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pubs.acs.org/JPCLLetterImpactofΔESTonDelayedFluorescenceRate,Lifetime,andIntensityRatioofTetrahedralCu(I)Complexes:TheoreticalSimulationinSolutionandSolidPhasesTeng-FeiHe,Ai-MinRen,Guo-HuiLi,Ze-XingQu,Jing-FuGuo,Xue-LiHao,Yuan-NanChen,LuShen,Yun-LiZhang,andLu-YiZou*CiteThis:J.Phys.Chem.Lett.2021,12,2232−2244ReadOnlineACCESSMetrics&MoreArticleRecommendations*sıSupportingInformationABSTRACT:Profoundunderstandingoftheluminescencemechanismandstructure−propertyrelationshipisvitalforCu(I)thermallyactivateddelayedfluorescence(TADF)emitters.Herein,wetheoreticallysimulatedluminescentbehaviorinbothsolutionandsolidphasesfortwoCu(I)complexesandfoundthefollowing:(i)Thestrengthenedspin−orbitcoupling(SOC)effectbymoredx2−y2orbitalcontributionsandwell-restrictedstructuraldistortionviaremarkableintramolecularinteractionin[Cu(dmp)(POP)]+enabletheemissionatroomtemperaturetobeamixtureofdirectphosphorescence(10%)andTADF(90%).(ii)Benefitingfromenhancedsterichindranceandtheelectron-donatingabilityoftheparacyclophanegroup,thenarrowedS−Tenergyseparation(ΔE)in[Cu(dmp)(phanephos)]+acceleratesthereverse11STintersystemcrossing,promotingtheTADFrate(1.88×105s−1)andintensityratio(98.3%).TheseresultsindicatethatthesmallΔESTissuperiorforreducingthelifetimeandthatthestrongSOCstimulatesthephosphorescencetocompetewithTADF,whicharebothconducivetoavoidingcollision-inducedexcitonquenchingandreducingtheroll-offindevices.Efficientlyharvestingbothsingletandtripletexcitonstostructure−propertyrelationships.Itiswell-knownthatthemaintheoreticallyachieve100%internalquantumyield(Φ)isandistinctionbetweenTADFandphosphorescenceiswhethertheaimrequiringcontinuouseffortsinorganiclight-emittingdiodesreverseintersystemcrossing(RISC)cansuccessfullytakeplace,1−4(OLEDs).Cu(I)complexes,aspromisingOLEDmateri-inwhichtheΔESTplaysadecisiverole.Asreported,whentheals,5−10haveattractedgreatscientificinterestinrecentdecades.2ΔESTissmallenough(<0.37eV),theenergybarriercanbeInadditiontotheadvantagesofenvironmentalfriendlinessandeasilyovercomebythethermalvibrationwiththeaidofthelowcost,Cu(I)emittersareenjoyingthespotlightbecauseofsurroundingtemperature;theRISCwouldthenproceedtheabilitytomaximizeexcitonutilizationthroughphosphor-smoothly.Aftertheup-conversiononthebasisofsmallΔEST,escenceorthermallyactivateddelayedfluorescence(TADF)orwhichalsohassignificanteffectonfurtherTADFproperties,DownloadedviaUNIVOFCALIFORNIASANTABARBARAonMay16,2021at12:50:39(UTC).Seehttps://pubs.acs.org/sharingguidelinesforoptionsonhowtolegitimatelysharepublishedarticles.thecooperationoftwo,6−8,11−14benefitingfromtheirmoderatesuchastheradiativerateofdelayedfluorescence(kTADF),thespin−orbitcoupling(SOC)effectandthesmallenergyintensityratioofTADFanddirectphosphorescence,aswellasseparationbetweentheS1andT1states(ΔEST).Intheearlythelifetime.Theserelationshipsareconvolutedandneedtobe2000s,mostCu(I)complexeswithhighquantumyieldandfurtherdelineatedtheoretically.microsecondlifetimewereconsideredasphosphorescentHerein,wecarriedoutasimplifiedthree-statemodeltomaterialsinOLEDs,suchastheheteroleptic[Cu(dmp)-+validatethatasmallΔESTcouldeffectivelyimprovetheTADF(POP)](dmp=2,9-dimethyl-1,10-phenanthroline;POP=6,15throughacceleratingkTADFandexpandingitsproportiontobis[2-(diphenylphosphino)phenyl]ether).From2012,furtherobtainashortlifetime.WhenappliedinpracticaldevicespopularizedbyAdachiandco-workers,theinvestigationof16asflexiblelarge-scaledisplays,theintrinsicluminescentTADFmaterialsattractedsignificantattention.Alongwiththeimprovementofcorrespondingtesttechnologyandmethods,someCu(I)complexeswererecognizedasTADFemitters,Received:January12,2021including[Cu(dmp)(POP)]+.17,18SeveralCu(I)complexesAccepted:February23,2021wereevenfoundtopresentdualphosphorescenceandTADFPublished:February26,202112−14emissionsimultaneously.ThevariousluminescencemechanismsinCu(I)complexesnecessitatethedeepexplorationofthemicroscopictransitionprocesstorevealthe©2021AmericanChemicalSocietyhttps://dx.doi.org/10.1021/acs.jpclett.1c001192232J.Phys.Chem.Lett.2021,12,2232−2244

1TheJournalofPhysicalChemistryLetterspubs.acs.org/JPCLLetterpropertiesofemittersinbothsolutionandsolidconditionsareessential.Zhangandco-workersrecentlyreportedthattheΔESTissensitivetotheelectricfieldmicroenvironmentcreatedbya19charge-transferstate.Thetransitionprocessesshowsignificantdistinctionsinasufficientlyfluidsolution,dopedfilm,andsinglecrystal.Forexample,theΔESTvaluesofbis[4-(3,6-dimethoxycarbazole)phenyl]sulfone(DMOC-DPS)and9-(4-(4,6-diphenyl-1,3,5-triazin-2-yl)phenyl)-9′-phenyl-9H,9′H-3,3′-bicarbazole(BCz-TRZ)insolutionaretoolargetoaccomplishtheRISC(0.27eVforDMOC-DPSand0.36eVforBCz-TRZ),buttheTADFphenomenonisobservedinthedopedfilmbyprecisetime-resolvedemissionspectroscopy(TRES)withaveragelifetimesof250μsforDMOC-DPSand97μsforBCz-TRZ.Theintrinsiccharacteristicsofemittersinsolutionandsolidhavearousedgreatinterestintheoreticalinvestigationandareworthexploringcomprehensively.Figure1.(a)Chemicalstructureofcomplex1.(b)PCMmodel.