Crystal Symmetry and Static Electron Correlation Greatly Accelerate Nonradiative Dynamics in Lead Halide Perovskites - Smith, Shakiba, A

《Crystal Symmetry and Static Electron Correlation Greatly Accelerate Nonradiative Dynamics in Lead Halide Perovskites - Smith, Shakiba, A》由会员上传分享，免费在线阅读，更多相关内容在学术论文-天天文库。

pubs.acs.org/JPCLLetterCrystalSymmetryandStaticElectronCorrelationGreatlyAccelerateNonradiativeDynamicsinLeadHalidePerovskites§§BrendanSmith,MohammadShakiba,andAlexeyV.Akimov*CiteThis:J.Phys.Chem.Lett.2021,12,2444−2453ReadOnlineACCESSMetrics&MoreArticleRecommendations*sıSupportingInformationABSTRACT:Usingarecentlydevelopedmany-bodynonadiabaticmoleculardynamics(NA-MD)frameworkforlargecondensedmattersystems,westudythephonon-drivennonradiativerelaxationofexcesselectronicexcitationenergyincubicandtetragonalphasesoftheleadhalideperovskiteCsPbI3.Wefindthatthemany-bodytreatmentoftheelectronicexcitedstatessignificantlychangesthestructureoftheexcitedstates’coupling,promotesastrongernonadiabaticcouplingofstates,andultimatelyacceleratestherelaxationdynamicsrelativetothesingle-particledescriptionofexcitedstates.Theaccelerationofthenonadiabaticdynamicscorrelateswiththedegreeofconfigurationalmixing,whichiscontrolledbythecrystalsymmetry.Thehigher-symmetrycubicphaseofCsPbI3exhibitsstrongerconfigurationmixingthandoesthetetragonalphaseandsubsequentlyyieldsfasternonradiativedynamics.Overall,usingamany-bodytreatmentofexcitedstatesandaccountingfordecoherencedynamicsareimportantforclosingthegapbetweenthecomputationallyderivedandexperimentallymeasurednonradiativeexcitationenergyrelaxationrates.Nonadiabatic(NA)moleculardynamics(MD)isaformationmaybestronglyfavored.Furthermore,modelingpromisingmethodforrevealingmechanismsandprocessesthatinvolveexcitedstates’interaction,suchas28−31characterizingthedynamicsofNAprocesses.MultipleNA-triplet−tripletannihilationandphotonupconversion,MDstudiesofbulkperovskiteshavebeenundertakentodate,32−3435,36singletfission,andexcimerformation,wouldalso12providinginsightintotheroleofcationandhalideidentity,requiresteppingbeyondthecommonlyadoptedSPapprox-34symmetrybreakingatgrainboundaries,andvacanciesinimationandextendingtheNAmethodologytotheMBdeterminingthekineticsofsuchprocesses.Otherworkshave(multiconfigurational)treatmentoftheelectronicstates.reportedNA-MDstudiesofthenonradiativehotcarrierNA-MDcalculationsthatutilizeahigh-leveldescriptionofrelaxationandelectron−holerecombinationprocessesinelectronicexcitedstates(naturallyincludingMBeffects)are56−8perovskitenanocrystals,2Dperovskites,andrelatedroutinelypossiblenowadaysdirectlyforrelativelysmallDownloadedviaUNIVOFCONNECTICUTonMay16,2021at05:33:09(UTC).heterostructuresystems.9−11Currently,NA-MDsimulations37−41molecularsystemsorviaQM/MMapproachesforlargerofcomplexsystemssuchascondensedphaseornanoscalesystems.Incontrast,theinclusionofMBeffectsintheNA-MDmaterials,includingleadhalideperovskites(LHPs),relyontheofnanoscale,periodic,andextendedmolecularsystemscanbeSeehttps://pubs.acs.org/sharingguidelinesforoptionsonhowtolegitimatelysharepublishedarticles.useofasingle-particle(SP)descriptionoftheelectronicprohibitivelyexpensive.WhileanMBdescriptionofelectronic12−18excitedstates.Withinthisdescription,theCoulombandexcitedstatesincondensedmattersystemsispossible,42−48exchangeinteractionsbetweenelectronsandholesaresuchcalculationsareextremelyexpensivefortheirroutineneglected,andtheelectronsandholesareconsideredfreeapplicationsindynamics.Anumberofworkshavereportedparticles.variousapproachestoincorporateMBeffectsintotheNA-MDWhiletheSPtreatmentoftheelectronicstateshasbeen4919inthepast.Nakaiutilizedthetime-dependentdensityshowntobereasonableundercertainconditions,itbreaks50,5120,21functionaltight-binding(TD-DFTB)approachtomodeldowninmanyothercases.Notably,forsystemspossessing52NA-MDinLHPs.Bonafehaverecentlydevelopedansymmetry,electronicstatedegeneraciesbecomeimportant,EhrenfestTD-DFTBapproachtomodelingcoupledelec-suggestingthatthetrueexcitedstatesmaybebestdescribedbythesuperpositionsofsuch(nearly)-degeneratestates.Undersuchconditions,thestaticelectroniccorrelationbecomesReceived:December24,2020importanttoinclude,becausenearlyallexcitedstates,buttheAccepted:March1,2021lowestfew,typicallycontainmultipleSPexcitations(SlaterPublished:March4,2021determinants).Amany-body(MB)descriptionoftheexcitedelectronicstatesisalsonecessaryinquantum-confined22−2526,27systemsandatlowtemperatures,whereexciton©2021AmericanChemicalSocietyhttps://dx.doi.org/10.1021/acs.jpclett.0c037992444J.Phys.Chem.Lett.2021,12,2444−2453

1TheJournalofPhysicalChemistryLetterspubs.acs.org/JPCLLetterFigure1.ThermallyaveragedprojecteddensityofstatesfortheconsideredCsPbI3systemsandschematicsofsomeoftheconsideredelectronicexcitations.(a)pDOSforthecubicphase;(b)schematicofelectronicexcitationresultingin∼0.8eVofexcesselectronicenergyforthecubicphase;(c)pDOSforthetetragonalphase;(d)schematicofelectronicexcitationresultingin∼0.4eVofexcesselectronicenergyforthetetragonalphase.50tron−nucleardynamicswithintheDFTB+packageandcontaining40and160atoms,respectively(Figure1,panelsaappliedittostudytheexcited-statedynamicsinseveralandc,insets).Thegeometryoptimization,molecularexamplesystems.TheTretiakgrouphasdevelopedthedynamics,ground-statedensityfunctionaltheory(DFT),and53,54NEXMDsoftwarepackagethatreliesonthecollectiveTD-DFTcalculationsareperformedusingtheCP2Ksoftware55,5664,65electronoscillator(CEO)approachforNA-MDmodelingpackage.Intheelectronicstructurecalculations,theinextendedorganicsystems.AnumberofschemesbasedonvalenceelectronsforallatomtypesaredescribedusingatheTD-DFTdescriptionofelectronicexcitedstateshavebeenmixedGaussianandplane-wavebasisset.Theexchangeand57−59reportedrecentlyasanaffordablewayofincorporatingcorrelationofthevalenceelectronsisdescribedbythe60,6166MBeffectsintoNA-MD,includingourownimplementa-Perdew−Burke−Ernzerhof(PBE)densityfunctional.tionusingtheneglect-of-back-reactionapproximation(NBRA)Although,thispuredensityfunctionalhasanumberofwell-62,6367−71ofNA-MDwithintheLibrasoftware.Despitetheserecentknownproblems,theuseofgenerallymorereliablehybridadvances,theuseoftheSPdescriptionofelectronicexcitedfunctionalsintheMDcalculationssuchasthoseundertakeninstatesintheNA-MDofnanoscaleandperiodicsystemsisstillthepresentworkisprohibitivelyexpensive.Weanticipatethatprevailing.Todate,littleattentionhasbeenpaidtocriticallythequalitativetrendsdiscussedinthisworkwillholdevenifassessingtheapproximateapproachesinviewofthemorethehybridfunctionalsareused,exceptforthecasesexplicitlyrigorousmethodscurrentlyavailable.Thus,anassessmentofdiscussedlater.Theeffectsofthecoreelectronsareaccounted72theroleofMBeffectsintheNA-MDofsuchextendedsystemsforusingGoedecker−Teter−Hutter(GTH)pseudopoten-isofhighimportance.tials.Theplane-wavebasisisdeterminedbythechargedensityInthiswork,wereportourstudiesofMBeffectsintheNA-cutoffof300Ry.Thedouble-ζ-valence-polarized(DZVP)73MDofperiodiccondensedmattersystemsunderconditionsbasissetisusedastheGaussianbasis.Toensurethefavoringhigh(quasi)degeneraciesoftheelectronicstates,asaccuracyoftheforcecalculations,thek-pointsamplinguses74maybethecaseforLHPs.Inparticular,wefocusonmodelingthe4×4×4and2×2×2Monkhorst−PackgridsfortheexcessexcitationenergyrelaxationintheCsPbI3LHP,whichiscubicandtetragonalsystems,respectively.Dispersioninter-knowntoexistinthecubicandtetragonalphases(amongactionsareaccountedforusingGrimme’sDFT-D3dispersion75others).Ourexpectationhereisthatthedifferenceincorrection.Eachsystemisfirstthermalizedto300KusingsymmetriesofthecrystalstructuresofthetwophasescanMDfollowedbyproductionMD.TheproductionMDaffectthedegeneraciesofelectronicstates,leadingtotrajectoriesarerunfor1.8psandaresampledusingnucleardifferencesinthemany-bodycompositionoftheexcitedintegrationtimestepsof1fs.Thermaleffectsofthebathareelectronicstatesforthetwosystems.Inthisway,weexaminedescribedbyacanonicalsamplingthroughvelocityrescaling76theroleofcrystalsymmetryontheNAdynamicsincondensed(CSVR)thermostatwithatimeconstantof200fs,aswasmattersystems.Furthermore,weassesstherolethatMBusedinapreviousstudybyUrataniandNakai,whichiswithin49effectshaveintheNA-MDbystudyingthedynamicsinthesetherangeofphononmodesforthisperovskite.ForalltwosystemsatboththeMBandSPlevels.geometryoptimizationcalculations,optimizationisperformedWeemployatomisticmodelsofthecubicandtetragonalusingtheBroyden−Fletcher−Goldfarb−Shannon(BFGS)77phasesofCsPbI3composedas2×2×2supercellsandalgorithm.Thegeometryoptimizationprocessiscontinued2445https://dx.doi.org/10.1021/acs.jpclett.0c03799J.Phys.Chem.Lett.2021,12,2444−2453

2TheJournalofPhysicalChemistryLetterspubs.acs.org/JPCLLetterFigure2.Comparisonofdensitiesofexcitedstatesandthermallyaveragednonadiabaticcouplingsforthecubic(a,c,ande)andtetragonal(b,d,andf)phasesofCsPbI3.ThethermallyaveragedNACsarecomputedattheSP(candd)andMB(eandf)levels.foreachstructureuntilthemaximumforceoneachatomexcesselectronicenergyinthetetragonalphase.Inaddition,becomeslessthan15meV/Åandthemaximumgeometrythetetragonalsystemhastwogroupsofconductionbandchangebecomeslessthan0.002Bohr.statesintheenergywindow2−4eV,whereasthecubichasForbothsystems,thethermallyaveragedelectronicbandonlyone.Thegroupofstatesnear2eVissplitinto3substatesgapsareroughly1.8eV(Figure1),whichisingoodagreementinthecubicsysteminthestaticstructure(FigureS1),butthis78,79withexperiments.ThermalaveragingisdoneoverallthefinestructureishiddeninthethermallyaveragedpDOSconfigurationssampledbytheMDtrajectories.Wefindthat(Figure1).ThetwobandsofthetetragonalsystemdonotaveragingyieldsaconvergedpDOS(FigureS1).Consideringshowanynotablefinestructureinthestaticcalculations.Thethelevelofelectronicstructurecalculationsusedinthiswork,pDOSstructurecanberationalizedbythesystemsymmetries:suchagoodagreementofthebandgapvaluesfortheseLHPsthe3-foldsplittingofasinglebandinthecubicstructurecanlikelystemsfromtheknownerrorcancellationthatoccursbeattributedtothe3-foldsymmetryofthesystem,whereasthewhenusingpurefunctionalswithoutspin−orbitcouplingpresenceofthetwonotablysplitbandsinthetetragonal(SOC)effects.Theprojecteddensityofstates(pDOS)systemcanbeattributedtoanotableanisotropyofitscrystalcalculationsrevealthatforbothsystems,thevalencebandsstructure,withatleast2distinctdirections(e.g.,cvsaorb).areprimarilycomposedofatomicorbitalsoftheiodineatoms,WecomparepropertiesrelevantforNA-MDcalculationswhereastheconductionbandsarecomposedprimarilyofleadcomputedattheSPandMBlevels(Figure2).Aswasshown82,83orbitalswithasmallerfractionofiodineorbitals(Figure1),inearlier,NACsbetweendistinctSlaterdeterminants(SDs)80,81agreementwithprevioustheoreticalworks.ThemaincanbereducedtotheNACsbetweenorbitals.Forthisreason,differencesbetweenthecubicandtetragonalphasesisthethebasisofsingleSDexcitationsisconsideredaSPincreasedpDOSinthelatter,whichisaconsequenceofadescription.Incontrast,theMBelectronicstatesaredescribedlargersizeofthecell.Thus,onemayexpectfasterrelaxationofbysuperpositionsoftheSDexcitations.Becausethedensities2446https://dx.doi.org/10.1021/acs.jpclett.0c03799J.Phys.Chem.Lett.2021,12,2444−2453

3TheJournalofPhysicalChemistryLetterspubs.acs.org/JPCLLetterofexcitedstatesareratherhigh,weconsideredonlyfiniteTakentogether,weexpectthatboththeshiftoftheNACenergywindowsofexcitedstatestocompute:roughly0.9eVprobabilitydensitytowardlargervaluesandthechangedforthecubicand0.5eVforthetetragonalphases.AttheMBstructureoftheNACmatrixshouldacceleratetheexcited-statelevel,151and76excitedstatesfitintotheseenergyspansfordynamics(e.g.,excited-staterelaxation)whencomputedatthethecubicandtetragonalphases,respectively.TheseMBstatesMBlevelrelativetodynamicsattheSPlevel.areformedinthebasisof229and118uniqueSDsfortheItisillustrativetodiscusstheoriginofthedifferenceinthecubicandtetragonalsystems,respectively.However,someofNACmagnitudescomputedattheSPandMBlevels.Ateverytheseexcitationsareoutsideoftheenergywindowsconsideredtimeinstant,theMBstates,{Ψi},aregivenbyaunitaryandthereforemaybeexcludedfromtheSP-onlymodelingandtransformation(U)oftheSPexcitations,{Φi}:Ψi=∑jUjiΦj.82TheNACsbetweentheMBstatesaregivenbydMB=calculations.Followingtheearlierapproximationcommonlyij84−93usedinmanySP-basedNA-MDstudies,theenergiesofΨΨ∂=∑UU*ΦΦ∂+∑UU*⟨Φ|Φ⟩∂=theSPexcitedstatesareestimatedviathedifferencesoforbitali∂tjab,iabja∂tbab,iaab∂tbjSP∂energies,neglectingtheCoulombandexchangeintegrals.