . . 8
1.6 ThePhotoelectricEffect. . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
1.7 TechniquesforMeasuringAbsorbance. . . . . . . . . . . . . . . . . . 11
1.8 Pump-ProbeandPhoton-EchoExperiments. . . . . . . . . . . . . . 15
1.9 LinearandCircularDichroism. . . . . . . . . . . . . . . . . . . . . . . . 16
1.10 DistortionsofAbsorptionSpectrabyLightScatteringor
NonuniformDistributionsoftheAbsorbingMolecules. . . . . . 18
1.11 Fluorescence. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
1.12 IRandRamanSpectroscopy. . . . . . . . . . . . . . . . . . . . . . . . . 25
1.13 Lasers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
1.14 Nomenclature. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
1.15 Questions. .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
2 BasicConceptsofQuantumMechanics. . . . . . . . . . . . . . . . . . . . . . 35
2.1 Wavefunctions,OperatorsandExpectationValues. . . . . . . . . 35
2.1.1 Wavefunctions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
2.1.2 OperatorsandExpectationValues. . . . . . . . . . . . . . . . 36
2.2 TheTime-DependentandTime-IndependentSchrödinger
Equations. .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
2.2.1 SuperpositionStates. . . . . . . . . . . . . . . . . . . . . . . . . . 47
2.3 SpatialWavefunctions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
2.3.1 AFreeParticle. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
2.3.2 AParticleinaBox. . . . . . . . . . . . . . . . . . . . . . . . . . . 50
2.3.3 TheHarmonicOscillator. . . . . . . . . . . . . . . . . . . . . . . 53
2.3.4 AtomicOrbitals. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
2.3.5 MolecularOrbitals. . . . . . . . . . . . . . . . . . . . . . . . . . . 60
2.3.6 WavefunctionsforLargeSystems. . . . . . . . . . . . . . . . 66
vv
vi Contents
2.4 SpinWavefunctionsandSingletandTripletStates. . . . . . . . . 69
2.5 TransitionsBetweenStates:Time-DependentPerturbation
Theory. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
2.6 LifetimesofStatesandtheUncertaintyPrinciple. . . . . . . . . . . 80
2.7 Questions. .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
3 Light. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
3.1 ElectromagneticFields. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
3.1.1 ElectrostaticForcesandFields. . . . . . . . . . . . . . . . . . 87
3.1.2 ElectrostaticPotentials. . . . . . . . . . . . . . . . . . . . . . . . 88
3.1.3 ElectromagneticRadiation. . . . . . . . . . . . . . . . . . . . . 91
3.1.4 EnergyDensityandIrradiance. . . . . . . . . . . . . . . . . . 98
3.1.5 ElectromagneticMomentum. . . . . . . . . . . . . . . . . . . . 101
3.2 TheBlack-BodyRadiationLaw. . . . . . . . . . . . . . . . . . . . . . . 103
3.3 LinearandCircularPolarization. . . . . . . . . . . . . . . . . . . . . . . 105
3.4 QuantumTheoryofElectromagneticRadiation. . . . . . . . . . . . 107
3.5 SuperpositionStatesandInterferenceEffectsinQuantum
Optics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
3.6 Refraction,EvanescentRadiation,andSurfacePlasmons. . . . . 115
3.7 TheClassicalTheoryofDielectricDispersion. . . . . . . . . . . . . 118
3.8 NonlinearOptics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
3.9 BirefringenceandElectro-OpticEffects. . . . . . . . . . . . . . . . . 124
3.10 OpticalWavepacketsandMode-LockedLasers. . . . . . . . . . . . 127
3.11 Local-FieldCorrectionFactors. . . . . . . . . . . . . . . . . . . . . . . . 130
3.12 Questions. .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
4 ElectronicAbsorption. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
4.1 InteractionsofElectronswithOscillatingElectricFields. . . . . 137
4.2 TheRatesofAbsorptionandStimulatedEmission. . . . . . . . . . 142
4.3 TransitionDipolesandDipoleStrengths. . . . . . . . . . . . . . . . . 146
4.4 CalculatingTransitionDipolesforπ MolecularOrbitals. . . . . . 156
4.5 TheRoleofMolecularSymmetryinElectronicTransitions. . . 158