(c)Inthiswork,theeffectsofthesurroundingenvironment(bothONIOMmodel.solutionandsolid)aswellasthemolecularstructural20−27rigidity,whichthetetrahedralCu(I)complexesaresusceptibleto,werecontemplatedindetail.Normally,themorerigidastructureis,thesmallerthePLQYimprovementtheQMatomswereallowedtomovewhilethoseintheMMpartinducedbyenhancingtherigidityofthesurroundingenviron-werefrozen.Inaddition,inordertoconsidertheimpactofmentwouldbe.Becauseofthesimilarstructuresbetweenstackinginteraction,wecalculatedtheenergiesonthebasisof[Cu(dmp)(POP)]+and[Cu(dmp)(phanephos)]+(phanephosthe6-311+G(d)basisset.=4,12-bis(diphenylphosphino)-[2.2]paracyclophane),thein-TheSOCperturbationeffectandtheT1→S0transitionternalquantumyieldof[Cu(dmp)(POP)]+inthesolidphaseoscillatorstrengthswereinvestigatedbytheAmsterdamDensity(28%)wasonlyalittlebitlargerthanthatinCHClsolution41−4322Functional(ADF)2016programbasedontheoptimized17+(22.6%);however,the[Cu(dmp)(phanephos)],withmorestructures.ThePBE0functionalandSlatertypeall-electrontherigid,bulkierlinkageoftwodiphenylphosphino,presents44,45triple-ζbasiswithpolarizations(TZP)wereadoptedwithinremarkableenhancementfromtheCH2Cl2solution(40%)totheone-componentzeroth-orderregularapproximationthesolidphase(80%).28−30Beyondthecurrentresultsfromthe46,47(ZORA).ThereorganizationenergiesandHuang−Rhysexperiment,isthereanythingelsethatweignorebutseriouslyfactorswereobtainedfromanormal-modeanalysiswiththeinfluencestheQY?Thisarousedourcuriositytotheoretically48−52MOMAPprogram.investigatetheluminescentpropertiesandcharacteroftheTherateconstantsofnaturalfluorescence(kS)andrmicroscopicmechanismofTADFtoprovideusefulinformationphosphorescence(kT)werecalculatedaccordingtotheEinsteinrfortheexperimentalist.Oursimulatedresultsofthephoto-spontaneousemissionrateequation:physicalpropertiesindicatethatinadditiontotheligandsteric22hindranceandenvironmentalrigidity,theconspicuousintra-S/T2πνekr=3fSorTS→molecularinteractionalsoseriouslyaffectsthestructuralεmc110(1)0deformationandnonradiativetransition.Itwouldbevaluableinwhichvandearetheemissionenergyandelementaryelectrictoadvanceourunderstandingtowardfurtherdevelopmentofcharge,respectively.ε0isthevacuumpermittivity,mthemassofhigh-efficiencyOLEDmaterials.Densityfunctionaltheory(DFT)31andtime-dependentDFTelectron,andcthespeedoflight.fs1orT1→S0representsthe(TDDFT)32methodswereemployedtoobtaintheequilibriumoscillatorstrengthofS1→S0orT1→S0radiativetransition.Atroomtemperature,thethreesublevelsofT(markedasTI,TII,geometriesandthevibrationfrequenciesofgroundandexcited1113334andTIII)weredeterminedtobeathermalpopulationstateswithintheGaussian16package.TheLANL2DZbasis135distributionaccordingtoBoltzmannstatistics.kTcanbesetwasappliedfortheCuatom,andthe6-31G(d)basissetrwasappliedfortheothersduringthestructuraloptimizationandapproximatelytreatedastheaveragerateofthreesubstates.Thenonradiativerateconstant(kT)ofT→Scouldbespectrasimulation,whichareallcarriedoutwithinthehybridnr10functionalPBE0.36,37Here,weinvestigatedthepropertiesincalculatedbyFermi’sgoldenruleundertheFranck−Condon53solutionandsolidphases.Forthesolutioncircumstances,theapproximationas38polarizablecontinuummodel(PCM)withdefaultparameters2π22ofCH2Cl2wasusedtoimplicitlyconsiderthehomogeneouskT=||fi∑∑Piv|⟨Θ|Θ⟩|fv′′ivδ(Efv−E)ivdielectricsolvationeffects.Forthesolidstate,thequantumℏvv′(2)mechanics/molecularmechanics(QM/MM)methodintheinwhich|⟨Θ|Θ⟩|2istheFranck−Condonfactor.Tdescribes39fv′ivfiONIOMmodelwascarriedout,whichwasconstructedthecouplingeffectbetweenthefinalandinitialstates,whichforaaccordingtotheX-raycrystalstructures(thedetailpackingtransition-metalcomplexsystemisthespin−orbitcouplingstructureof3×3×3supercellsareshowninFigures1andS1).matrixelement(SOCME).AssumingthatbothpotentialenergyIntheQM/MMcalculation,oneinnermostmoleculewassurfacesofthetwostatesconsistofacollectionofharmonictreatedasahigh-layerbyanaccuratehigh-levelquantumoscillators,afterconsideringthestrongcouplinglimit(ΣjSj≫1),mechanicsmethodandtheoutermost26moleculesweretreated()itω2jasalow-layerbytheefficientuniversalforcefield(UFF)short-timeapproximation[exp(itωj)=1+itωj+2!+···],4054,55method.DuringtheQM/MMgeometryoptimizations,onlythenwehavetheMarcus−Levich−Jortnerformulation:2233https://dx.doi.org/10.1021/acs.jpclett.1c00119J.Phys.Chem.Lett.2021,12,2232−2244

2TheJournalofPhysicalChemistryLetterspubs.acs.org/JPCLLetterTable1.SelectedBondLengths(Å),BondAngles(deg),andDihedralAngles(deg)attheOptimizedS0,S1,andT1GeometriesaforComplexes1and21-solution1-solidbexptlS0S1T1S0S1T1Cu−N12.10412.15622.00901.97622.17712.04531.9969Cu−N22.08432.17772.10822.07272.18162.04722.0138Cu−P12.26912.38192.52252.48592.39612.52242.5052Cu−P22.27282.35712.41932.44242.38712.53712.5258C1−C21.43911.44411.40441.39921.44381.40321.3962N1−Cu−N280.8878.2582.9783.5477.9583.9384.14P1−Cu−P2116.44112.79104.03105.45114.86107.05108.16N1−Cu−P1115.22107.2196.7398.97115.79125.63124.93N1−Cu−P2107.76119.70139.94135.74110.36105.25105.60N2−Cu−P1110.00119.43121.39124.18109.23105.69106.93N2−Cu−P2121.43115.23113.03110.62123.62130.44127.44DHA79.1399.09106.24108.6479.8774.9675.252-solution2-solidcexptlS0S1T1S0S1T1Cu−N12.10542.15522.03852.01142.17022.03421.9881Cu−N22.11572.15492.03832.01012.17772.06532.0181Cu−P12.31472.38272.48402.47772.41642.56232.5417Cu−P22.30462.38382.48402.47752.40902.49092.5058C1−C21.42551.44341.40481.39991.44361.40541.3973N1−Cu−N280.2878.9384.0484.2378.1284.0284.32P1−Cu−P2115.58115.16107.56107.83114.67107.57108.37N1−Cu−P1116.86116.49108.66108.41116.86108.95109.54N1−Cu−P2112.01112.38123.92123.90113.92125.92124.29N2−Cu−P1109.47112.65123.94124.04110.61116.30117.00N2−Cu−P2117.99116.34108.65108.30117.78113.04112.17DHA83.2186.1598.89100.2985.7498.0597.89abcDHA:thedihedralangle(DHA)betweentheN∧NplaneandP∧Pplane.Experimentalvaluesfromref6.Experimentalvaluesfromref28.T2π2summarizedinTable1togetherwiththeexperimentaldata.InkHnr(T10→=S)|⟨|ST0SOC|⟩|1comparisonwiththeX-raycrystalstructures,theground-stateℏ∞ÄÅÅ2ÉÑÑbondanglesanddihedralangles(DHAs,betweentheN∧Nand1SnÅÅ()Δ−EnTSλωlf−ℏeffÑÑP∧Pplanes)insolidsimulationpresentmuchsmallervariations,∑e−SexpÅÅ−10−ÑÑn!