∑UdU*+∑UU*.Here,weutilizedtheortho-ab,iaabbjaia∂tajSomewhatsurprisingly,thedensitiesoftheexcitedstatesnormalizationoftheSPstates,⟨Φi|Φj⟩=δij.UnderthespecialcomputedatbothSPandMBlevelsforeachsystemarenearlycaseofthetime-independenttransformationmatrixU,thesame(Figure2,panelsaandb).Thissimilarityindicates∂U=0,onecanshowthattheaveragemagnitudeofthethattheexcitoniceffects(staticcorrelationandCoulombic∂tinteractionofelectron−holepairs)arerelativelysmall.ThisNACsinthetwobasesareequal,asforinstancecouldbequantifiedby∑,|d|2.UsingthefactthatthematrixUisaresultisconsistentwithexperimentalstudiesreportingsmallijijexcitonbindingenergiesinLHPs.94,95Smallexcitoniceffectsinunitarytransformation,onecanshowthatthepresentlystudiedsystemsarealsoexpectedbecauseofthe22∑||=dd∑||.Thus,theaveragemagnitudeij,M∈{B}ijij,S∈{P}ijlackofquantumconfinementononehandandtheuseofaofthecouplingwouldnotdependonwhethertheSPorMBpuredensityfunctionalontheother.AssuggestedbyIzmaylov9697descriptionofexcitedstatesisused.However,inmostandScuseria,andasalsofollowsfromotherstudies,situations,thetransformationmatrixUistime-dependent,capturingexcitoniceffectsinTD-DFTcalculationsrequiresthebecauseofthetime-dependenceoftheHamiltonianviaitsfunctionalwiththecorrectasymptoticbehavioroftheparametricdependenceonnucleartrajectories.Assuch,theexchange,suchasachievedviatheuseofhybridfunctionals,∂especiallythelong-rangecorrectedones.However,suchterm∑aUUia*∂tajcannotbeneglected.Itisthistermthatiscalculationsareprohibitivelyexpensive,andweleavethisresponsibleforthedifferenceintheaverageNACmagnitudesquestionanopenproblem.(asquantifiedbythecentersofgravityintheprobabilityGiventhesimilarityoftheDOSintheMBandSPbases,densitydistributionsshowninFigureS2).Inotherwords,theonemayexpectthattheNACsintheMBandSPexcitationtime-dependenceoftheMBstatescompositionintermsofthebaseswouldbecomparable.However,adetailedanalysisofthecorrespondingSPstatesdeterminesthedifferenceinaverageNACsbetweenthepairsofMBandSPstatesbreaksthisNACs.Havingsaidthat,eventheconditionexpectation.Thefirstdistinctioncomesinthestructureofthe∑||=dd2∑||2doesnotimplyasimilarityofij,M∈{B}ijij,S∈{P}ijNACmatrices.AttheSPexcitationlevel,thetime-averagedthedynamicscomputedinthetwobases.TherelativeNACsbetweenelectronicstateshaveascattered-likemagnitudeofthecouplingsbetween“equivalent”states(ifappearance(Figure2,panelscandd).SuchastructurearisessuchamappingoftheSPtoMBbasiscanbemade)maybebecauseinthespaceofSPstatesoftypeHOMO−N→changed,suchthatsomechannelsofthedynamicsmaybeLUMO+M,withvaryingNandM,andorderedbyenergy,thefavoredinonebasisovertheother.Finally,althoughourcorrespondingSDsmaydifferbymorethanoneelectroncurrentcalculationssuggestfasterdynamicsintheMBbasis,excitation,leadingtozerocouplingbetweensuchpairsofthereisnoreasontoexpectthistobeageneraltrend.Instates.Ontheotherhand,theMBelectronicexcitedstatesare∂composedofmultipleSPtransitions,andtwoMBstatesmayprinciple,thereisnolimitationfortheterm∑aUUia*∂tajtotakebecomecoupledviathecouplingoftheunderlyingSDs.Asavaluesoppositeinsigntothoseofthe∑U*dSPUterm,thusa,biaabbjresult,theNACmatrixhasamore“filled-in”structurewhendecreasingtheeffectiveNACsintheMBbasisasopposedtocomputedinthebasisofMBexcitedstates(Figure2,panelsethoseintheSPbasis.andf).Furthermore,wefindthattheprobabilitydistributionsComparingthecrystalsymmetries,wefindthatNACsareoftheNACsbetweenMBstatesisshiftedtowardlargervalueslargerinthecubicsystemthaninthetetragonalone(Figures2comparedtotheprobabilitydistributionsoftheNACsandS2).ThisdifferencecanberationalizedbythelargerbetweenSPstates(FigureS2).Thismeansthatoneismoredegreeofconfigurationalmixinginthecubicsystem.WelikelytoencounterlargermagnitudesofNACsduringthequantifythedegreeofconfigurationalmixingbythesquaredcourseofthedynamicsifMBeffectsareaccountedfor.Theamplitudesoftheconfigurationinteractioncoefficientsofprobabilitytofindnear-zeroNACsishigherattheSPleveldominantSDsenteringthecompositionoftheMBstatesthanattheMBlevel.Forbothcubicandtetragonalphases,the(FiguresS3andS4).OuranalysisshowsthatthefirstfewprobabilitytofindNACvaluesgreaterthanca.0.2meVinexcitedstatesaremainlySPinbothsystemsattheiroptimizedabsolutevalueislargerintheMBbasisthantheSPbasisgeometries,whichvalidatesthewidelyusedSPapproximation(FigureS2,panelsaandd).TheprobabilityoffindingNACsinmodelingNAprocessessuchaselectron−holerecombina-85,98,99withtheabsolutevaluesof5−50meVissmallforbothtion.Inthetetragonalsystem,electronicstatesretainasystems,whichisordersofmagnitudesmallerthantostrongSPcharacterformanyofthelow-lyingelectronicstatesencounterNACsintherange0−0.5meV.However,forall(FiguresS4),whereasinthecubicsystem,allbutthelowestvaluesofNACmagnitudes,theprobabilitydensityisexcitedstatesexhibitsignificantconfigurationalmixing(FigureconsistentlylargerattheMBlevelthatitisattheSPlevel.S3).WeattributesuchapronouncedmixingoftheSPstatesto2447https://dx.doi.org/10.1021/acs.jpclett.0c03799J.Phys.Chem.Lett.2021,12,2444−2453

4TheJournalofPhysicalChemistryLetterspubs.acs.org/JPCLLetterFigure3.ExcesselectronicenergyrelaxationdynamicscomputedwiththeFSSHmethodologyincubicCsPbI3:(a)attheSPleveland(b)attheMBlevel.theincreasedsymmetrypresentinthecubicsystem.HighTheMBeffectsontheNAdynamicscanbebestseenbysymmetryleadstohighdegeneracyofelectronicstatesinthecomparingtheexcitationenergyexcessdecaykineticsatthespaceofSPtransitionsandpromotestheirmixingintheMBFSSHlevelforbothsystems.WhenMBeffectsareaccountedpicture.Atlowertemperatures,whenthermallyinducedatomicfor,therelaxationofexcessexcitationenergyisacceleratedbymotionisreduced,thesymmetryofthecrystalstructureisthefactorof2.6(Figure3).Moreover,theinclusionofMBbetterpreserved.Thisexplainsthestrongerconfigurationaleffectsqualitativelychangesthedynamics.AttheMBlevel,itismixingpresentattheoptimizedgeometries(0K,FigureS3,typicallythecasethattheexponentialcomponentineq1ispanelsaandb;FigureS4,panelsaandb)comparedtothesmallerthanitisintheSPbasis(e.g.,seeTableS1ofthethermallysampledsetofconfigurationsat300K(FigureS3,SupportingInformation),whichsignifiesthatcoherentpanelscandd;FigureS4,panelscandd).At300K,thedynamicsisprominentintheMBbasis.ThecoherentatomicmotionbreaksthesymmetryandreducesthedegreeofdynamicsintheMBbasisisfavoredbythemoreextensiveconfigurationalmixing.However,theinfluenceofthesystems’couplingofallstatestoeachotherascomparedtotheSPsymmetryisstillpresent.Forthecubicsystem,significantpicture.AttheSPlevel,thedynamicsexhibitslittletonodecayconfigurationalmixingoftheelectronicstatesisstillpresentatforthefirst100fsandisfollowedbyaslowdecay(Figure3a).300K,especiallyforhigher-energyexcitations.IntheSPbasis,thedecaykineticsisdominatedbytheTodirectlyassesstheroleofMBeffectsontheNAexponentialcomponentineq1(e.g.,seeTableS1ofthedynamics,weconductexplicitNA-MDcalculationsusingtheSupportingInformation),whichsignifiesthatthecoherentfewestswitchessurfacehopping(FSSH),100Belyaev−Leb-dynamicsissuppressedorintrinsicallyslowerintheSPbasis.edev−Landau−Zener(BLLZ),101,102andseveraldecoherenceThissuppressionofthecoherentdynamicscanbeexplainedbycorrectionmethodologies,103−105asalsodetailedinthesectionlargerenergygapsbetweenthecoupledstates.Inthisregard,4oftheSupportingInformation.WeemployarecentlyoneshouldnotbemisleadbytheapparentlysimilardensitiesdevelopedinterfaceoftheLibrasoftwareforNA-MDofexcitedstatesintheSPandMBbases(Figure2,panelsacalculations62,63andtheCP2K64code.Thedetailsofourandb).Althoughthedensitiesaresimilar,theydonotreflectthestructureofthecouplingofthestatestheenergeticallycomputationalsetupsaresummarizedinsection5ofthenearbySPstatesmaybeuncoupled,whereastheaverageSupportingInformation.FurtherdetailsofourNA-MD106energygapsbetweenthecoupledstateswouldbelargerinthisframeworkarediscussedelsewhere.Thedynamicsofexcessbasis.electronicexcitationenergyrelaxationfortheconsideredWecomputethetimescalesofexcessexcitationenergysystemsisquantifiedbyfittingtheaverageexcesselectronicdecayinbothcubicandtetragonalphasesofCsPbI3usingbothexcitationenergyrelaxationdynamicsoverallNA-MDtheSPandMBdescriptionofexcitedstatesandseveralNA-trajectoriestothefollowingfunctionalform:MDmethodologies(Table1,alsoseesection6oftheiiyyiiy2ySupportingInformationformoredetails).OurmainjjjjjjtzzzzzzjjjjjjtzzzzzzobservationisthatthedynamicswiththeMBeffectsaccountedf(;tE0)=−+−−Aexpjjjjzzzz(EA0)expjjjjjzzzzzkkττ1{{jkk2{z{(1)forisgenerallyfasterthanitisinthebasisofSPstates.ThisconclusionisconsistentwiththechangesoftheNACmatrixstructurediscussedabove.TheinclusionoftheMBeffectsSuchafittingfunctionhasbeenusedinpastNA-MDstudiestoacceleratesthedynamicsmoreinthecubicsystemthanitdoescharacterizethedecayofexcessexcitationenergyincondensed1,13,107inthetetragonalsystem:thetimescalesaredecreasedbythematterandnanoscalesystems.Thisformaccountsforfactorof1.4−2.6inthecubicsystemandbyafactorofonlytheGaussiandecaykineticstypicalforcoherentdynamicsof1.6inthetetragonaloneincomparisontothecorrespondingelectronsindensemanifoldsofexcitedstatesintheshort-timeSP-basedtimescales.SuchtrendsarealsoconsistentwithrangeandtheexponentialdecaykineticstypicalforincoherentslightlylargerNACsinthecubicsystemthaninthetetragonal,dynamicsatthelongertimescalesorinthesparsemanifoldsofasaconsequenceofthecrystalsymmetries(e.g.,seeFiguresexcitedstates.TheoverallrelaxationtimescaleisthenS2−S4).computedaccordingtoAsexpected,accountingforelectronicdecoherence(viaID-104103,105AandmSDMmethods)leadstoslowingtheA()EA0−τ=+ττ12dynamicsdownrelativetoFSSH.Ofthetwodecoherence-E0E0(2)correctedTSHschemestested,theID-Atypicallyyieldsa2448https://dx.doi.org/10.1021/acs.jpclett.0c03799J.Phys.Chem.Lett.2021,12,2444−2453

5TheJournalofPhysicalChemistryLetterspubs.acs.org/JPCLLetterTable1.Excited-StateEnergyDecayTimeConstants,τ(fs),accelerationisnotablylargerthantheapproximately2.6-foldComputedUsingVariousSurfaceHoppingMethodsataccelerationbecauseofweakexcitoniceffectsseenintheEithertheSPorMBDescriptionoftheElectronicExcitedpresentwork,althoughthetwovaluescannotbecomparedaStatesdirectlyastheyareobtainedfordistinctsystems.AnanalysisofTable1showsthatthecomputedenergy108476,Bretschneideretal.,109,110relaxationtimescalesmaybeinagoodagreementwiththeexperiment,1.4eV,0.8eV∼1000Shenetal.reportedexperimentaldatadependingonthecombinationofcubicFSSHID-AmSDMBLLZtheexcitedstates’descriptionlevelandtheTSHmethodologyMB0.8eV48012091187486used.SuchagreementsanddisagreementsshouldbetakenSP0.8eV122617572492444criticallybecausetheymaybeduetofortuitouserrorMB0.4eV67911201645984cancellationsorthelackofknowneffectsthataretooSP0.4eV111613231858889expensivetoinclude,respectively.AttheMBlevel,theFSSHtetragonalFSSHID-AmSDMBLLZcalculationsforthecubicsystemareinexcellentagreementMB0.4eV1002161718231865withtheexperimentaltimescalesofapproximately476fsofSP0.4eV1655242430901843Bretschneideretal.108AttheSPlevel,thecomputedtimeaE0(eV)istheinitialexcesselectronicexcitationenergyusedinthescalesarenearlytwiceasslow:1.1−1.2psforarangeofinitialcalculationsetupandthefittingfunction,eq1.excitationenergylevels.Thesetimescalesareconsistentwiththevaluesreportedinapreviouscomputationalstudythat1fasterdynamicsthanmSDM.IncontrasttoalltheNAC-basedreliedonasimilarSPdescriptionofexcitedstates.Incontrast,109,110TSHmethodsused(FSSH,ID-A,andmSDM),theenergy-Shenetal.reporttimescalesintherangeof1−30psbasedBLLZmethodpredictshighlysimilardynamicsofthedependingonthecarrierdensity,withasubpicosecond(0.8−excitedstatesatboththeMBandSPlevels.MBeffectscan1.0ps)rangeforlowcarrierdensitiesstudiedintheirinfluencethedynamicsintwoways.Oneisviathewaveexperiment.OnemaythinkthattheFSSHattheSPlevelfunctions(andhencetheNACs),viathemixingofexcitedyieldsareasonableagreementwiththeexperiment.However,SDs,asdiscussedabove,whichwerefertoasweakexcitonictheFSSHdoesnotaccountfordecoherenceeffectspresentineffects.Theotherisviatheenergiesoftheexcitonicstates,realisticsystems.Thus,oneneedstoshiftattentiontotheID-Awhichwerefertoasstrongexcitoniceffects.AsdiscussedandmSDMresults.AttheMBlevel,thedynamicscomputedpreviously,thestrongexcitoniceffectswouldmanifestusingtheseschemescomesintocloseragreementwiththeca.1109,110themselvesinquantum-confinedsystemsandrequiretheusepstimescalesofShenetal.TheSPdescriptionwouldofdensityfunctionalswiththeproperasymptoticbehaviorofoverestimatethetimescalesbyapproximatelyafactorof2theexchangeterms97(pragmaticallyspeaking,theuseofrange-comparedtothedataofShenetal.andbyafactorof4−5correctedhybridfunctionals).Inotherwords,thestrongcomparedtothedataofBretschneideretal.Thus,theexcitoniceffectswouldmanifestthemselvesviaanotableinclusionofevenweakexcitoniceffectsiscriticalformergingexcitonbindingenergy.Forthesystemsconsideredinthisthegapbetweencomputedandexperimentallymeasuredtimework,thedensitiesoftheMBandSPexcitedstatesagreewithscalesofexcitationenergyrelaxation.eachother(Figure2,panelsaandb),suggestingtheexcitonTheabovediscussionshouldbetakencritically.OurbindingenergiesaresmallandtheSPpictureworksasfarassimulationsdonotexplicitlyincludeSOCeffects,whichhave111theenergiesoftheelectronicexcitedstatesareconcerned.ThisbeenshowntosignificantlyacceleratedynamicsinLHPs.Atobservationagreeswiththe10meVvalueforcubicCsPbI3thesametime,weuseapuredensityfunctionalinsteadofthereportedbythepriorstudies.94,95Thisenergyissmallerthancomputationallymoreexpensivehybridfunctionals,andithasthermalenergyatroomtemperature,sotheexcitoniceffectsbeendemonstratedbeforethattheuseofhybridfunctionals68arenegligible.Thesimilarityofthedensitiesofexcitedstatesatmayslowdownthedynamics.ItispossiblethatthetwotheSPandMBlevelsexplainstheinsensitivityoftheenergy-approximationsmaycountereachother’seffect,althoughwebasedBLLZtothelevelofthedescriptionofexcited-statecannottelltowhatextent.Nonetheless,asshowninthiswork,energies.Thisbehaviormayberegardedasaconsequenceofweakexcitoniceffectsmayleadtoanotableaccelerationofthethelackofstrongexcitoniceffectsorinabilitytocaptureit,dynamics.ThiseffectislikelytoholdregardlessofwhatwhichcanbeaconsequenceofthelackofquantumfunctionalisusedandwhethertheSOCeffectsareincluded,confinement(3Dsystems)andtheuseofpuredensityalthoughfurtherstudiesonthismatterwouldbehighlyfunctional.Withthe“strongexcitoniceffects”ruledoutinthedesirable.presentstudy,weconcludethataccelerationoftheNA-MDweAnotherpotentiallimitationofthecurrentmethodology,asobserveinperiodicLHPscanbeattributedtothe“weak”wellasofothersimilartechniques,concernsthetreatmentofexcitoniceffects,thatis,themixingofthequasi-degenerateelectronandphononk-points.Ononehand,includingalargerstates,whichinturncanbeaffectedbyasystem’ssymmetry.numberofk-points(or,equivalently,usingalargersupercell)Weanticipatethoughthatapplyingthecurrentapproachtocouldincreasethedensityofelectronicstatesandaccelerate2Dor0Dperovskites/systemsand/orusinghybridfunctionalsthedecaydynamics.Ontheotherhand,describingthe(whichisprohibitivelyexpensiveatthispoint)maychangethetransitionsbetweenthek-pointsrequiresaccountingforcomputedtimescalesandthequalitativecomparisonofthephononquantization(q-points),whichwouldrequireatimescalescomputedwiththeBLLZapproach.Inthisregard,differentcomputationalmethodologythatisnotavailablein60recentworkbyLiuetal.demonstratedthataccountingforthecurrentscheme.Suchcalculationsmayalsoinvolvean112strongexcitoniceffectsinquantum-confinedsystemsliketheextremelylargenumberofk-points,whichisprohibitivelyMoS2/WS2heterojunctionmayleadtouptoa10-foldexpensivefortheatomisticsystemsconsideredhere(especiallyaccelerationofthedynamicscomparedtothecommonlyusedattheTD-DFTlevel).Atthesametime,enablingrelaxationSPKohn−Sham-DFTprescriptionofexcitedstates.Suchanchannelsthatincludemultiplek-pointsmayslowthedecay2449https://dx.doi.org/10.1021/acs.jpclett.0c03799J.Phys.Chem.Lett.2021,12,2444−2453

6TheJournalofPhysicalChemistryLetterspubs.acs.org/JPCLLetterdynamics,becauseafractionoftherelaxationwilltakeplaceNotesacrossdifferentk-pointsoratk-pointsotherthantheΓ-point.Theauthorsdeclarenocompetingfinancialinterest.Inourexperience,NACsarelargerforthek-pointsclosertoDetailedscriptsandinputfilesusedforalltypesofcalculationstheΓ-pointandaresmalleracrossthek-points,atleastfor113areavailableindigitalformonlinefromtheZenodoserver.directgapsemiconductors.Thus,onaverage,enablingrelaxationdynamicsacrossmultiplek-pointstatesmaylead■ACKNOWLEDGMENTStoasloweraveragedecayoftheexcitedstates,whichmaycountertheeffectoftheincreaseddensitiesofstates.Overall,A.V.A.acknowledgesthefinancialsupportoftheNationaltheinclusionofmultiplek-pointsmayormaynotbeanotherScienceFoundation(GrantOAC-NSF-1931366).SupportoffactortolowerthegapbetweenthecomputationallyderivedcomputationsisprovidedbytheCenterforComputationalcarrierrelaxationtimes(onthehigherend)andtheResearchattheUniversityatBuffalo.experimentallydeterminedones(onthesmallerend).Forbothoutcomes,however,MBeffectsareexpectedtoaccelerate■REFERENCESthedynamicsoftheexcited-staterelaxation,whetheritbrings(1)Madjet,M.E.;Berdiyorov,G.R.;El-Mellouhi,F.;Alharbi,F.H.;thecomputedresultsclosertoorfartherawayfromtheAkimov,A.V.;Kais,S.CationEffectonHotCarrierCoolinginexperimentalreferences.HalidePerovskiteMaterials.J.Phys.Chem.Lett.2017,8,4439−4445.Insummary,weshowthatincludingMBeffectsinNA-MD(2)He,J.;Vasenko,A.S.;Long,R.;Prezhdo,O.V.HalidesimulationsmaygreatlyacceleratethenonradiativerelaxationCompositionControlsElectron−HoleRecombinationinCesium−ofexcesselectronicexcitationenergy.WedemonstratethatforLeadHalidePerovskiteQuantumDots:ATimeDomainAbInitiotheCsPbIperovskite,thisaccelerationfactorreachesavalueStudy.J.Phys.Chem.Lett.2018,9,1872−1879.3(3)Wang,Y.;Fang,W.-H.;Long,R.;Prezhdo,O.V.Symmetryof2.6butnonethelessissufficienttobringthecomputedNA-BreakingatMAPbI3PerovskiteGrainBoundariesSuppressesChargeMDtimescalesintoacloseragreementwithexperiments.TheRecombination:Time-DomainAbInitioAnalysis.J.Phys.Chem.Lett.nonadiabaticexcesselectronicexcitationenergyrelaxation2019,10,1617−1623.ratesarelargerinsystemswithhighsymmetry,suchasinthe(4)He,J.;Long,R.LeadVacancyCanExplaintheSuppressedcubicphaseofCsPbI3,ascomparedtothelower-symmetry,NonradiativeElectron−HoleRecombinationinFAPbI3Perovskitetetragonalphase.HighspatialsymmetryfacilitatesthemixingunderIodine-RichConditions:ATime-DomainAbInitioStudy.J.ofmultipleexcitedSDscomprisingtheexcitedstates,leadstoPhys.Chem.Lett.2018,9,6489−6495.anincreasedcouplingbetweentheexcitedstates,andleadsto(5)Boehme,S.C.;Brinck,S.ten;Maes,J.;Yazdani,N.;Zapata,F.;fasterNA-MD.Chen,K.;Wood,V.;Hodgkiss,J.M.;Hens,Z.;Geiregat,P.;etal.Phonon-MediatedandWeaklySize-DependentElectronandHoleCoolinginCsPbBr3NanocrystalsRevealedbyAtomisticSimulations■ASSOCIATEDCONTENTandUltrafastSpectroscopy.NanoLett.2020,20,1819−1829.*sıSupportingInformation(6)Zhang,Z.;Fang,W.-H.;Long,R.;Prezhdo,O.V.ExcitonTheSupportingInformationisavailablefreeofchargeatDissociationandSuppressedChargeRecombinationat2DPerovskitehttps://pubs.acs.org/doi/10.1021/acs.jpclett.0c03799.Edges:KeyRolesofUnsaturatedHalideBondsandThermalDisorder.J.Am.Chem.Soc.2019,141,15557−15566.(1)pDOSattheoptimizedgeometries,(2)comparison(7)Zhang,S.-F.;Chen,X.-K.;Ren,A.-M.;Li,H.;Bredas,J.-L.oftheNACprobabilitydistributions,(3)analysisoftheImpactofOrganicSpacersontheCarrierDynamicsin2DHybriddegreeofconfigurationalmixinginthemany-bodyLead-HalidePerovskites.ACSEnergyLett.2019,4,17−25.excitedstates,(4)nonadiabaticmoleculardynamics(8)He,J.;Fang,W.