two-dimensional vibronic spectra from classical trajectories kritanjan polley资料.pdf

该【two-dimensional vibronic spectra from classical trajectories kritanjan polley资料 】是由【宝钗文档】上传分享，文档一共【11】页，该文档可以免费在线阅读，需要了解更多关于【two-dimensional vibronic spectra from classical trajectories kritanjan polley资料 】的内容，可以使用淘豆网的站内搜索功能，选择自己适合的文档，以下文字是截取该文章内的部分文字，如需要获得完整电子版，请下载此文档到您的设备，方便您编辑和打印。:..Two-dimensionalvibronicspectrafromclassicaltrajectoriesCiteas:,164114(2019);https:///:::24April2019KritanjanPolley,,164103(2019);https:///,090901(2019);https:///-dimensionalvibrationalspectroscopyTheJournalofChemicalPhysics150,100901(2019);https:///.,164114(2019);https:///,164114?2019Author(s).:..TheJournal/journal/jcpofChemicalPhysicsTwo-dimensionalvibronicspectrafromclassicaltrajectoriesCiteas:,164114(2019);doi::25February2019?Accepted:3April2019?PublishedOnline:)AFFILIATIONSDepartmentofChemistryandChemicalBiology,BakerLaboratory,CornellUniversity,Ithaca,NewYork14853,USAa)Electronicmail:roger.******@?rstmappedtotheassociatedMeyer-MillerHamiltonianforNquantumharmonicoscil-,-mean-trajectoryapproach,originallydevelopedfornonlinearvibrationalspectroscopyandsubsequentlyextendedtovibronicspectroscopy,:///.-sicallimit,“oldquan-electronicstateswithoscillators,takingtheclassicallimit,andintro-tumtheory,”1–4whichpreservedtheconceptoftheclassicaltra-ducingnnucdegreesoffreedomyieldaclassicalHamiltonianforjectory,+,matrixele-supersededbyquantummechanics,putedfromseveralhistoricalperiodsasthebasisforapproximationstoquan-,ordingtowindowfunctionsact-,theseideashavebeenappliedtomodel-ingoninitialand?nalphasepoints,whichimposeacoarse-–13Quasiclassicalor,moregenerally,–alcula-,unphysicaldispositionofzero-,thehasbeenshowntobebettersuitedtopropagatingpopulations29,38timescalesrelevanttoultrafastmeasurementscanreducetheburdenthanthecoherencesrelevanttolinearspectroscopy,theabsorp-(SQC)–29treatselectronicorvibronicdynam---approach30,31beginswiththeMeyer-Miller(MM)representa-–37htionofaquantumHamiltonianactinginaspaceofNdis-statespaceofanharmonicmodesistruncatedata?nitenumbercretestatesintermsofsingleexcitationsofNquantumharmonicsnuc,,164114(2019);doi:,164114-1PublishedunderlicensebyAIPPublishing:..TheJournal/journal/jcpofChemicalPhysicsclassicalHamiltonianhasN+snuc+nhdegreesoffreedom,largerofnuclearstate,butintheabsenceofradiationdonotinteractwiththanN+-putingpopulationpledinthepresenceofradiationtoaclassicalelectric?(OMT)approximationwasH?(1)(t)=?μ?E(t),(3)originallydevisedtocalculatenonlinearinfraredspectrafromaNquasiclassicalapproximationtonucleardynamicsonasinglesur-μ?=Q(μ?1j+μ?j1),(4)–45TheOMTapproximationtoanonlinearresponsefunctionj=2isexpressedthroughamappingbetweendouble-sideddynamicalperturbationdiagramsforthedensityoperator46,47andsemiclassi-μ?jk=VjkSje`kS.(5)caldiagramswhoseevaluationrequirespropagationofclassicaltra-TheCondonapproximationhasbeeninvokedtoneglectdepen--to-oneatzerotemperatureandtwo-to-?,-MillerHamiltonian32–37associatedwiththepurelyOMThasbeenshowntoreproducedisparatephenomenainclud-(0)inglinebroadeningfromdissipationandfrompuredephasing44andelectronicHamiltonianH?inEq.(2)describesNcoupledhar-òNwithastrategybasedonthesameclassicalHamiltonianastheH?(0)=h?x?2+p?2?1?+hòJ(x?x?+p?p?),(6)=1j<k≠?jandp?jdimensionlesscoordinateandmomentumoperators,mixedvibrationalandelectronicexcitation,49–56bothsetsoftransi-–29,38,40ofthisHamiltonianH(0),third-orderisexpressedintermsofthedimensionlessaction??nandanglevibronicandvibrational-putedwiththroughx=2(n+γ)cosandp=?2(n+γ)sin,theOMTforanelectronictwo-(0)NNanharmoniceffectsinpurevibrationalspectroscopysuggeststhatitHel=hòQjQjj+hòQJjk?Qjk+Qkj?,(7)maynotrequiretreatingquantumstatesofanharmonicmodesasj=1j<k≠1distinctMeyer-Milleroscillators,40butthisconjectureremainstobeQjk=njδjk+gjkexp[i?j?k?](1?