ÅÅÅÅ4λkTÑÑÑÑwhereasthemetal−ligandbondlengthsturnouttobelonger4πλlfBkTn=0ÅÇlfBÑÖthanthoseinsolution.Thegeometryinthecrystalseemstobe(3)“looser”,andthisistheresultoftheirtetrahedralconfigurationofwhere⟨S0|HSOC|T1⟩denotestheSOCMEbetweenS0andT1Cu(I)complexes,whichprovidessomespaceforstructurestates,λlfthereorganizationenergyoflow-frequencyvibrations,“stretching”duringoptimization.InsumofthesestructurekBtheBoltzmannconstant,Ttemperature,ℏωefftheeffectiveparameters,thetetrahedralskeletonsarerestrainedbetterintheenergyofamoderepresentingtherelevanthigh-frequencysolidthaninsolution.InthecaseofbothS1andT1states,theℏωeffCu−NandCu−Pbondlengthsaredramaticallyshortenedandintramolecularvibrations(≫1),andStheeffectivekTBelongatedrelativetothoseofS0state,indicatingthatthehighestHuang−Rhysfactorcorrespondingtothismode.occupiedmolecularorbital(HOMO)andlowestunoccupiedTherateconstantsofforwardandreverseintersystemmolecularorbital(LUMO)mainlylocateatP∧PandN∧Ncrossings(ISCandRISC)couldalsobecalculatedfromeq2.ligands,respectively.ThiscouldberationallyinterpretedfromAfterthethermalvibrationcorrelationfunction(TVCF)isthenaturalpopulationanalysis(NPA)(showninTableS1).applied,theequationtransformedasWhenthecomplexisexcitedfromthegroundstatetothe12i∞ωt−1charge-transferstate,thecentralCu(I)atomandP∧PmoietykH|⟨|Sd|⟩|T∫t[eS1,T1Z(t,T)]ISC=1SOC1T1ρISCactedasthepartsoflosingelectrons,theiratomicnetchargesℏ−∞turnedtobeincreased;incontrast,thenetchargeoftheN∧N(4)liganddecreasedbecauseelectronsweregained.AstrongerinwhichtheTVCFformisρ(t,T)=Tr[eiπS1ĤeiπT1Ĥ].TheelectrostaticattractionbetweenCu(I)andNatomswasfoundinISCS1T1calculationwasperformedintheMOMAPprogram,andthecomplex2,leadingtotheslightlyshorteraveragebondlengthsdetailedsolutionscanbefoundinrefs48−52.(ABLs)ofCu−N.AffectedbythedifferentsterichindranceGeometricstructurescouldsignificantlyinfluencethebetweentheetherlinkageandparacyclophanegroup,theelectronicstructuresandfurtherthephotophysicalproperties,summedABLsofCu−NandCu−Pincomplex2elongatedsoweoptimizedthestableS0/S1/T1geometriesinsolutionand0.0019Å/0.0157Åinsolution/solidphaserelativetothatofsolidphases,andthecorrespondinggeometricparametersarecomplex1intheS0state.Thismeansthatcomplex2withthe2234https://dx.doi.org/10.1021/acs.jpclett.1c00119J.Phys.Chem.Lett.2021,12,2232−2244

3TheJournalofPhysicalChemistryLetterspubs.acs.org/JPCLLetterFigure2.DHAinS0,S1,andT1statesforthestudiedcomplexes.Figure3.Meanseparationdistance(DH−L)andtheoverlapextent(SH−L)betweenHOMOandLUMOofthestudiedcomplexes(orange,blue,andpurpleregionrepresentHOMO,LUMO,andtheoverlap,respectively).longerdistancebetweenN∧NandP∧Pligands(approximatelyUsually,thecriticalRISCprocessinaTADFemitteristhedistancebetweenHOMOandLUMO)isinfavorofaensuredbyasmallΔESTwhichistheoreticallyproportionalto55relativelysmallerΔEST(videinfra).Apartfromtheabove-theelectronexchangeintegral(J):mentionedgeometries,wearesurprisedthatcomplex1,withtheΔEEEST=−=ST2J(5)11lessrigidetherlinkageintheP∧Pligand,exhibitedsmallertetrahedraldistortionbetweentheS0andS1/T1statesineitherThevalueofJdependsontheelectrondensityoverlapofthesolutionorthesolidphase(asshowninFigure2,theHOMOandLUMO(∫ϕLϕHdr)aswellastheirspatialdistancedifferencesofDHAbetweenS0andS1(T1)insolution/solid(r1−r2)(eq6):phaseare7.15°/4.91°(9.55°/4.62°)for1and12.74°/12.31°e2(14.14°/12.15°)for2).ConsideringtheorientationofbulkyJr=∫∫ϕϕL()()1Hr2ϕϕL()()ddrr2H112rrrr12−(6)N∧NandP∧Pligands,itseemsthatthereissomeintra-molecularinteractionincomplex1.Toverifythis,weperformedwhereeistheelectronchargeandϕHandϕLarethewaveindependentgradientmodel(IGM)56interactionanalysisandfunctionsofHOMOandLUMO,respectively.Obviously,decreasingtheoverlapofHOMOandLUMOorelongatingthefoundarelativelystrongerintramolecularinteractionoccurredspatialdistancecouldefficientlyreducetheΔEST.Thebetweenoneofthe−CH3inthedmpligandandtheethercorrespondingoverlapextent(SH−L)andmeanseparationlinkageaswellasoneofthephenylsinthePOPligandindistance(DH−L)ofHOMOandLUMOareobtainedbythecomplex1(FigureS2).Besidestheseconsiderations,itisalsoMultiwfnprogram57(depictedinFigure3).IncomparisonwithworthnotingthattherapidISCandRISCareexpectedinboththeSH−LandDH−Linsolution,theSH−LandDH−Lofcomplexescomplexes1and2fromthesmallgeometricdiscrepancies1and2arealldecreasedandincreasedinsolid,respectively.ThebetweenS1andT1states.ΔESTareconjecturedtobemuchsmallerinthesolidphase2235https://dx.doi.org/10.1021/acs.jpclett.1c00119J.Phys.Chem.Lett.2021,12,2232−2244