-H.;Long,R.Two-DimensionalPerovskitemethodology,(5)computationaldetailsfortheNAMD,CappingLayerSimultaneouslyImprovestheChargeCarriers’LifetimeandStabilityofMAPbI3Perovskite:ATime-DomainAband(6)detailsoftheexcessexcitationenergydecayInitioStudy.J.Phys.Chem.Lett.2020,11,5100−5107.fittingfunctions(PDF)(9)Long,R.;Prezhdo,O.V.DopantsControlElectron−HoleRecombinationatPerovskite−TiO2Interfaces:AbInitioTime-■DomainStudy.ACSNano2015,9,11143−11155.AUTHORINFORMATION(10)Zhang,J.;Hong,H.;Zhang,J.;Fu,H.;You,P.;Lischner,J.;Liu,CorrespondingAuthorK.;Kaxiras,E.;Meng,S.NewPathwayforHotElectronRelaxationinAlexeyV.Akimov−DepartmentofChemistry,UniversityatTwo-DimensionalHeterostructures.NanoLett.2018,18,6057−6063.Buffalo,TheStateUniversityofNewYork,Buffalo,NewYork(11)Long,R.;Fang,W.-H.;Prezhdo,O.V.StrongInteractionatthe14260,UnitedStates;orcid.org/0000-0002-7815-3731;Perovskite/TiO2InterfaceFacilitatesUltrafastPhotoinducedChargeEmail:alexeyak@buffalo.eduSeparation:ANonadiabaticMolecularDynamicsStudy.J.Phys.Chem.C2017,121,3797−3806.Authors(12)He,J.;Fang,W.-H.;Long,R.;Prezhdo,O.V.WhyOxygenIncreasesCarrierLifetimesbutAcceleratesDegradationofBrendanSmith−DepartmentofChemistry,UniversityatCH3NH3PbI3underLightIrradiation:Time-DomainAbInitioBuffalo,TheStateUniversityofNewYork,Buffalo,NewYorkAnalysis.J.Am.Chem.Soc.2020,142,14664−14673.14260,UnitedStates;orcid.org/0000-0003-3460-9984(13)Banerjee,S.;Kang,J.;Zhang,X.;Wang,L.-W.TheEffectsofMohammadShakiba−DepartmentofMaterialsScienceandInterstitialIodineinHybridPerovskiteHotCarrierCooling:ANon-Engineering,ShahidBahonarUniversityofKerman,Kerman,AdiabaticMolecularDynamicsStudy.J.Chem.Phys.2020,152,Iran091102.(14)Carof,A.;Giannini,S.;Blumberger,J.HowtoCalculateChargeCompletecontactinformationisavailableat:MobilityinMolecularMaterialsfromSurfaceHoppingNon-Adiabatichttps://pubs.acs.org/10.1021/acs.jpclett.0c03799MolecularDynamics−beyondtheHopping/BandParadigm.Phys.Chem.Chem.Phys.2019,21,26368−26386.AuthorContributions(15)Oliboni,R.S.;Yan,H.;Fan,H.;Abraham,B.;Avenoso,J.P.;§B.S.andM.S.contributedequallytothiswork.Galoppini,E.;Batista,V.S.;Gundlach,L.;Rego,L.G.C.Vibronic2450https://dx.doi.org/10.1021/acs.jpclett.0c03799J.Phys.Chem.Lett.2021,12,2444−2453

7TheJournalofPhysicalChemistryLetterspubs.acs.org/JPCLLetterEffectsintheUltrafastInterfacialElectronTransferofPerylene-inTwo-DimensionalHybridPerovskites.J.Phys.Chem.Lett.2020,11,SensitizedTiO2Surfaces.J.Phys.Chem.C2019,123,12599−12607.2247−2255.(16)Ziogos,O.G.;Giannini,S.;Ellis,M.;Blumberger,J.Identifying(36)Banerjee,T.;Hill,S.P.;Hermosilla-Palacios,M.A.;Piercy,B.High-MobilityTetraceneDerivativesUsingaNon-AdiabaticMolec-D.;Haney,J.;Casale,B.;DePrince,A.E.,III;Losego,M.D.;Kleiman,ularDynamicsApproach.J.Mater.Chem.C2020,8,1054−1064.V.D.;Hanson,K.DiphenylisobenzofuranBoundtoNanocrystalline(17)Agrawal,S.;Lin,W.;Prezhdo,O.V.;Trivedi,D.J.AbInitioMetalOxides:ExcimerFormation,SingletFission,ElectronInjection,QuantumDynamicsofChargeCarriersinGraphiticCarbonNitrideandLowEnergySensitization.J.Phys.Chem.C2018,122,28478−Nanosheets.J.Chem.Phys.2020,153,054701.28490.(18)Candiotto,G.;Torres,A.;Mazon,K.T.;Rego,L.G.C.Charge(37)Chakraborty,P.;Liu,Y.;Weinacht,T.;Matsika,S.ExcitedStateGenerationinOrganicSolarCells:InterplayofQuantumDynamics,DynamicsofCis,Cis−1,3-Cyclooctadiene:Non-AdiabaticTrajectoryDecoherence,andRecombination.J.Phys.Chem.C2017,121,SurfaceHopping.J.Chem.Phys.2020,152,174302.23276−23286.(38)Heindl,M.;González,L.AXMS-CASPT2Non-Adiabatic(19)Fischer,S.A.;Habenicht,B.F.;Madrid,A.B.;Duncan,W.R.;DynamicsStudyonPyrrole.Comput.Theor.Chem.2019,1155,38−Prezhdo,O.V.RegardingtheValidityoftheTime-DependentKohn−46.ShamApproachforElectron-NuclearDynamicsviaTrajectory(39)Polyak,I.;Hutton,L.;Crespo-Otero,R.;Barbatti,M.;Knowles,SurfaceHopping.J.Chem.Phys.2011,134,024102.P.J.UltrafastPhotoinducedDynamicsof1,3-CyclohexadieneUsing(20)Barbatti,M.;Crespo-Otero,R.SurfaceHoppingDynamicswithXMS-CASPT2SurfaceHopping.J.Chem.TheoryComput.2019,15,DFTExcitedStates.Top.Curr.Chem.2014,368,415−444.3929−3940.(21)Maitra,N.T.OnCorrelatedElectron-NuclearDynamicsUsing(40)Peng,W.-T.;Fales,B.S.;Levine,B.G.SimulatingElectronTime-DependentDensityFunctionalTheory.J.Chem.Phys.2006,DynamicsofComplexMoleculeswithTime-DependentComplete125,014110.ActiveSpaceConfigurationInteraction.J.Chem.TheoryComput.(22)Wang,H.;Liu,W.;He,X.;Zhang,P.;Zhang,X.;Xie,Y.An2018,14,4129−4138.ExcitonicPerspectiveonLow-DimensionalSemiconductorsfor(41)Park,J.W.;Shiozaki,T.On-the-FlyCASPT2Surface-HoppingDynamics.J.Chem.TheoryComput.2017,13,3676−3683.Photocatalysis.J.Am.Chem.Soc.2020,142,14007−14022.(42)Lewis,D.K.;Ramasubramaniam,A.;Sharifzadeh,S.Tunedand(23)Blancon,J.-C.;Stier,A.V.;Tsai,H.;Nie,W.;Stoumpos,C.C.;ScreenedRange-SeparatedHybridDensityFunctionalTheoryforTraoré,B.;Pedesseau,L.;Kepenekian,M.;Katsutani,F.;Noe,G.T.;DescribingElectronicandOpticalPropertiesofDefectiveGalliumetal.ScalingLawforExcitonsin2DPerovskiteQuantumWells.Nat.Nitride.Phys.Rev.Mater.2020,4,063803.Commun.2018,9,2254.(43)Lewis,D.K.;Sharifzadeh,S.Defect-InducedExciton(24)Li,Y.;Shu,H.;Wang,S.;Wang,J.ElectronicandOpticalLocalizationinBulkGalliumNitridefromMany-BodyPerturbationPropertiesofGrapheneQuantumDots:TheRoleofMany-BodyTheory.Phys.Rev.Mater.2019,3,114601.Effects.J.Phys.Chem.C2015,119,4983−4989.(44)Wu,Y.;Xia,W.;Zhang,Y.;Zhu,W.;Zhang,W.;Zhang,P.(25)Hong,X.;Ishihara,T.;Nurmikko,A.V.DielectricConfinementRemarkableBand-GapRenormalizationviaDimensionalityoftheEffectonExcitonsinPbI4-BasedLayeredSemiconductors.Phys.Rev.LayeredMaterialC3B.Phys.Rev.Appl.2020,14,014073.B:Condens.MatterMater.Phys.1992,45,6961−6964.(45)Zhang,Y.;Xia,W.;Wu,Y.;Zhang,P.PredictionofMXene(26)Milot,R.L.;Eperon,G.E.;Snaith,H.J.;Johnston,M.B.;Herz,Based2DTunableBandGapSemiconductors:GWQuasiparticleL.M.Temperature-DependentCharge-CarrierDynamicsinCalculations.Nanoscale2019,11,3993−4000.CH3NH3PbI3PerovskiteThinFilms.Adv.Funct.Mater.2015,25,(46)Iskakov,S.;Yeh,C.-N.;Gull,E.;Zgid,D.Ab-InitioSelf-Energy6218−6227.EmbeddingforthePhotoemissionSpectraofNiOandMnO.Phys.(27)Wehrenfennig,C.;Liu,M.;Snaith,H.J.;Johnston,M.B.;Herz,Rev.B:Condens.MatterMater.Phys.2020,102,085105.L.M.ChargeCarrierRecombinationChannelsintheLow-(47)Wilhelm,J.;Golze,D.;Talirz,L.;Hutter,J.;Pignedoli,C.A.TemperaturePhaseofOrganic-InorganicLeadHalidePerovskiteTowardGWCalculationsonThousandsofAtoms.J.Phys.Chem.Lett.ThinFilms.APLMater.2014,2,081513.2018,9,306−312.(28)Luo,X.;Liang,G.;Han,Y.;Li,Y.;Ding,T.;He,S.;Liu,X.;Wu,(48)Wilhelm,J.;DelBen,M.;Hutter,J.GWintheGaussianandK.TripletEnergyTransferfromPerovskiteNanocrystalsMediatedbyPlaneWavesSchemewithApplicationtoLinearAcenes.J.Chem.ElectronTransfer.J.Am.Chem.Soc.2020,142,11270−11278.TheoryComput.2016,12,3623−3635.