δjk),(8)tested.?Inthepresentwork,theOMTisimplementedformodelswithgjk=(nj+γ)(nk+γ).(9)-tothepurelyelectroniclinearandthird-orderresponseforamodelansofthisformwiththeeffectivezero-.(9)assignedvaluesdeterminedbyapplication-dependentargu-ucleardegreeoffree-,57–59Asshownbelow,thechoiceof1/2inthepresentcon-,theOMTprocedurethatproducedEq.(7)fromEq.(2)totheinteractioncalculationofthe2DspectrumisexactlycorrectatzeroevolutionHamiltonianinEq.(3)givesitsclassicalanalogH(1)(t)=?ME(t),=Q(M1j+Mj1),(10)j=2Thematerialsystemisrepresentedbyonegroundelectronicstate|1eandamanifoldofN?1excitedelectronicstates(|2e,:::,Mjk=VjkQjk,(11)|Ne),withHamiltonianH?(0)andwithQjkgiveninEq.(8).(0)(0)NWeaddnuclearphasespacevariablesintheclassicalHamilto-H?=H?el+QSjeh?j`jS,(1)j=1nianofEq.(7)byintroducingtheclassicalnuclearHamiltonians{hj}(0)(0)N(0)?N?H=H+QQjjhj,(12)H?=hòQSjej`jS+QSjeJjk`kS,(2)elel??j=1j=1j≠k≠1wherehjistheclassicallimitofthequantumnuclearHamiltonianuclearHamiltonianforstateh?inEq.(1).Ourstrategyforcalculatingopticalnonlinearresponse(0)j|jeandH?.(12)istoapplythestatesarearbitrarilycoupledthrough{J},takentobeindependentsemiclassicalquantizationrulesoftheOMT42,,164114(2019);doi:,164114-2PublishedunderlicensebyAIPPublishing:..TheJournal/journal/.(7),,opticalresponsefunctionsmaybeexpressedintermsofequilibriumcorrelationfunc-tionsofthequantumdipoleoperatorμ?inEq.(4).IntheOMTapproximation,thesecorrelationfunctionsarecalculatedfromthedynamicsofMinEq.(10),theclassicalanalogofthedipoleoper--{Qjk}inEq.(8).Intheabsenceofradiation,theseordingto±hò/˙(t)={H(0),Q}(13)-(0)ponentsaredetermined,with+and?labelingthephaseofthe=iQLjk,rsQrs(t),(ponentsinEq.(10);+indicatesMs1and?,sOMTapproximatesthequantumdynamicsof|le`k|withclassicalL(0)≡?H?(0)?δ??H?(0)?δ,(15)trajectorieshavingactionvariablesnj=(δkj+δlj)/,jk,rseljrkselskjrtwodimensionlessactionshavevalue1/2,whileforapopulation,awhereH(0)inEq.(13)lassicalHamilto-→kresultsinnj→nj?1/2andnk→nknianinEq.(7)andH?(0)inEq.(15)isitsquantumanaloginEq.(2).el+1/,(14)followsfromthePoissonthequantumdescription,theinitialinteractionwithradiationtrans-bracketformsthegroundstatepopulation|1e`1|intothecoherence|se`1|,{Qrs,Qjk}=i(δrkQjs?δjsQrk).(16),anglevari-2(0)ablesassociatedwitheachquantumstatearechosenfromauniformTheN-dimensionaldynamicalmatrixLinEq.(14)isidenticaldistribution,andtheinitialactionvariableforstatejisδj1,represent-tothequantumLiouvillianassociatedwiththeHamiltonianH?(0).?rstspectroscopictransitionEquation(14)maybesolvedformallyintermsofthetetradicquan-leavestheseanglevaluesunchangedbutdecrementstheactionoftumpropagatorforobservablesG(t)≡exp(iL(0)t),givingfortheoscillator1by1/2andincrementstheactionofoscillatorsby1/.(11)TheinitialvertexrepresentsthetransitiondipoleMs1(0),andthe?nalvertexgeneratesM1r(t)givingthesemiclassicalformoftheMjk(t)=Vjk(G(t)Q(0))jk.(17)dipoleautocorrelationfunctionThetime-evolutionofthequantumtransitiondipoleisalsoexpress-T(t)=QV1rVs1SdnSdPs(n,)Q1r(t)Qs1(0),(20)r,sμjk(t)=(G(t)μ?(0))jk.(18)?NPs(n,)=(2π)δ(n1?1~2)δ(ns?1~2)Mδ(nk).(21)Thepresenceofthesamepropagatorintheclassicalequation(17)k≠1,sandthequantumequation(18)allowsforthepossibilitythatdipolecorrelationfunctionscalculatedinasemiclassicalapproximationTheeffectivephasespacedistributionPs(n,)enforcestheOMTfromtheclassicalHamiltonianinEq.(7)?(t)asinforEq.(17)andontheassumedrelationshipbetweenMjk(t)andEq.(17)andperformingthephase-spaceintegrationyieldaresultthecorrelationfunction,asillu