4TheJournalofPhysicalChemistryLetterspubs.acs.org/JPCLLetterFigure4.Frontiermolecularorbitalenergylevels,theHOMOandLUMOenergygapsofcomplexes1and2atthestatesofS0andS1insolutionandsolidphases.Table2.AbsorptionFluorescenceandPhosphorescenceTransitionsObtainedbytheTD-DFTMethodinSolutionandSolidPhasesforComplexes1and2,TogetherwithExperimentalValueselectronictransitionexcitationenergies(eV)λ(nm)fconfigurationabsorptiona1-solutionS0−S13.29376.81/3830.0719HOMO→LUMO93%1-solidS0−S13.24382.600.0493HOMO→LUMO93%b2-solutionS0−S13.28377.87/3800.0808HOMO→LUMO95%2-solidS0−S13.14395.010.0558HOMO→LUMO96%fluorescencea1-solutionS1−S02.27545.54/5650.0426HOMO→LUMO94%a1-solidS1−S02.32534.14/5270.0206HOMO→LUMO89%HOMO−1→LUMO9%b2-solutionS1−S02.24553.60/5580.0485HOMO→LUMO91%HOMO−2→LUMO8%b2-solidS1−S02.28544.95/5300.0276HOMO→LUMO87%HOMO−2→LUMO7%phosphorescence1-solutionT1−S02.04606.890.0000HOMO→LUMO92%1-solidT1−S02.06601.120.0000HOMO→LUMO88%HOMO−1→LUMO7%2-solutionT1−S02.01617.600.0000HOMO→LUMO89%HOMO−2→LUMO7%2-solidT1−S02.02612.640.0000HOMO→LUMO83%HOMO−2→LUMO12%abExperimentalvaluesfromref17.Experimentalvaluesfromref28.becauseoftheir“looser”geometries,whichbenefitsexcellent1and4.01eV/3.84eVforcomplex2insolution/solidphases,TADFperformance.Inaddition,itisnotablethatthereisanmeaningthatcomplex2willpresentared-shiftofabsorptionobviousdistributionontheparacyclophane(inbothsolutionspectrarelativetothatofcomplex1duetotheobviouslysmallerandsolid)intheHOMOofcomplex2(fromFigure3),ΔH−L.TomakeacomparisonbetweenS0andS1states,theindicatingthatcomplex2isexpectedtohaveasmallerΔESTHOMOenergylevelsareobviouslyrising(0.56eVfor1-thancomplex1fromitselongatedDH−LandreducedSH−L.solution,0.38eVfor1-solid,0.45eVfor2-solution,and0.31eVTofurtherexplorethepropertiesofelectronicstructures,thefor2-solid)relativetothatofS0state.Theseincreasescanbeselectedfrontiermolecularorbital(FMO)energylevelsinS0attributedtotheintrinsicmetal-to-ligandchargetransferandS1statesaredepictedinFigure4.Comparedwiththe(MLCT),inwhichthegeometriesdeviatefromtetrahedraltosolutionphaseattheS0state,theHOMOandLUMOenergyplanarquadrilateralintheexcitedstate,makingstrongereffectslevelsinthesolidphasearelower,1.84and1.91eVfor1andontheσ*antibondingformedbetweenthemetalandligandin26,271.84and2.01eVfor2,respectively.ThisindicatesthatthesolidS1thanthatinS0state.Intheory,themoreittendstobephaseenvironmentlargelystabilizesthecomplextoguaranteeplanar,thehighertheHOMOenergyincreases.Thereisnotheirhighluminousefficiency.TheenergygapsbetweendoubtthatthetetrahedralgeometriesofthetwocomplexesinHOMOandLUMO(ΔH−L)are4.12eV/4.05eVforcomplexthesolidphasearemaintainedbetterthanthatinsolution.But2236https://dx.doi.org/10.1021/acs.jpclett.1c00119J.Phys.Chem.Lett.2021,12,2232−2244

5TheJournalofPhysicalChemistryLetterspubs.acs.org/JPCLLetterFigure5.TransitiondipolemomentvectorofthecontributionsfromN∧Nligand(inred),Cu(blue),P∧Pligand(purple),andthewholecomplex(green)inS1→S0.theconfusingphenomenonisthatcomplex1,incomparisonthecorrespondingsimulatedabsorptionspectraindichloro-withthatofcomplex2,presentsinboththehigherHOMOmethanesolutionandsolidinFigureS5.Thecalculatedenergylevelincreases(inbothsolutionandsolid)andthemaximumwavelengthabsorption(λmax)insolutionare376.81smallerdifferencesofDHA.Thereasonisthattheplanarizationand377.87nmforcomplexes1and2,whichareslightlydeformationofcomplex1isinhibitedbyitsstrongerdifferentfromtheirexperimentalvaluesmeasuredinCH2Cl2intramolecularinteraction(FigureS2).solution(383nmfor1and380nmfor2),indicatingthegoodTodeeplyunderstandtherelationshipbetweenthepropertiessimulationoftheabsorptionbehaviorbytheTDDFT/PBE0andmicrostructuresofthetwocomplexes,investigatingthecalculation.ThecalculatedλmaxinthesolidphaseareindeedalldetailsoftheorbitalinformationattheS0stateisinstructive;red-shiftedrelativetothesolutionconditionaspredictedfromthesedetailsarelistedinTableS2.FromTableS2,thed-orbitalstheΔH−L.Uponcomparingthefofcomplexes1and2,theofCucontributedtotheHOMOincomplex1(36.0%/34.9%inslightlyhigherfincomplex2indicatesitsmoreexcellentdelayedsolution/solid)areallhigherthanthatofcomplex2(24.5%/fluorescenceperformance.Moreover,accordingtotheelec-22.6%insolution/solid).ThespecificcompositionsofCud-tronicconfigurationsofthoseS0→S1transitions,theorbitalsaredifferentbetweencomplexes1and2.Incomplex1,itabsorptionsofcomplexes1and2allmainlycomefromtheisprimarilycomposedby2-folddegenerateeorbitals(>17.4%HOMO→LUMOtransitioncharacterizedasd(Cu)+π(P∧P)dx2−y2),butincomplex2,itturnstobe3-folddegeneratet2sets→π*(N∧N).22,58(>12.7%dxy).Thecrystalfieldtheory(CFT)andmolecularAsfortheS1→S0fluorescencetransition,thecalculatedorbitaltheory(MOT)areadoptedtoclarifytheimpactoforbitalfluorescencewavelengthsare545.54(534.14)nmand553.60compositionsonthetransitionpropertiesbetweencomplexes1(544.95)nmforcomplexes1and2insolution(solid),and2.AccordingtotheCFTforthetetrahedralcomplex,therespectively.Theyareingoodagreementwiththeexperimentalelectrostaticrepulsionwouldbeweakerforanelectronresults[565(527)nmfor1and558(530)nmfor2insolutionapproachingtotheeorbitalthantothetorbitalbecauseof17,282(solid)].Thiscouldhelpustofurtherreliablystudythethelongerdistancebetweentheligandandcentralmetalphotophysicalproperties.Unliketheabsorption,theoccupied(presentedinFigureS3);thatis,themorecontributionsoftheeorbitalsinvolvedintheS1→S0transitionhavenonnegligiblesetthereare,thestrongerthecoordinationinteractionbetweencontributionsfromπ(N∧N),introducinglocalizedexcitationthemetalandligandwouldbe.Thisindicatesthatastronger(LE)(FigureS4andTableS2).TheLEisinstrumentalinSOCeffectisexpectedincomplex1.Inaddition,therearealsopromotingfluorescencetransitionintensity.Todeterminetheπ-orbitalsfromtheP∧PligandcontributedtotheHOMOoriginoftheintensitycontribution,wetransformedthefintoa(>57.9%,seeTableS2andFigureS4)inthetwostudieddipolemomentvector(MS,whichcouldbeexpressedinboth1complexes.FortheLUMO,bothcomplexes1and2havemajormagnitudeanddirection)andfurtherdecomposeditintodistributionontheπ*-orbitaloftheN∧Nligand(>91.3%).ThecontributionsofthreefragmentsofN∧Nligand,Cu,andP∧PelectronicabsorptiontransitionsofthetwostudiedcomplexesligandbyMultiwfnandVMDsoftwarepackages(showninwouldactasamixtureofMLCTandligand-to-ligandchargeFigure5).ThevaluesoftotalMSare1.9441(1.5901)andtransfer(LLCT).1OnthebasisoftheSoptimizedgeometries,wecalculatedthe2.0125(1.8524)Debyeforcomplexes1and2insolution0verticalexcitationenergies,oscillatorstrengths(f),and(solid),respectively.TheMS1incomplex1insolutionorsolidelectronicconfigurationsofthestudiedcomplexes(summarizedphasedecreasedobviouslycomparedtothatofcomplex2.ThisinTable2alongwiththeexperimentalresults),andwepresentmightbeattributedtotheDHAsintheS1stateofcomplex12237https://dx.doi.org/10.1021/acs.jpclett.1c00119J.Phys.Chem.Lett.2021,12,2232−2244

6TheJournalofPhysicalChemistryLetterspubs.acs.org/JPCLLetter(106.24°insolutionand74.96°insolid)deviatingfrom90°andsolidphasesweretheresultsofenhanceddipolemoment,morethanthatofcomplex2(98.89°insolutionand98.05°inwhichvalidatesthepreviouspredictionfromthedipolemomentsolid),leadingtothenoncollinearcontributionsofthosevectors.AsforthenaturalnonradiativedecayoftheS1→S0fragmentsandthetotaldipolemoment.Thiscanberationalized,transition,weconsidereditfromtwoessentialfactors:adiabaticbyanalogywiththeperpendicularDHAinaregulartetrahedron,excitationenergy(ΔES1−S0)andgeometricdistortionbetweenbynotingthatthetotaltransitiondipolemomentvectorsofthethetwoelectronicstates.ThevaluesofΔES1−S0are2.80eVfor1-tetrahedralheteroleptic[Cu(N∧N)(P∧P)]complexareparallelsolution,2.76eVfor1-solid,2.80eVfor2-solution,and2.70eVwiththeN∧NligandplaneandperpendiculartotheplanedefinedbytheCuandtwoPatoms.Therefore,inthetetrahedralfor2-solid.Thereorganizationenergies(λ)betweenS0andS1statesare5077cm−1for1-solution,4988cm−1for1-solid,4860Cu(I)complex,thecloserto90°theDHAis,themorecollinearcm−1for2-solution,and6289cm−1for2-solid.Largeadiabaticthecontributionswouldbe.FasterkSandratesofdelayedrexcitationenergiestogetherwithrestrictedgeometricdistortionfluorescence(videinfra)areexpectedincomplex2becauseofS2aresufficientforourpurposestodeceleratethenaturalthedecisiverelationofkr∝|MS1|.nonradiativedecayofS→S.10ThetransitionprocessesamongS0,S1,andT1statesduringNext,accordingtoeq1,theradiativeratesofT1→S0TADFemissionaresophisticatedandfundamental.Herewetransition(kT)couldalsobeobtainedwiththeaidoftheSOCrfocusedontheinterconversionratesrelatedtotheexcitonperturbationeffect.ThekTvaluesare2.86×103s−1for1-rharvestandtransformationtoexplorethenatureofphoto-solution,3.62×103s−1for1-solid,1.98×103s−1for2-solution,physicalprocesses.First,weobtainedtherateofthepromptand3.20×103s−1for2-solid(Table3).Becausethetransitionfluorescenceaccordingtoeq1;thecalculatednaturalradiativeS6−16−17−1intensityoftheT1stateisderivedfromthesingletexcitedstates,rates(kr)are9.53×10s(4.81×10s)and1.05×10sstrongSOCeffectandlargetransitionintensityofsingletexcited(6.19×106s−1)for1and2insolution(solid),respectivelystatesareconducivetopromotingthephosphorescencedecay.(Table3).ThelargerkSvaluesofcomplex2inbothsolutionrTherapidphosphorescenceratesincomplex1largelydependonitsstrongSOCeffect,whichcouldbededucedfromlarged-Table3.EmissionEnergies(eV),OscillatorStrengths,orbitalparticipationinvolvedinT1→S0transition.Asforthe−1RadiativeRates(s),andLifetimes(μs)ofComplexes1andnonradiativedecayofT→S,therates(kT)couldbeobtained10nr2attheS1andT1StatesbytheMarcus−Levich−Jortnerformulation(eq3)transformedoscillatorfromFermi’sgoldenrule.Fromeq3,theSOCME,energygap,emissionenergystrengthsradiativerateτandstructuraldeformationparameter(Huang−Rhysfactoror1-solutionreorganizationenergy)betweentheT1andS0statesaretheTTS2.27274.26×10−29.53×1060.10threedecisivefactorsfortheknr(showninTable4).Theknr1TI1.74532.36×10−53.11×103321valuesofcomplex1(forbothsolutionandsolidphases)present1TII1.74738.08×10−61.07×103937muchsmallerthanthatof2,eventhoughtheSOCeffectin1TIII1.74753.33×10−54.40×103227complex1isobviouslystronger.Wethenattributethesmaller1TT2.86×103349knrtoitsbetterrestrainedstructuraldistortionandshiftour1,av1-solidsightstotheeffectiveenergygap(ΔE′=ΔET1−S0−λlf),whichisS2.32122.06×10−24.81×1060.211influencedbyboththeenergygap(ΔET−S)andreorganizationTI1.85099.99×10−61.48×103675101energy(λ:betweentheSandTstates).ThevaluesofΔE′areTII1.85109.40×10−61.39×10371701117342cm−1(17974cm−1)and16315cm−1(17105cm−1)forTIII1.85135.37×10−57.97×1031251complexes1and2insolution(solid).FromTable4,wecanseeT3.62×1032771,avthatthelargerΔE′incomplex1resultsfromitsrelativelysmaller2-solution−27λlf.Fordetailedinvestigationofreorganizationenergy,weS12.23964.85×101.05×100.09performednormal-modeanalysisforstudiedcomplexes.