(29)Luo,X.;Han,Y.;Chen,Z.;Li,Y.;Liang,G.;Liu,X.;Ding,T.;(49)Uratani,H.;Nakai,H.SimulatingtheCoupledStructural−Nie,C.;Wang,M.;Castellano,F.N.;etal.MechanismsofTripletElectronicDynamicsofPhoto-ExcitedLeadIodidePerovskites.J.EnergyTransferacrosstheInorganicNanocrystal/OrganicMoleculePhys.Chem.Lett.2020,11,4448−4455.Interface.Nat.Commun.2020,11,28.(50)Hourahine,B.;Aradi,B.;Blum,V.;Bonafé,F.;Buccheri,A.;(30)Wieghold,S.;Nienhaus,L.PrechargingPhotonUpconversion:Camacho,C.;Cevallos,C.;Deshaye,M.Y.;Dumitrică,T.;InterfacialInteractionsinSolution-ProcessedPerovskiteUpconver-Dominguez,A.;etal.DFTB+,aSoftwarePackageforEfficientsionDevices.J.Phys.Chem.Lett.2020,11,601−607.ApproximateDensityFunctionalTheoryBasedAtomisticSimu-(31)Kafle,T.R.;Kattel,B.;Yao,P.;Zereshki,P.;Zhao,H.;Chan,lations.J.Chem.Phys.2020,152,124101.W.-L.EffectoftheInterfacialEnergyLandscapeonPhotoinduced(51)Aradi,B.;Hourahine,B.;Frauenheim,ThDFTB+,aSparseChargeGenerationattheZnPc/MoS2Interface.J.Am.Chem.Soc.Matrix-BasedImplementationoftheDFTBMethod.J.Phys.Chem.A2019,141,11328−11336.2007,111,5678−5684.(32)Miyata,K.;Conrad-Burton,F.S.;Geyer,F.L.;Zhu,X.-Y.(52)Bonafe,F.P.;etal.AReal-TimeTime-DependentDensityTripletPairStatesinSingletFission.Chem.Rev.2019,119,4261−FunctionalTight-BindingImplementationforSemiclassicalExcited4292.StateElectron−NuclearDynamicsandPump−ProbeSpectroscopy(33)Breen,I.;Tempelaar,R.;Bizimana,L.A.;Kloss,B.;Reichman,Simulations.J.Chem.TheoryComput.2020,16,4454−4469.D.R.;Turner,D.B.TripletSeparationDrivesSingletFissionafter(53)Malone,W.;Nebgen,B.;White,A.;Zhang,Y.;Song,H.;FemtosecondCorrelatedTripletPairProductioninRubrene.J.Am.Bjorgaard,J.A.;Sifain,A.E.;Rodriguez-Hernandez,B.;Freixas,V.Chem.Soc.2017,139,11745−11751.M.;Fernandez-Alberti,S.;etal.NEXMDSoftwarePackageforNon-(34)Akimov,A.V.;Prezhdo,O.V.NonadiabaticDynamicsofAdiabaticExcitedStateMolecularDynamicsSimulations.J.Chem.ChargeTransferandSingletFissionatthePentacene/C60Interface.J.TheoryComput.2020,16,5771−5783.Am.Chem.Soc.2014,136,1599−1608.(54)Sifain,A.E.;Bjorgaard,J.A.;Nelson,T.R.;Nebgen,B.T.;(35)Tian,Y.;Li,Y.;Chen,B.;Lai,R.;He,S.;Luo,X.;Han,Y.;Wei,White,A.J.;Gifford,B.J.;Gao,D.W.;Prezhdo,O.V.;Fernandez-Y.;Wu,K.SensitizedMolecularTripletandTripletExcimerEmissionAlberti,S.;Roitberg,A.E.;etal.PhotoexcitedNonadiabatic2451https://dx.doi.org/10.1021/acs.jpclett.0c03799J.Phys.Chem.Lett.2021,12,2444−2453

8TheJournalofPhysicalChemistryLetterspubs.acs.org/JPCLLetterDynamicsofSolvatedPush−Pullπ-ConjugatedOligomerswiththe(76)Bussi,G.;Donadio,D.;Parrinello,M.CanonicalSamplingNEXMDSoftware.J.Chem.TheoryComput.2018,14,3955−3966.throughVelocity-Rescaling.J.Chem.Phys.2007,126,014101.(55)Tretiak,S.;Mukamel,S.DensityMatrixAnalysisand(77)Press,W.H.;Teukolsky,S.A.;Vetterling,W.T.;Flannery,B.P.SimulationofElectronicExcitationsinConjugatedandAggregatedNumericalRecipes3rded.:TheArtofScientificComputing;CambridgeMolecules.Chem.Rev.2002,102,3171−3212.UniversityPress:Cambridge,U.K.,2007.(56)Mukamel,S.ElectronicCoherenceandCollectiveOptical(78)Sutton,R.J.;Eperon,G.E.;Miranda,L.;Parrott,E.S.;Kamino,ExcitationsofConjugatedMolecules.Science1997,277,781−787.B.A.;Patel,J.B.;Hörantner,M.T.;Johnston,M.B.;Haghighirad,A.(57)Shimojo,F.;Hattori,S.;Kalia,R.K.;Kunaseth,M.;Mou,W.;A.;Moore,D.T.;etal.Bandgap-TunableCesiumLeadHalideNakano,A.;Nomura,K.;Ohmura,S.;Rajak,P.;Shimamura,K.;etal.PerovskiteswithHighThermalStabilityforEfficientSolarCells.Adv.ADivide-Conquer-RecombineAlgorithmicParadigmforLargeEnergyMater.2016,6,1502458.SpatiotemporalQuantumMolecularDynamicsSimulations.J.Chem.(79)Eperon,G.E.;Paterno,G.M.;Sutton,R.J.;Zampetti,A.;̀Phys.2014,140,18A529.Haghighirad,A.A.;Cacialli,F.;Snaith,H.J.InorganicCaesiumLead(58)Miyamoto,Y.;Rubio,A.ApplicationoftheReal-TimeTime-IodidePerovskiteSolarCells.J.Mater.Chem.A2015,3,19688−DependentDensityFunctionalTheorytoExcited-StateDynamicsof19695.Moleculesand2DMaterials.J.Phys.Soc.Jpn.2018,87,041016.(80)Chu,W.;Saidi,W.A.;Zhao,J.;Prezhdo,O.V.SoftLatticeand(59)Provorse,M.R.;Isborn,C.M.ElectronDynamicswithReal-DefectCovalencyRationalizeToleranceofβ-CsPbI3PerovskiteSolarTimeTime-DependentDensityFunctionalTheory.Int.J.QuantumCellstoNativeDefects.Angew.Chem.,Int.Ed.2020,59,6435−6441.Chem.2016,116,739−749.(81)Zhou,L.;Neukirch,A.J.;Vogel,D.J.;Kilin,D.S.;Pedesseau,(60)Liu,J.;Zhang,X.;Lu,G.ExcitonicEffectDrivesUltrafastL.;Carignano,M.A.;Mohite,A.D.;Even,J.;Katan,C.;Tretiak,S.DynamicsinvanDerWaalsHeterostructures.NanoLett.2020,20,DensityofStatesBroadeninginCH3NH3PbI3HybridPerovskites4631−4637.UnderstoodfromAbInitioMolecularDynamicsSimulations.ACS(61)Wu,G.;Li,Z.;Zhang,X.;Lu,G.ChargeSeparationandEnergyLett.2018,3,787−793.ExcitonDynamicsatPolymer/ZnOInterfacefromFirst-Principles(82)Akimov,A.V.;Prezhdo,O.V.ThePYXAIDProgramforNon-AdiabaticMolecularDynamicsinCondensedMatterSystems.J.Simulations.J.Phys.Chem.Lett.2014,5,2649−2656.Chem.TheoryComput.2013,9,4959−4972.(62)Akimov,A.V.Libra:AnOpen-Source“Methodology(83)Akimov,A.V.;Prezhdo,O.V.AdvancedCapabilitiesoftheDiscovery”LibraryforQuantumandClassicalDynamicsSimulations.PYXAIDProgram:IntegrationSchemes,DecoherenceEffects,J.Comput.Chem.2016,37,1626−1649.MultiexcitonicStates,andField-MatterInteraction.J.Chem.Theory(63)Akimov,A.V.;Smith,B.;Shakiba,M.;Sato,K.;Temen,S.;Li,Comput.2014,10,789−804.W.;Sun,X.;Chan,M.Quantum-Dynamics-Hub/Libra-Code:Hotfixfor(84)Chen,Z.;Zhang,P.-Z.;Zhou,Y.;Zhang,X.;Liu,X.;Hou,Z.;theTD-DFT/NAMDwithLibra(Version4.9.1);Zenodo,2020-10-31.Tang,J.;Li,W.ElucidatingtheInfluenceofSulfurVacanciesonDOI:10.5281/zenodo.4162542.(64)Kühne,T.D.;Iannuzzi,M.;DelBen,M.;Rybkin,V.V.;NonradiativeRecombinationDynamicsinCu2ZnSnS4SolarAbsorb-ers.J.Phys.Chem.Lett.2020,11,10354−10361.Seewald,P.;Stein,F.;Laino,T.;Khaliullin,R.Z.;Schütt,O.;(85)Li,W.;Chen,Z.;Tang,J.;Prezhdo,O.V.Anti-CorrelationSchiffmann,F.;etal.CP2K:AnElectronicStructureandMolecularbetweenBandGapandCarrierLifetimeinLeadHalidePerovskitesDynamicsSoftwarePackage-Quickstep:EfficientandAccurateunderCompressionRationalizedbyAbInitioQuantumDynamics.ElectronicStructureCalculations.J.Chem.Phys.2020,152,194103.Chem.Mater.2020,32,4707−4715.(65)Hutter,J.;Iannuzzi,M.;Schiffmann,F.;VandeVondele,J.(86)Niu,X.;Bai,X.;Zhou,Z.;Wang,J.RationalDesignandCP2K:AtomisticSimulationsofCondensedMatterSystems.WileyCharacterizationofDirectZ-SchemePhotocatalystforOverallWaterInterdiscip.Rev.Comput.Mol.Sci.2014,4,15−25.SplittingfromExcitedStateDynamicsSimulations.ACSCatal.2020,(66)Perdew,J.P.;Burke,K.;Ernzerhof,M.GeneralizedGradient10,1976−1983.ApproximationMadeSimple.Phys.Rev.Lett.1996,77,3865−3868.