4.6 UsingGroupTheorytoDetermineWhetheraTransitionIs
AllowedbySymmetry. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164
4.7 LinearDichroism. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176
4.8 ConfigurationInteractions. . . . . . . . . . . . . . . . . . . . . . . . . . . 180
4.9 CalculatingElectricTransitionDipoleswiththeGradient
Operator. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184
4.10 TransitionDipolesforExcitationstoSingletandTriplet
States. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193
4.11 TheBorn-OppenheimerApproximation,Franck-Condon
Factors,andtheShapesofElectronicAbsorptionBands. . . . . 195
4.12 SpectroscopicHoleBurning. . . . . . . . . . . . . . . . . . . . . . . . . . 204
Contents vii
4.13 EffectsoftheSurroundingsonMolecularTransition
Energies. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207
4.14 TheElectronicStarkEffect. . . . . . . . . . . . . . . . . . . . . . . . . . 216
4.15 SpectroscopyofTransition-MetalComplexes. . . . . . . . . . . . . 223
4.16 ThermodynamicsofPhotoexcitation. . . . . . . . . . . . . . . . . . . . 228
4.17 Questions. .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 236
5 Fluorescence. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245
5.1 TheEinsteinCoefficientsforAbsorptionandEmission. . . . . . 245
5.2 TheStokesShift. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 248
5.3 TheMirror-imageLaw. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 250
5.4 TheStrickler-BergEquationandOtherRelationshipsBetween
AbsorptionandFluorescence. . . . . . . . . . . . . . . . . . . . . . . . . 253
5.5 QuantumTheoryofAbsorptionandEmission. . . . . . . . . . . . . 259
5.6 FluorescenceYieldsandLifetimes. . . . . . . . . . . . . . . . . . . . . 264
5.7 FluorescentProbesandTags. . . . . . . . . . . . . . . . . . . . . . . . . 271
5.8 QuantumDotFluorescence. . . . . . . . . . . . . . . . . . . . . . . . . . 274
5.9 Photobleaching. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 276
5.10 FluorescenceAnisotropy. . . . . . . . . . . . . . . . . . . . . . . . . . . . 277
5.11 Single-moleculeFluorescenceandHigh-resolution
FluorescenceMicroscopy.. . . .. . . .. . . . .. . . .. . . . .. . . .. 284
5.12 FluorescenceCorrelationSpectroscopy. . . . . . . . . . . . . . . . . . 289
5.13 IntersystemCrossing,Phosphorescence,andDelayed
Fluorescence. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 295
5.14 ElectronTransferfromExcitedMolecules. . . . . . . . . . . . . . . 298
5.15 SolarCellsandLight-emittingDiodes. . . . . . . . . . . . . . . . . . 306
5.16 Aggregation-inducedEmission. . . . . . . . . . . . . . . . . . . . . . . . 309
5.17 Questions. .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 311
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 312
6 VibrationalAbsorption. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 331
6.1 VibrationalNormalModesandWavefunctions. . . . . . . . . . . . 331
6.2 VibrationalExcitation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 340
6.3 SelectionRulesandEffectsofAnharmonicity. . . . . . . . . . . . . 342
6.4 ComparisonsofIRandRamanSpectroscopy. . . . . . . . . . . . . 345
6.5 EffectsofMolecularSymmetryinIRandRaman
Spectroscopy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 348
6.6 RotationalAbsorptionandFineStructure. . . . . . . . . . . . . . . . 353
6.7 InfraredSpectroscopyofProteinsandNucleicAcids. . . . . . . . 357
6.8 VibrationalStarkEffects. . . . . . . . . . . . . . . . . . . . . . . . . . . . 362
6.9 IRLasers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 364
6.10 Questions. .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 365
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 367
viii Contents
7 ResonanceEnergyTransfer. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 377
7.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 377
7.2 TheFörsterTheory. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 379
