Charge and Energy Transfer Dynamics in Molec. Systs.

578 Pages·2011·7.849 MB·English

by  V. May, et. al.

VolkhardMayandOliverKühn
ChargeandEnergyTransfer
DynamicsinMolecularSystems
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Volkhard May and Oliver Kühn
Charge and Energy Transfer Dynamics
in Molecular Systems
Third, Revised and Enlarged Edition
WILEY-VCH Verlag GmbH & Co. KGaA
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V
Contents
PrefacetotheThirdEdition XIII
PrefacetotheSecondEdition XV
PrefacetotheFirstEdition XVII
1 Introduction 1
2 ElectronicandVibrationalMolecularStates 9
2.1 Introduction 9
2.2 MolecularSchrödingerEquation 11
2.3 Born–OppenheimerSeparation 13
2.3.1 Born–OppenheimerApproximation 15
2.3.2 SomeEstimates 17
2.4 ElectronicStructureMethods 18
2.4.1 TheHartree–FockEquations 21
2.4.2 DensityFunctionalTheory 23
2.5 CondensedPhaseApproaches 24
2.5.1 DielectricContinuumModel 25
2.5.2 ExplicitQuantum-ClassicalSolventModel 31
2.6 PotentialEnergySurfaces 33
2.6.1 HarmonicApproximationandNormalModeAnalysis 35
2.6.2 OperatorRepresentationoftheNormalModeHamiltonian 39
2.6.3 ReactionPaths 44
2.7 DiabaticversusAdiabaticRepresentation
oftheMolecularHamiltonian 50
2.8 Supplement 56
2.8.1 TheHartree–FockEquations 56
2.8.2 Franck–CondonFactors 59
2.8.3 TheTwo-LevelSystem 60
2.8.4 TheLinearMolecularChainandtheMolecularRing 64
References 66
FurtherReading 66
ChargeandEnergyTransferDynamicsinMolecularSystems.VolkhardMay,OliverKühn
Copyright©2011WILEY-VCHVerlagGmbH&Co.KGaA,Weinheim
ISBN:978-3-527-40732-3
VI Contents
3 DynamicsofIsolatedandOpenQuantumSystems 67
3.1 Introduction 67
3.2 Time-DependentSchrödingerEquation 74
3.2.1 WavePackets 74
3.2.2 TheInteractionRepresentation 78
3.2.3 MultidimensionalWavePacketDynamics 80
3.3 TheGoldenRuleofQuantumMechanics 83
3.3.1 TransitionfromaSingleStateintoaContinuum 84
3.3.2 TransitionRateforaThermalEnsemble 87
3.3.3 Green’sFunctionApproach 91
3.4 TheNonequilibriumStatisticalOperatorandtheDensityMatrix 94
3.4.1 TheDensityOperator 94
3.4.2 TheDensityMatrix 97
3.4.3 EquationofMotionfortheDensityOperator 99
3.4.4 WignerRepresentationoftheDensityOperator 100
3.4.5 DynamicsofCoupledMultilevelSystemsinaHeatBath 103
3.5 TheReducedDensityOperatorandtheReducedDensityMatrix 107
3.5.1 TheReducedDensityOperator 107
3.5.2 EquationofMotionfortheReducedDensityOperator 108
3.5.3 Mean-FieldApproximation 109
3.5.4 TheInteractionRepresentationoftheReducedDensityOperator 111
3.5.5 TheProjectionSuperoperator 112
3.5.6 Second-OrderEquationofMotionfortheReducedDensityOperator 115
3.6 TheReservoirCorrelationFunction 117
3.6.1 GeneralPropertiesofC (t) 117
uv
3.6.2 HarmonicOscillatorReservoir 120
3.6.3 TheSpectralDensity 122
3.6.4 LinearResponseTheoryfortheReservoir 125
3.6.5 ClassicaldescriptionofC (t) 127
uv
3.7 QuantumMasterEquation 128
3.7.1 MarkovApproximation 130
3.8 ReducedDensityMatrixinEnergyRepresentation 134