(87)Zhang,L.;Chu,W.;Zheng,Q.;Benderskii,A.V.;Prezhdo,O.(67)Kümmel,S.Charge-TransferExcitations:AChallengeforV.;Zhao,J.SuppressionofElectron−HoleRecombinationbyTime-DependentDensityFunctionalTheoryThatHasBeenMet.IntrinsicDefectsin2DMonoelementalMaterial.J.Phys.Chem.Lett.Adv.EnergyMater.2017,7,1700440.2019,10,6151−6158.(68)Lin,Y.;Akimov,A.V.DependenceofNonadiabaticCouplings(88)Xu,C.;Gu,F.L.;Zhu,C.UltrafastIntersystemCrossingforwithKohn−ShamOrbitalsontheChoiceofDensityFunctional:PureNitrophenols:AbInitioNonadiabaticMolecularDynamicsSimu-vsHybrid.J.Phys.Chem.A2016,120,9028−9041.lation.Phys.Chem.Chem.Phys.2018,20,5606−5616.(69)Cohen,A.J.;Mori-Sánchez,P.;Yang,W.Challengesfor(89)Liang,Y.;Li,J.;Jin,H.;Huang,B.;Dai,Y.PhotoexcitationDensityFunctionalTheory.Chem.Rev.2012,112,289−320.DynamicsinJanus-MoSSe/WSeHeterobilayers:AbInitioTime-2(70)Autschbach,J.Charge-TransferExcitationsandTime-Depend-DomainStudy.J.Phys.Chem.Lett.2018,9,2797−2802.entDensityFunctionalTheory:ProblemsandSomeProposed(90)Li,W.;Tang,J.;Casanova,D.;Prezhdo,O.V.Time-DomainSolutions.ChemPhysChem2009,10,1757−1760.AbInitioAnalysisRationalizestheUnusualTemperatureDependence(71)Dreuw,A.;Weisman,J.L.;Head-Gordon,M.Long-RangeofChargeCarrierRelaxationinLeadHalidePerovskite.ACSEnergyCharge-TransferExcitedStatesinTime-DependentDensityFunc-Lett.2018,3,2713−2720.tionalTheoryRequireNon-LocalExchange.J.Chem.Phys.2003,119,(91)Wei,Y.;Zhou,Z.;Fang,W.-H.;Long,R.GrainBoundary2943−2946.FacilitatesPhotocatalyticReactioninRutileTiO2DespiteFast(72)Hartwigsen,C.;Gøedecker,S.;Hutter,J.RelativisticSeparableChargeRecombination:ATime-DomainAbInitioAnalysis.J.Phys.Dual-SpaceGaussianPseudopotentialsfromHtoRn.Phys.Rev.B:Chem.Lett.2018,9,5884−5889.Condens.MatterMater.Phys.1998,58,3641.(92)Wiebeler,C.;Plasser,F.;Hedley,G.J.;Ruseckas,A.;Samuel,I.(73)VandeVondele,J.;Hutter,J.GaussianBasisSetsforAccurateD.W.;Schumacher,S.UltrafastElectronicEnergyTransferinanCalculationsonMolecularSystemsinGasandCondensedPhases.J.OrthogonalMolecularDyad.J.Phys.Chem.Lett.2017,8,1086−1092.Chem.Phys.2007,127,114105.(93)Zhou,X.;Li,L.;Dong,H.;Giri,A.;Hopkins,P.E.;Prezhdo,O.(74)Monkhorst,H.J.;Pack,J.D.SpecialPointsforBrillouin-ZoneV.TemperatureDependenceofElectron−PhononInteractionsinIntegrations.Phys.Rev.B1976,13,5188−5192.GoldFilmsRationalizedbyTime-DomainAbInitioAnalysis.J.Phys.(75)Grimme,S.;Antony,J.;Ehrlich,S.;Krieg,H.AConsistentandChem.C2017,121,17488−17497.AccurateAbInitioParametrizationofDensityFunctionalDispersion(94)Yang,Z.;Surrente,A.;Galkowski,K.;Miyata,A.;Portugall,O.;Correction(DFT-D)forthe94ElementsH-Pu.J.Chem.Phys.2010,Sutton,R.J.;Haghighirad,A.A.;Snaith,H.J.;Maude,D.K.;132,154104.Plochocka,P.;etal.ImpactoftheHalideCageontheElectronic2452https://dx.doi.org/10.1021/acs.jpclett.0c03799J.Phys.Chem.Lett.2021,12,2444−2453

9TheJournalofPhysicalChemistryLetterspubs.acs.org/JPCLLetterPropertiesofFullyInorganicCesiumLeadHalidePerovskites.ACSExcitedStatesDynamicsinCubicandTetragonalCsPbI3(VersionEnergyLett.2017,2,1621−1627.v1.0.0);Zenodo,2020-12-18.DOI:10.5281/zenodo.4358464.(95)Miyata,A.;Mitioglu,A.;Plochocka,P.;Portugall,O.;Wang,J.T.-W.;Stranks,S.D.;Snaith,H.J.;Nicholas,R.J.DirectMeasurementoftheExcitonBindingEnergyandEffectiveMassesforChargeCarriersinOrganic−InorganicTri-HalidePerovskites.Nat.Phys.2015,11,582−587.(96)Izmaylov,A.F.;Scuseria,G.E.WhyAreTime-DependentDensityFunctionalTheoryExcitationsinSolidsEqualtoBandStructureEnergyGapsforSemilocalFunctionals,andHowDoesNonlocalHartree−Fock-TypeExchangeIntroduceExcitonicEffects?J.Chem.Phys.2008,129,034101.(97)Pradhan,E.;Sato,K.;Akimov,A.V.Non-AdiabaticMolecularDynamicswithΔSCFExcitedStates.J.Phys.:Condens.Matter2018,30,484002.(98)Yang,Y.;Tokina,M.V.;Fang,W.-H.;Long,R.;Prezhdo,O.V.InfluenceofTungstenDopingonNonradiativeElectron−HoleRecombinationinMonolayerMoSe2withSeVacancies.J.Chem.Phys.2020,153,154701.(99)Ghosh,D.;Neukirch,A.J.;Tretiak,S.OptoelectronicPropertiesofTwo-DimensionalBromidePerovskites:InfluencesofSpacerCations.J.Phys.Chem.Lett.2020,11,2955−2964.(100)Tully,J.C.MolecularDynamicswithElectronicTransitions.J.Chem.Phys.1990,93,1061−1071.(101)Belyaev,A.K.;Lebedev,O.V.NonadiabaticNuclearDynamicsofAtomicCollisionsBasedonBranchingClassicalTrajectories.Phys.Rev.A:At.,Mol.,Opt.Phys.2011,84,014701.(102)Smith,B.;Akimov,A.V.HotElectronCoolinginSiliconNanoclustersviaLandau−ZenerNonadiabaticMolecularDynamics:SizeDependenceandRoleofSurfaceTermination.J.Phys.Chem.Lett.2020,11,1456−1465.(103)Smith,B.;Akimov,A.V.AComparativeAnalysisofSurfaceHoppingAcceptanceandDecoherenceAlgorithmswithintheNeglectofBack-ReactionApproximation.J.Chem.Phys.2019,151,124107.(104)Nelson,T.;Fernandez-Alberti,S.;Roitberg,A.E.;Tretiak,S.NonadiabaticExcited-StateMolecularDynamics:TreatmentofElectronicDecoherence.J.Chem.Phys.2013,138,224111.(105)Granucci,G.;Persico,M.CriticalAppraisaloftheFewestSwitchesAlgorithmforSurfaceHopping.J.Chem.Phys.2007,126,134114.(106)Smith,B.;Shakiba,M.;Akimov,A.V.NonadiabaticDynamicsinSiandCdSeNanoclusters:Many-BodyvsSingle-ParticleTreatmentofExcitedStates.J.Chem.TheoryComput.2021,17,678−693.(107)Cui,P.EffectofBoronandNitrogenDopingonCarrierRelaxationDynamicsofGrapheneQuantumDots.Mater.Res.Express2018,5,065034.(108)Bretschneider,S.A.;Weickert,J.;Dorman,J.A.;Schmidt-Mende,L.ResearchUpdate:PhysicalandElectricalCharacteristicsofLeadHalidePerovskitesforSolarCellApplications.APLMater.2014,2,040701.(109)Shen,Q.;Ripolles,T.S.;Even,J.;Zhang,Y.;Ding,C.;Liu,F.;Izuishi,T.;Nakazawa,N.;Toyoda,T.;Ogomi,Y.;etal.UltrafastSelectiveExtractionofHotHolesfromCesiumLeadIodidePerovskiteFilms.J.EnergyChem.2018,27,1170−1174.(110)Shen,Q.;Ripolles,T.S.;Even,J.;Ogomi,Y.;Nishinaka,K.;Izuishi,T.;Nakazawa,N.;Zhang,Y.;Ding,C.;Liu,F.;etal.SlowHotCarrierCoolinginCesiumLeadIodidePerovskites.Appl.Phys.Lett.2017,111,153903.(111)Li,W.;Zhou,L.;Prezhdo,O.V.;Akimov,A.V.Spin−OrbitInteractionsGreatlyAccelerateNonradiativeDynamicsinLeadHalidePerovskites.ACSEnergyLett.2018,3,2159−2166.(112)Bernardi,M.;Vigil-Fowler,D.;Lischner,J.;Neaton,J.B.;Louie,S.G.AbInitioStudyofHotCarriersintheFirstPicosecondafterSunlightAbsorptioninSilicon.Phys.Rev.Lett.2014,112,257402.(113)Smith,B.;Shakiba,M.AkimovLab/Project_-CsPbI3_MB_vs_SP:DataFilesforNonadiabaticDynamicsStudiesof2453https://dx.doi.org/10.1021/acs.jpclett.0c03799J.Phys.Chem.Lett.2021,12,2444−2453