7.3 UsingEnergyTransfertoStudyFastProcessesinSingle
ProteinMolecules. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 394
7.4 ExchangeCoupling. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 396
7.5 EnergyTransferinPhotosyntheticAntennas. . . . . . . . . . . . . . 398
7.6 Questions. .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 402
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 404
8 ExcitonInteractions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 409
8.1 StationaryStatesofSystemswithInteractingMolecules. . . . . 409
8.2 EffectsofExcitonInteractionsontheAbsorptionSpectraof
Oligomers. . . . . . .. . . . . .. . . . . .. . . . . .. . . . . . .. . . . . .. 418
8.3 Transition-MonopoleTreatmentsofInteractionMatrix
ElementsandMixingwithCharge-TransferTransitions. . . . . . 424
8.4 ExcitonAbsorptionBandShapesandDynamicLocalization
ofExcitations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 428
8.5 ExcitonStatesinPhotosyntheticAntennaComplexes. . . . . . . 431
8.6 ExcimersandExciplexes. . . . . . . . . . . . . . . . . . . . . . . . . . . . 433
8.7 Questions. .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 436
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 439
9 CircularDichroism. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 445
9.1 MagneticTransitionDipolesandn-π(cid:1)Transitions. . . . . . . . 445
9.2 TheOriginofCircularDichroism. . . . . . . . . . . . . . . . . . . . . . 456
9.3 CircularDichroismofDimersandHigherOligomers. . . . . . . . 462
9.4 UVCircularDichroismofProteinsandNucleicAcids. . . . . . . 467
9.5 VibrationalCircularDichroism. . . . . . . . . . . . . . . . . . . . . . . 470
9.6 MagneticCircularDichroism. . . . . . . . . . . . . . . . . . . . . . . . . 473
9.7 Questions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 476
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 478
10 CoherenceandDephasing. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 483
10.1 OscillationsBetweenQuantumStatesofanIsolated
System. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 483
10.2 TheDensityMatrix. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 487
10.3 TheStochasticLiouvilleEquation. . . . . . . . . . . . . . . . . . . . . 493
10.4 EffectsofStochasticRelaxationsontheDynamicsof
QuantumTransitions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 495
10.5 ADensity-MatrixTreatmentofAbsorptionofWeak,
ContinuousLight. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 501
10.6 TheRelaxationMatrix. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 504
10.7 MoreGeneralRelaxationFunctionsandSpectral
Lineshapes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 513
10.8 AnomalousFluorescenceAnisotropy. . . . . . . . . . . . . . . . . . . 519
Contents ix
10.9 Questions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 525
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 526
11 Pump-ProbeSpectroscopy,PhotonEchoes,Two-Dimensional
SpectroscopyandVibrationalWavepackets. . . . . . . . . . . . . . . . . . 529
11.1 First-OrderOpticalPolarization. . . . . . . . . . . . . . . . . . . . . . . 529
11.2 Third-OrderOpticalPolarizationandNon-linearResponse
Functions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 538
11.3 Pump-ProbeSpectroscopy. . . . . . . . . . . . . . . . . . . . . . . . . . . 543
11.4 PhotonEchoes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 547
11.5 Two-DimensionalElectronicandVibrationalSpectroscopy. . . 553
11.6 TransientGratings. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 558
11.7 VibrationalWavepackets. . . . . . . . . . . . . . . . . . . . . . . . . . . . 561
11.8 WavepacketPicturesofSpectroscopicTransitions. . . . . . . . . . 568
11.9 Questions. .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 572
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 573
12 RamanScatteringandOtherMulti-photonProcesses. . . . . . . . . . . 583
12.1 TypesofLightScattering. . .. . . .. . . . .. . . . .. . . . .. . . . .. 583