(TheTI1.66957.84×10−79.46×101105661II−62largestcontributionofλinthelow-frequencyregionandtheT11.66964.04×104.87×102053III−53effectivemodeinthehigh-frequencyregionarealsoinsertedinT11.66984.44×105.36×101873Figure6.)Inthelow-frequencyregion,thestructuraldistortionsT1,av1.98×10505originatingfromthetwistingvibrationofthemolecularskeleton2-solid−26areinhibitedbetterincomplex1owingtoitsstrongerS12.27522.76×106.19×100.16I−62intramolecularinteraction.Inthecaseofthehigh-frequencyT11.84183.52×105.16×101937TII1.84462.57×10−53.79×103264region,itisobviousthatthereisaneffectivemode(ωeff)which1TIII1.84503.60×10−55.31×103188couldbetreatedasrepresentative.Theωeffandcorresponding1T1,av3.20×103312Huang−Rhysfactors(Seff)incomplexes1and2aretoosimilartodeterminethekT.Takingthesefactorsintoaccount,itiseasynrTable4.ValuesofΔE,⟨T|H|S⟩,λandω(cm−1),andSandkT(s−1)CalculatedatRoomTemperaturefortheT1−S01SOC0lfeffeffnrStudiedComplexesΔE⟨S|H|T⟩λωSkTT1−S00SOC1lfeffeffnr1-solution2122741.3438851617.270.431.06×1021-solid2190744.2239331621.500.544.56×1022-solution2134838.9550331615.180.421.14×1032-solid2169643.6245911616.520.465.03×1022238https://dx.doi.org/10.1021/acs.jpclett.1c00119J.Phys.Chem.Lett.2021,12,2232−2244

7TheJournalofPhysicalChemistryLetterspubs.acs.org/JPCLLetterFigure6.CalculatedreorganizationenergiesforthestudiedcomplexesbetweenT1andS0states.Inset:shiftvectorsforthenormalmodeswiththelargestreorganizationenergiesinthelow-frequencyregionandtheeffectivemodeinthehigh-frequencyregion.Table5.ValuesofΔE,⟨S|H|T⟩(atToptgeometry),⟨T|H|S⟩(atSoptGeometry),λandλ(cm−1),andkandkST1SOC111SOC11STISCRISC(s−1)CalculatedatRoomTemperaturefortheStudiedComplexesΔEST⟨T1|HSOC|S1⟩⟨S1|HSOC|T1⟩λSλTkISCkRISC1-solution198127.0434.014266304.11×10109.04×1061-solid81425.1435.365707188.87×10102.24×1092-solution166619.6023.601261292.48×10108.73×1062-solid50021.5226.573323691.69×10119.98×109Figure7.kISCandkRISCasafunctionofΔESTatdifferentvaluesoftheSOCMEsandreorganizationenergiesforcomplex1inthesolidphase.toverifythatthesmallerkTofcomplex1mainlybenefitsfromForTADFemitters,theISCandRISCaretheimportantnritsreducedgeometricdeformation.channelsforharvestingexcitons.ThecorrespondingratesofISC2239https://dx.doi.org/10.1021/acs.jpclett.1c00119J.Phys.Chem.Lett.2021,12,2232−2244

8TheJournalofPhysicalChemistryLetterspubs.acs.org/JPCLLetterandRISC(kISCandkRISC)arecalculatedbytheMOMAPλ,whichisvalidatedtobeefficacioustofurtherincreasethekISCprogram,andtheparametersarelistedinTable5.FromTable5,andk.26Likewise,asimilarstructuralmodificationcouldbeRISCthecomputedkareall>1010s−1,whichexceedthepromptISCcarriedoutforcomplexes1and2inthiswork.Moreover,itisfluorescenceradiativeratesbymorethan3ordersofmagnitude.well-knownthatrapidkISCandkRISCcouldexpeditetherateofThisultrafastISCrateisinstrumentalinutilizingtheexcitonsoftheTstate.Thecalculatedkare9.04×106s−1and8.73×delayedfluorescence,butthequantitativerelationshipbetween1RISC106s−1forcomplexes1and2insolution,whereasthevaluesintheseratesisblurry.Herein,weadoptasimplifiedthree-statethesolidare2.24×109s−1for1and9.98×109s−1for2.The3modeltorationalizeit.ThekineticderivationisbasedontheordersofmagnitudesmallerkRISCforbothcomplexes1and2insolutioncouldbeattributedtothelargeΔE(1891cm−1for1-STsolution,1666cm−1for2-solution;814cm−1for1-solid,500cm−1for2-solid).ItisconsistentwiththevulnerabilityofΔESTonthesolutionenvironmentwhichhasbeenconfirmedbythe19precisetime-resolvedemissionspectroscopy.TherelativelyslowkRISCvaluesinsolutionareresponsibleforthelowerluminousefficiencyinsolutionmeasuredinexperiments.TheΔESTvaluesinsolutionarealwaysnotcorrectlymeasuredinexperimentsbecauseofthedisturbanceofphasetransformationuponloweringthetemperatureto77K.ΔESTissusceptibletosolvationeffectinthefluidsolution,leadingtothelackofexperimentalΔESTvaluesinsolutionforcomparison.Therefore,Figure8.SchemefortheillustrationofTADFrate.wetakethestudiedcomplexesinsolidconditionsasanexampletogainacomprehensiveappreciationoftheimpactofΔEST,schemeinFigure8,assumingtheT1substatesaredegenerate,reorganizationenergy,andSOCMEonthekISCandkRISC.AthenfunctionoftheseparameterswasinvestigatedonthebasisoftheTTsimplifiedMarcusequation:59−62kkkr++nrRISC(1−ΦISC)kTADF=ÄÅÅ2ÉÑÑ1+kRISCSτ1(8)21π2ÅÅÅÅ()λ+ΔGfiÑÑÑÑkHR(ISC)=SOC|−expÅÅÑÑinwhichτisthenaturallifetimeoftheSstate(τ=1ℏ4πλkTBÅÅÇ4λkTBÑÑÖ(7)S11S1kkkS++SnrrISC)andΦtheefficiencyofforwardISC(Φ=kISC).whereΔGfi(ΔGfi=ℏωfi=Ef−Ei)isfreeenergychangebetweenISCISCkkkS++SnrrISCthefinal(f)andinitial(i)states.TheΔGfiis−ΔESTforISCandSubstitutingthemintoeq863ΔESTforRISC.TherelationshipofrateasafunctionofΔEST,λ,andSOCMEisdepictedinFigures7andS6forcomplexes1andTTkISCkkkr++nrRISC()1−kkkS++S2,respectively.FromtheMarcusequationandFigure7,wecannrrISCkTADF=1findthefollowing:1+kRISCSSkkknr++rISC(9)(i)TheratesareproportionaltothesquareofSOCMEforbothforwardandreverseISC.ForthesetwostudiedCu(I)DuringtheTADFemission,ifweassumethefollowing:complexes,whentheSOCMEdecreasedto10cm−1,even−11thoughtheΔESTincreasedto1800cm,thekISCandkRISCkRISCSS≪1remainover109s−1and106s−1,respectively.Thismeansthekkknr++rISCRISCchannelinthestudiedcomplexesisnotsubjectedtotheTTSOCME.kkr,nr≪kRISC(ii)WhenthereorganizationenergyissmallerthantheΔESTkkS≪S,knrrISCorclosetoit,thekISCwouldbeaparabolagoingdownwardastheΔESTincreases,whichcouldreachitsparabolicapexatΔEST=λ.thentherateofTADFcouldbesimplifiedasHowever,whenthereorganizationenergyismuchlargerthantheΔE(suchasΔE=814cm−1;λ=5000cm−1),thekijjkISCyzzSTSTISCkkTADF=−RISCjj1zzwouldbemonotonicallyincreasingastheΔEincreasesowingjS+zSTkkkrISC{(10)tothemonotonicallydecreasing(λ−ΔE)2intheeindexterm.STAsforthekRISC,astheΔESTincreases,theratesreduceSubstitutingk=−kEISCexp()ΔST,eq10becomesmonotonicallyregardlessoftherelativesizeofΔEandλ.TheRISC3kTBSTlargertheλis,thesmallerthekRISCis;however,withtheincreasekEISCijjΔSTyzzijjkISCyzzofλ,thekdecreasesslowlyastheΔEincreases.kTADF=−expjjjzzzjjj1−SzzzRISCST3kkTB{kkkr+ISC{(11)ThekISCandkRISCvaluesarethecooperationofΔEST,λ,andSOCME.Amongthem,theratesaremoresensitivetotheΔEThecalculatedkvaluesare3.66×102s−1for1-solution,STTADFandλ,whicharealsoeasilyadjustedfromstructural3.24×104s−1for1-solid,1.19×103s−1for2-solution,and1.88modification.TokeepexpeditiousISCandRISC(k,1010−×105s−1for2-solid.ThecorrespondingexperimentaldataofISC1012s−1;k,108−1010s−1),thebalanceofthoseparametersradiativeratesatroomtemperatureare1.97×104s−1for1-RISCcouldberegulatedwithinthecoloredregionsinFigures7andsolution,1.02×104s−1for1-solid,4.00×104s−1for2-solution,S6.Inourpreviousresearch,introducingthedmdpq(3,6-and5.71×104s−1for2-solid,respectively.ThecalculatedkTADFdimethyl-dipyrido[3,2-f:2′,3′-h]-quinoxaline)asanN∧Nligandinsolidareingoodagreementwiththeexperimentalvalues,intetrahedralCu(I)complexcouldleadtoareducedΔESTandindicatingthatthethree-statemodelisappropriateto2240https://dx.doi.org/10.1021/acs.jpclett.1c00119J.Phys.Chem.Lett.2021,12,2232−2244

9TheJournalofPhysicalChemistryLetterspubs.acs.org/JPCLLetterFigure9.%TADFand%phosphorescenceasafunctionoftemperatureforcomplexes1and2inthesolidphase(A).Trendof%TADFasincreasingΔESTatroomtemperatureforcomplex2inthesolidphase(B).quantitativelyevaluatetherateofTADF.ThemuchsmalleriSy−1jjkrijjΔESTyzzzzkTADFvaluesinsolutionarecausedbytheoverestimatedΔEST.%Phosphorescence=+jjj1Texpjjj−zzzzzz×100%TheseresultsagainprovethattheΔESTactsastheon−offswitchk3krkkTB{{forTADF.(13)OneofthetypicalcharacteristicsofTADFemittersistheÄÅÅÉÑÑ−1dependenceofemissiondecaytime(τ)andtemperature.ÅÅijjkSijjΔEyzzyzzÑÑÅÅrSTÑÑGenerally,τ(T)canbedescribedasaBoltzmann-type%TADF=−+ÅÅ1jj1expjj−zzzzÑÑ×100%30ÅÅj3kTjkTzzÑÑequation:ÅÅÇkrkB{{ÑÑÖ(14)ΔEST3e+−xp()kTAccordingtothesetwoequations,weplottedthe%TADFversusBτ()T=%Phosphorescenceasafunctionoftemperatureforcomplexes1ΔEST3(T)kk11+−(S)exp()kTand2insolidandsolutioninFigures9AandS8,respectively.B(12)The%TADFofcomplexes1and2inthesolidphasedominatetheemissiongraduallyasthetemperatureincreases.Forinwhichk(S1)andk(T1)aretheradiativedecayratesoftheS1STcomplex1,at300K,thereisstill10%contributionfromandT1states,namely,thekrandkraswementionedbefore.InTaneffectiveTADFemitter,ans-shapedcurveofτ(T)versusphosphorescenceduetoitsenhancedkrinducedbystrongSOCeffect.Whereasincomplex2,theemissionat300Kistemperaturecouldbeobtainedaccordingtoeq12(depictedinalmostallTADF(98.3%),leadingtoitsrapiddelayedFigureS7A,B).OwingtothelargeΔESTinsolution,thefluorescencerate.Fromeqs13and14andFigure9B,itisnotcomputedτ(300K)valuesare310and315μsforcomplexes1hardtodetereminethattheΔESTstronglyinfluencestheand2,whicharemuchlargerthantheirexperimentalvaluesofintensityratioofTADFandphosphorescence.AsmallΔEST11.5and10μs,respectively.Whileinthesolid,thesimulatedpermitstheRISCtobefulfilledquickly,whilealargeΔESTτ(300K)valuesare28.0and5.4μsforcomplexes1and2,wellwouldblocktheRISC.Moreover,theSOCeffectisanotherconsistwiththeirmeasured27.5and14μsinexperiment.Here,factorinfluencingtheintensityratiothroughpromotingthewetookcomplex2(insolid)asanexampletostudytheimpactphosphorescencetocomparableorovertheTADF(astheofΔESTonτ(T)(asshowninFigureS7C).Itcanbeclearlyseenluminescenceinsolutionofcomplex1inFigureS8).ThedualthattheΔESThasalmostnoeffectonτ(T)inthelow-emissionmodelofTADFandphosphorescenceisinterestingtemperatureregion(hereτ(T)≈τ(T1))becausetheemissionisandpreferable.Thesingleradiativetransitionprocessfromrecognizedasphosphorescencedecayatthatmoment.WiththeeithertheS1orT1statewouldinevitablyengenderaccumulationtemperatureincreasing,theenergybarrierofRISCcouldbeofsingletandtripletexcitonsforTADFandphosphorescence,easilyovercomewiththehelpofthermalactivation.Thentherespectively.Thenitmightworsencollision-inducedexcitonshort-livedS1stateparticipatesintheradiativetransition,quenching,especiallysinglet−tripletandtriplet−tripletannihi-resultinginthesharplydecreasedlifetime.Thethermalactivatedlation(STAandTTA),whichisadversetoimprovinghighenergybarrierislargelydeterminedbyΔEST.Therefore,externalquantumefficiency(EQE)inOLEDdevices.13reducingΔESTcouldeffectivelyshortenthelifetimeofemission,However,therelationshipbetweenTADFandphosphorescencewhichfavorsreducingefficiencyroll-offwithintheOLEDintensityratioandquantumyieldisstillconvolutedandisdevice.worthyofmorecomprehensiveandin-depthinvestigation,Inaddition,accordingtothedemonstrationofYersinetal.,whichisthefocusofourfuturework.theemissionatroomtemperaturemightbenotonlyTADFbutInthiswork,wecarriedoutDFTandTDDFTcalculationsforalsodirectphosphorescence.12−14Inspiredbythisresearch,we+twoheteroleptic[Cu(dmp)(POP)]and[Cu(dmp)-arecuriousaboutthenatureoftheemissionofbothcomplexes1(phanephos)]+complexes(dmp=2,9-dimethyl-1,10-phenan-and2.WeestimatedtheintensityratioofTADFandthroline,POP=bis[2-(diphenylphosphino)phenyl]ether,pha-phosphorescenceasthefollowing:nephos=4,12-bis(diphenylphosphino)-[2.2]paracyclophane).2241https://dx.doi.org/10.1021/acs.jpclett.1c00119J.Phys.Chem.Lett.2021,12,2232−2244