3.8.1 TheQuantumMasterEquationinEnergyRepresentation 134
3.8.2 MultilevelRedfieldEquations 136
3.8.3 TheSecularApproximation 141
3.8.4 StateExpansionoftheSystem–ReservoirCoupling 142
3.8.5 FromCoherenttoDissipativeDynamics:ASimpleExample 144
3.8.6 CoordinateandWignerRepresentation
oftheReducedDensityMatrix 150
3.9 GeneralizedRateEquations:TheLiouvilleSpaceApproach 153
3.9.1 ProjectionOperatorTechnique 154
3.9.2 GeneralizedRateEquations 155
3.9.3 RateEquations 157
3.9.4 TheMemoryKernels 158
3.9.5 Second-OrderRateExpressions 160
Contents VII
3.9.6 Fourth-OrderRateExpressions 162
3.10 ThePathIntegralRepresentationoftheDensityMatrix 168
3.11 Quantum-ClassicalHybridMethods 174
3.11.1 TheMean-FieldApproach 174
3.11.2 TheSurfaceHoppingMethod 176
3.11.3 Partial Wigner Representation as a Quantum-Classical Hybrid
Method 179
3.12 Supplement 183
3.12.1 DifferentEquationsofMotionfortheReducedDensityOperator 183
3.12.2 LimitofUltrashortReservoirCorrelationTime 187
3.12.3 MarkovApproximationandtheFactorizedPart
oftheReservoirCorrelationFunction 188
References 189
FurtherReading 189
4 InteractionofMolecularSystemswithRadiationFields 191
4.1 Introduction 191
4.2 AbsorptionandEmissionofLight 196
4.2.1 LinearAbsorptionCoefficient 196
4.2.2 Dipole–DipoleCorrelationFunction 197
4.2.3 FieldQuantizationandSpontaneousEmissionofLight 199
4.3 NonlinearOpticalResponse 202
4.3.1 NonlinearResponseFunctions 205
4.4 LaserControlofMolecularDynamics 206
4.4.1 Introduction 206
4.4.2 OptimalControlTheory 212
References 219
FurtherReading 220
5 VibrationalDynamics:EnergyRedistribution,Relaxation,
andDephasing 221
5.1 Introduction 221
5.2 IntramolecularVibrationalEnergyRedistribution 225
5.2.1 Zeroth-OrderBasis 225
5.2.2 GoldenRuleandBeyond 228
5.3 IntermolecularVibrationalEnergyRelaxation 232
5.3.1 DiatomicMoleculeinSolidStateEnvironment 233
5.3.2 DiatomicMoleculesinPolyatomicSolution 238
5.4 PolyatomicMoleculesinSolution 243
5.4.1 System–BathHamiltonian 243
5.4.2 Higher-OrderMultiquantumRelaxation 245
5.5 Quantum-ClassicalApproachestoRelaxationandDephasing 250
5.6 Supplement 253
5.6.1 CoherentWavePacketMotioninaHarmonicOscillator 253
References 254
FurtherReading 254
VIII Contents
6 IntramolecularElectronicTransitions 255
6.1 Introduction 255
6.1.1 OpticalTransitions 256
6.1.2 InternalConversionProcesses 261
6.2 TheOpticalAbsorptionCoefficient 262
6.2.1 GoldenRuleFormulation 262
6.2.2 TheDensityofStates 265
6.2.3 AbsorptionCoefficientforHarmonicPotentialEnergySurfaces 268
6.2.4 AbsorptionLineshapeandSpectralDensity 271
6.3 AbsorptionCoefficientandDipole–DipoleCorrelationFunction 276
6.3.1 AbsorptionCoefficientandWavePacketPropagation 276
6.3.2 CumulantExpansionoftheAbsorptionCoefficient 281
6.3.3 AbsorptionCoefficientandReducedDensityOperatorPropagation 282
6.3.4 MixedQuantum-ClassicalComputationoftheAbsorptionCoefficient 285
6.4 TheEmissionSpectrum 287