12.2 TheKramers-Heisenberg-DiracTheory. . . . . . . . . . . . . . . . . . 587
12.3 TheWavepacketPictureofresonanceRamanScattering. . . . . 596
12.4 SelectionRulesforRamanScattering. . . . . . . . . . . . . . . . . . . 598
12.5 Surface-enhancedRamanScattering. . . . . . . . . . . . . . . . . . . . 601
12.6 ApplicationsofRamanSpectroscopy. . . . . . . . . . . . . . . . . . . 601
12.7 Coherent(Stimulated)RamanScattering. . . . . . . . . . . . . . . . . 603
12.8 Multi-photonAbsorption. . . . . . . . . . . . . . . . . . . . . . . . . . . . 605
12.9 Quasielastic(Dynamic)LightScattering(PhotonCorrelation
Spectroscopy). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 608
12.10 MiescatteringbyLargerParticles. . . . . . . . . . . . . . . . . . . . . 612
12.11 Questions. .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 614
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 615
AppendixA. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 623
Vectors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 623
Matrices. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 625
FourierTransforms. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 627
PhaseShiftandModulationAmplitudeinFrequency-Domain
Spectroscopy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 631
CGSandSIUnitsandAbbreviations. . . . . . . . . . . . . . . . . . . . . . . . . 633
Harmonic-OscillatorWavefunctionIntegrals. . . . . . . . . . . . . . . . . . . . 634
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 637
Index. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 639
List of Boxes
Box2.1 OperatorsforObservablePropertiesMustBeHermitian.......... 38
Box2.2 CommutatorsandFormulationsofthePosition,Momentum
andHamiltonianOperators........................................... 39
Box2.3 TheOriginoftheTime-DependentSchrödingerEquation........ 43
Box2.4 LinearMomentum.................................................... 51
Box2.5 HermitePolynomials................................................. 55
Box2.6 Boltzmann,Fermi-DiracandBose-EinsteinStatistics............. 74
Box3.1 Maxwell’sEquationsandtheVectorPotential..................... 93
Box4.1 EnergyofaDipoleinanExternalElectricField................... 138
Box4.2 MultipoleExpansionoftheEnergyofaSetofChargesina
VariableExternalField............................................... 140
Box4.3 TheBehavioroftheFunction[exp(iy)-1]/yasygoesto0........ 143
Box4.4 TheFunctionsin2x/x2andItsIntegral.............................. 145
Box4.5 TheOscillatingElectricDipoleofaSuperpositionState.......... 147
Box4.6 TheMean-SquaredEnergyofInteractionofanExternalField
withDipolesinanIsotropicSystem................................ 151
Box4.7 PhysicalConstantsandConversionFactorsforAbsorptionof
Light................................................................... 153
Box4.8 EvaluatingConfiguration-InteractionCoefficients................. 181
Box4.9 TheRelationshipbetweenMatrixElementsoftheElectric
DipoleandGradientOperators...................................... 185
Box4.10 MatrixElementsoftheGradientOperatorforAtomic2p
Orbitals................................................................ 188
Box4.11 SelectionRulesforElectric-DipoleExcitationsofLinear
Polyenes............................................................... 192
Box4.12 RecursionFormulasforVibrationalOverlapIntegrals............ 199
Box4.13 ThermallyWeightedFranck-CondonFactors...................... 201
Box4.14 ElectronicStarkSpectroscopyofImmobilizedMolecules........ 220
Box5.1 Theν3FactorintheStrickler-BergEquation....................... 256
Box5.2 CreationandAnnihilationOperators................................ 263
Box5.3 Binomial,PoissonandGaussianDistributions..................... 291
Box6.1 NormalCoordinatesandMolecular-dynamicsSimulations....... 332
Box7.1 Dipole-dipoleInteractions............................................ 383
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