Modern Optical Spectroscopy: With Examples from Biophysics and Biochemistry

511 Pages·2007·13.464 MB·English

by  William W. Parson

WilliamW.Parson
ModernOpticalSpectroscopy
William W. Parson
Modern Optical
Spectroscopy
With Examples from Biophysics
and Biochemistry
With191Figures
123
WilliamW.Parson
UniversityofWashington
DepartmentofBiochemistry
Box357350
Seattle,WA98195-7350
USA
e-mail:[email protected]
LibraryofCongressControlNumber:2006933734
ISBN-10 3-540-37535-X SpringerBerlinHeidelbergNewYork
ISBN-13 978-3-540-37535-7 SpringerBerlinHeidelbergNewYork
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Preface
This book began as lecture notes for a course on optical spectroscopy that I
taughtforgraduatestudentsinbiochemistry,chemistry,andourinterdisciplinary
programsinmolecularbiophysicsandbiomolecularstructureanddesign.Istarted
expanding the notes partly to try to illuminate the stream of new experimental
informationonphotosyntheticantennasandreactioncenters,butmostlyjustfor
fun.Ihopethatreaderswillfindtheresultsnotonlyuseful,butalsoasstimulating
asIhave.
One of my goals has been to write in a way that will be accessible to readers
with little prior training in quantum mechanics. But any contemporary discus-
sionofhowlightinteractswithmoleculesmustbeginwithquantummechanics,
just as experimental observations on blackbody radiation, interference, and the
photoelectric effect form the springboard for almost any introduction to quan-
tummechanics.Tomakethereasoningastransparentaspossible,Ihavetriedto
adoptaconsistenttheoreticalapproach,minimizejargon,andexplainanytermsor
mathematicalmethodsthatmightbeunfamiliar.Ihaveprovidednumerousfigures
torelatespectroscopicpropertiestomolecularstructure,dynamics,andelectronic
andvibrationalwavefunctions.Ialsodescribeclassicalpicturesinmanycasesand
indicatewheretheseeitherhavecontinuedtobeusefulorhavebeensupplantedby
quantummechanicaltreatments.Readerswithexperienceinquantummechanics
shouldbeabletoskipquicklythroughmanyoftheexplanations,butwillfindthat
thediscussionoftopicssuchasdensitymatricesandwavepacketsoftenprogresses
wellbeyondthelevelofatypical1-yearcourseinquantummechanics.Ihavetried
totakeeachtopicfarenoughtoprovideasolidsteppingstonetocurrenttheoretical
andexperimentalworkinthearea.
Although much of the book focuses on physical theory, I have emphasized
aspects of optical spectroscopy that are especially pertinent to molecular bio-
physics,andIhavedrawnmostoftheexamplesfromthisarea.Thebooktherefore
covers topics that receive little attention in most general books on molecular
spectroscopy, including exciton interactions, resonance energy transfer, single-
molecule spectroscopy, high-resolution fluorescence microscopy, femtosecond
pump–probe spectroscopy, and photon echoes. It says less than is customary
about atomic spectroscopy and about rotational and vibrational spectroscopy
of small molecules. These choices reflect my personal interests and the realiza-
tion that I had to stop somewhere, and I can only apologize to readers whose
selections would have been different. I apologize also for using work from my
ownlaboratoryinmanyoftheillustrationswhenotherexcellent illustrationsof
VI Preface
the same points are available in the literature. This was just a matter of conve-
nience.
I could not have written this book without the patient encouragement of my
wife Polly. I also have enjoyed many thought-provoking discussions with Arieh
Warshel, Nagarajan, Martin Gouterman, and numerous other colleagues and
students, particularly including Rhett Alden, Edouard Alphandéry, Hiro Arata,
Donner Babcock, Mike Becker, Bob Blankenship, Steve Boxer, Jacques Breton,
Jim Callis, Patrik Callis, Rod Clayton, Richard Cogdell, Tom Ebrey, Tom Engel,
Graham Fleming, Eric Heller, Dewey Holten, Ethan Johnson, Amanda Jonsson,
ChrisKirmaier,DavidKlug,BobKnox,RichMathies,EricMerkley,DonMidden-
dorf, Tom Moore, Jim Norris, Oleg Prezhdo, Phil Reid, Bruce Robinson, Karen
Rutherford,KenSauer,DustinSchaefer,CraigSchenck,PeterSchellenberg,Avig-
dorScherz,MickeySchurr,GerrySmall,RienkvanGrondelle,MauriceWindsor,
andNealWoodbury.PatrikCalliskindlyprovidedtheatomiccoefficientsusedin
Chaps.4and5forthemolecularorbitalsof3-methylindole.Anyerrors,however,
are entirely mine. I will appreciate receiving any corrections or suggestions for
improvements.
Seattle,October2006 WilliamW.Parson
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........................................................... 9
1.7 TechniquesforMeasuringAbsorbance........................................ 10
1.8 Pump–ProbeandPhoton-EchoExperiments............................... 13
1.9 LinearandCircularDichroism.................................................. 15
1.10 DistortionsofAbsorptionSpectrabyLightScattering
orNonuniformDistributionsoftheAbsorbingMolecules............. 17
1.11 Fluorescence........................................................................... 19
1.12 IRandRamanSpectroscopy...................................................... 24
1.13 Lasers.................................................................................... 25
1.14 Nomenclature......................................................................... 26
2 BasicConceptsofQuantumMechanics 29
2.1 Wavefunctions,Operators,andExpectationValues....................... 29
2.1.1 Wavefunctions ............................................................. 29
2.1.2 OperatorsandExpectationValues.................................... 30
2.2 TheTime-Dependent
andTime-IndependentSchrödingerEquations............................ 36
2.2.1 SuperpositionStates...................................................... 41
2.3 SpatialWavefunctions.............................................................. 42
2.3.1 AFreeParticle.............................................................. 42
2.3.2 AParticleinaBox......................................................... 43
2.3.3 TheHarmonicOscillator ............................................... 46
2.3.4 AtomicOrbitals ............................................................ 48
2.3.5 MolecularOrbitals......................................................... 51
2.3.6 ApproximateWavefunctionsforLargeSystems.................. 57
2.4 SpinWavefunctionsandSingletandTripletStates........................ 57
2.5 TransitionsBetweenStates:Time-DependentPerturbationTheory. 65
2.6 LifetimesofStatesandtheUncertaintyPrinciple.......................... 68
VIII Contents
3 Light 73
3.1 ElectromagneticFields............................................................. 73
3.1.1 ElectrostaticForcesandFields......................................... 73
3.1.2 ElectrostaticPotentials................................................... 74
3.1.3 ElectromagneticRadiation ............................................. 76
3.1.4 EnergyDensityandIrradiance........................................ 83
3.1.5 TheComplexElectricSusceptibilityandRefractiveIndex... 90
3.1.6 Local-FieldCorrectionFactors........................................ 94
3.2 TheBlack-BodyRadiationLaw.................................................. 96
3.3 LinearandCircularPolarization................................................ 98
3.4 QuantumTheoryofElectromagneticRadiation........................... 100
3.5 SuperpositionStatesandInterferenceEffectsinQuantumOptics... 104
3.6 DistributionofFrequenciesinShortPulsesofLight...................... 106
4 ElectronicAbsorption 109
4.1 InteractionsofElectronswithOscillatingElectricFields............... 109
4.2 TheRatesofAbsorptionandStimulatedEmission........................ 113
4.3 TransitionDipolesandDipoleStrengths..................................... 118
π
4.4 CalculatingTransitionDipolesfor MolecularOrbitals................ 126
4.5 MolecularSymmetryandForbiddenandAllowedTransitions ....... 128
4.6 LinearDichroism..................................................................... 142
4.7 ConfigurationInteractions........................................................ 148
4.8 CalculatingElectricTransitionDipoleswiththeGradientOperator 152
4.9 TransitionDipolesforExcitationstoSingletandTripletStates....... 161
4.10 TheBorn–OppenheimerApproximation,Franck–CondonFactors,
andtheShapesofElectronicAbsorptionBands........................... 163
4.11 SpectroscopicHole-Burning...................................................... 171
4.12 EffectsoftheSurroundingsonMolecularTransitionEnergies........ 174
4.13 TheElectronicStarkEffect........................................................ 182
5 Fluorescence 189
5.1 TheEinsteinCoefficients.......................................................... 189
5.2 TheStokesShift....................................................................... 192
5.3 TheMirror-ImageLaw............................................................. 195
5.4 TheStrickler–BergEquationandOtherRelationships
BetweenAbsorptionandFluorescence........................................ 197
5.5 QuantumTheoryofAbsorptionandEmission............................. 203
5.6 FluorescenceYieldsandLifetimes.............................................. 208
5.7 FluorescentProbesandTags...................................................... 214
5.8 Photobleaching....................................................................... 218
5.9 FluorescenceAnisotropy........................................................... 219
5.10 Single-MoleculeFluorescenceandHigh-ResolutionFluorescence
Microscopy............................................................................. 225
5.11 FluorescenceCorrelationSpectroscopy....................................... 231
5.12 IntersystemCrossing,Phosphorescence,andDelayedFluorescence 238
Contents IX
6 VibrationalAbsorption 241
6.1 VibrationalNormalModesandWavefunctions............................ 241
6.2 VibrationalExcitation.............................................................. 247
6.3 IRSpectroscopyofProteins....................................................... 253
6.4 VibrationalStarkEffects........................................................... 256
7 ResonanceEnergyTransfer 259
7.1 Introduction........................................................................... 259
7.2 TheFörsterTheory.................................................................. 261
7.3 ExchangeCoupling.................................................................. 275
7.4 EnergyTransfertoandfromCarotenoidsinPhotosynthesis.......... 277
8 ExcitonInteractions 281
8.1 StationaryStatesofSystemswithInteractingMolecules................ 281
8.2 EffectsofExcitonInteractionsontheAbsorptionSpectra
ofOligomers........................................................................... 290
8.3 Transition-MonopoleTreatmentsofInteractionMatrixElements
andMixingwithCharge-TransferTransitions.............................. 295
8.4 ExcitonAbsorptionBandShapesandDynamicLocalization
ofExcitations.......................................................................... 298
8.5 ExcitonStatesinPhotosyntheticAntennaComplexes................... 301
8.6 ExcimersandExciplexes........................................................... 304
9 CircularDichroism 307
π∗
9.1 MagneticTransitionDipolesandn– Transitions....................... 307
9.2 TheOriginofCircularDichroism.............................................. 317
9.3 CircularDichroismofDimersandHigherOligomers.................... 322
9.4 CircularDichroismofProteinsandNucleicAcids ........................ 328
9.5 MagneticCircularDichroism.................................................... 332
10 CoherenceandDephasing 335
10.1 OscillationsBetweenQuantumStatesofanIsolatedSystem........... 335
10.2 TheDensityMatrix.................................................................. 339
10.3 TheStochasticLiouvilleEquation.............................................. 344
10.4 EffectsofStochasticRelaxationsontheDynamics
ofQuantumTransitions............................................................ 346
10.5 ADensity-MatrixTreatmentofSteady-StateAbsorption............... 352
10.6 TheRelaxationMatrix.............................................................. 355
10.7 MoreGeneralRelaxationFunctionsandSpectralLineshapes......... 364
10.8 AnomalousFluorescenceAnisotropy.......................................... 370
11 Pump–ProbeSpectroscopy,PhotonEchoes,
andVibrationalWavepackets 377
11.1 First-OrderOpticalPolarization................................................ 377
X Contents
11.2 Third-OrderOpticalPolarization
andNonlinearResponseFunctions............................................ 386
11.3 Pump–ProbeSpectroscopy........................................................ 391
11.4 PhotonEchoes........................................................................ 395
11.5 TransientGratings................................................................... 401
11.6 VibrationalWavepackets........................................................... 404
11.7 WavepacketPicturesofSpectroscopicTransitions........................ 413
12 RamanScatteringandOtherMultiphotonProcesses 417
12.1 TypesofLightScattering........................................................... 417
12.2 TheKramers–Heisenberg–DiracTheory..................................... 422
12.3 TheWavepacketPictureofResonanceRamanScattering............... 430
12.4 SelectionRulesforRamanScattering ......................................... 432
12.5 Surface-EnhancedRamanScattering.......................................... 435
12.6 BiophysicalApplicationsofRamanSpectroscopy......................... 436
12.7 CoherentRamanScattering....................................................... 437
12.8 MultiphotonAbsorption........................................................... 439
12.9 Quasielastic(Dynamic)LightScattering
(PhotonCorrelationSpectroscopy)............................................ 442
Appendix1–Vectors 447
Appendix2–Matrices 451
Appendix3–FourierTransforms 455
Appendix4–FluorescencePhaseShiftandModulation 459
Appendix5–CGSandSIUnitsandAbbreviations 463
References 465
SubjectIndex 505