6.5 OpticalPreparationofanExcitedElectronicState 288
6.5.1 WaveFunctionFormulation 289
6.5.2 DensityMatrixFormulation 293
6.6 Pump–ProbeSpectroscopy 294
6.7 InternalConversionDynamics 298
6.7.1 TheInternalConversionRate 298
6.7.2 UltrafastInternalConversion 300
6.8 Supplement 302
6.8.1 AbsorptionCoefficientforDisplacedHarmonicOscillators 302
6.8.2 CumulantExpansionforHarmonicPotentialEnergySurfaces 305
References 307
FurtherReading 307
7 ElectronTransfer 309
7.1 ClassificationofElectronTransferReactions 309
7.2 TheoreticalModelsforElectronTransferSystems 321
7.2.1 TheElectronTransferHamiltonian 322
7.2.2 TheElectron–VibrationalHamiltonian
ofaDonor–AcceptorComplex 327
7.2.3 Electron–VibrationalStateRepresentationoftheHamiltonian 331
7.3 RegimesofElectronTransfer 332
7.3.1 Landau–ZenerTheoryofElectronTransfer 337
7.4 NonadiabaticElectronTransferinaDonor–AcceptorComplex 341
7.4.1 High-TemperatureCase 342
7.4.2 High-Temperature Case: Two Independent Sets of Vibrational
Coordinates 346
7.4.3 Low-TemperatureCase:NuclearTunneling 349
7.4.4 TheMixedQuantum-ClassicalCase 352
Contents IX
7.4.5 DescriptionoftheMixedQuantum-ClassicalCase
byaSpectralDensity 354
7.5 NonadiabaticElectronTransferinPolarSolvents 355
7.5.1 TheSolventPolarizationFieldandtheDielectricFunction 357
7.5.2 TheFreeEnergyoftheSolvent 360
7.5.3 TheRateofNonadiabaticElectronTransferinPolarSolvents 363
7.6 Bridge-MediatedElectronTransfer 367
7.6.1 TheSuperexchangeMechanism 369
7.6.2 ElectronTransferthroughArbitraryLongBridges 371
7.7 Nonequilibrium Quantum Statistical Description of Electron
Transfer 375
7.7.1 UnifiedDescriptionofElectronTransfer
inaDonor–Bridge–AcceptorSystem 376
7.7.2 TransitiontotheAdiabaticElectronTransfer 379
7.8 HeterogeneousElectronTransfer 380
7.8.1 Nonadiabatic Charge Injection into the Solid State Described in a
Single-ElectronModel 381
7.8.2 NonadiabaticElectronTransferfromtheSolidStatetotheMolecule 385
7.8.3 UltrafastPhotoinducedHeterogeneousElectronTransferfromaMolecule
intoaSemiconductor 388
7.9 ChargeTransmissionthroughSingleMolecules 390
7.9.1 InelasticChargeTransmission 393
7.9.2 ElasticChargeTransmission 396
7.10 PhotoinducedUltrafastElectronTransfer 402
7.10.1 QuantumMasterEquationforElectronTransferReactions 408
7.10.2 RateExpressions 412
7.11 ControllingPhotoinducedElectronTransfer 414
7.12 Supplement 417
7.12.1 Landau–ZenerTransitionAmplitude 417
7.12.2 TheMultimodeMarcusFormula 419
7.12.3 TheFreeEnergyFunctionaloftheSolventPolarization 420
7.12.4 Second-OrderElectronTransferRate 423
7.12.5 Fourth-OrderDonor–AcceptorTransitionRate 425
7.12.6 RateofElasticChargeTransmissionthroughaSingleMolecule 428
References 431
FurtherReading 432
8 ProtonTransfer 435
8.1 Introduction 435
8.2 ProtonTransferHamiltonian 440
8.2.1 HydrogenBonds 440
8.2.2 ReactionSurfaceHamiltonianforIntramolecularProtonTransfer 444
8.2.3 TunnelingSplittings 445
8.2.4 ProtonTransferHamiltonianintheCondensedPhase 450