10TheJournalofPhysicalChemistryLetterspubs.acs.org/JPCLLetterThepolarizablecontinuummodel(PCM)andquantumattentiontodeeplyexploretheessenceofluminescence,whichmechanics/molecularmechanics(QM/MM)methodinthecouldberegulatedbythecooperationofΔESTandSOC.ThisONIOMmodelwereemployedtosimulatethesolutionandmightbeaninstructivestrategytoavoidthecollision-inducedsolidenvironment,respectively.Fromtheresultsofcalculations,excitonquenching,especiallysinglet−tripletandtriplet−tripletthemetal−ligandbondlengthsofthegroundstateinthesolidannihilation(STAandTTA).Wehopethisworkprovidesphaseareall“looser”thanthatinsolution,leadingtoaslightlyvaluableinspirationforimprovingtheperformanceofTADFlongerdistancebetweenP∧PandN∧Nligandswherethematerials.HOMOandLUMOaremainlylocated,respectively.Thisprolongationisadvantageoustoreducetheenergyseparation■ASSOCIATEDCONTENTbetweentheS1andT1states(ΔEST).Thesolidcircumstance*sıSupportingInformationcouldalsoeffectivelylowertheenergylevelsofHOMOandTheSupportingInformationisavailablefreeofchargeatrestrictthestructuraldeformation,whichlargelystabilizesthehttps://pubs.acs.org/doi/10.1021/acs.jpclett.1c00119.complexandpromotestheluminescence.Uponcomparingtheinfluencesofsterichindranceandelectron-donatingabilityChemicalstructureofcomplex2;analysisofIGM;inducedbytheetherlinkageandparacyclophanegroup,aillustrationofCFTfortetrahedralCu(I)complex;FMOshortermetal−liganddistanceandmorecontributionsof2-foldcontoursurfacesinS0andS1states;simulatedabsorptiondegenerateeorbitals(mainlydx2−y2)werefoundincomplex1,spectra;k(R)ISCasafunctionofΔESTatdifferentSOCMEswhichcouldstrengthenitsspin−orbitcoupling(SOC)effectandλforcomplex2;dependenceoflifetimeonaccordingtothecrystalfieldtheory.Incomplex2,thetemperatureandthelifetimechangetrendasΔESTparacyclophanegroupwithlargesterichindranceelongatedincreases;%TADFvs%Phosphorescenceastemperaturethemetal−ligandbondlengthsandsimultaneouslyattractedtheincreasesinsolution;analysisofNPA;molecularorbitalcompositions;structure,transitions,andratecomparisonselectronslocatingonit,whichcouldeffectivelyreducetheofcomplex2andisomer2′;CartesiancoordinatesofoverlapoftheHOMOandLUMOandnarrowitsΔEST.optimizedstructures(PDF)Althoughtheetherlinkageislessrigidthanthatoftheparacyclophanegroup,thetetrahedralstructurevariationsbetweengroundandexcitedstatesforcomplex1were■AUTHORINFORMATIONunexpectedlysmallerthanthoseincomplex2.ThiscouldbeCorrespondingAuthorexplicatedfromindependentgradientmodel(IGM)interactionLu-YiZou−LaboratoryofTheoreticalandComputationalanalysis,whichindicatesthattherearerelativelystrongChemistry,InstituteofTheoreticalChemistry,JilinUniversity,intramolecularinteractionsbetweenoneofthe−CH3intheChangchun130023,P.R.China;orcid.org/0000-0001-dmpligandandtheetherlinkageaswellasonephenylinthe6849-4076;Email:zouly@jlu.edu.cnPOPligand.Also,thedetailedreorganizationenergies(λ)investigatedbythenormal-modeanalysisconfirmedthattheAuthorstwistingvibrationofthetetrahedralskeletonwasrestrictedmoreTeng-FeiHe−LaboratoryofTheoreticalandComputationaleffectivelyincomplex1.Chemistry,InstituteofTheoreticalChemistry,JilinUniversity,Giventhepointsdiscussedabove,thesethreedecisivefactorsChangchun130023,P.R.China(namely,theΔEST,λ,andSOCeffect)abouttheinfluenceoftheAi-MinRen−LaboratoryofTheoreticalandComputationalenvironmentandthemoleculeitself,thefollowingisabouttheChemistry,InstituteofTheoreticalChemistry,JilinUniversity,specificvaluesofinfluenceontheratesofforwardandreverseChangchun130023,P.R.China;orcid.org/0000-0002-ISC(kandk).Thecomputedkareallover1010s−1,ISCRISCISC9192-1483exceedingthenaturalfluorescenceradiativeratesbymorethan3Guo-HuiLi−LaboratoryofMolecularModelingandDesign,ordersofmagnitude,whichindicatesthesuccessofexcitonsStateKeyLaboratoryofMolecularReactionDynamics,DalianarrivingattheTstate.Thosekvaluesare9.04×106s−1for1RISCInstituteofChemicalPhysics,ChineseAcademyofScience,1-solution,2.24×109s−1for1-solid,8.73×106s−1for2-Dalian116023,P.R.China;orcid.org/0000-0001-8223-solution,and9.98×109s−1for2-solid.The3ordersof705XmagnitudelargerkRISCforbothcomplexes1and2inthesolidZe-XingQu−LaboratoryofTheoreticalandComputationalcouldbeattributedtotheirsmallerΔEST.OnthebasisoftheChemistry,InstituteofTheoreticalChemistry,JilinUniversity,Marcusequation,wefoundthattheforwardandreverseISCChangchun130023,P.R.China;orcid.org/0000-0003-ratesaremoresensitivetotheΔESTandλ,especiallyforthe3445-4003kRISC.SmallΔESTcouldmaketheRISCproceedpropitiously,Jing-FuGuo−SchoolofPhysics,NortheastNormalUniversity,buttheenhancementofkRISCisdominatedbythesmallλ.Changchun130024,P.R.ChinaAdditionally,thesetwofactorsarealsoeasilyadjustedfromXue-LiHao−LaboratoryofTheoreticalandComputationalstructuralmodification,suchasadoptingthemorerigiddmdpqChemistry,InstituteofTheoreticalChemistry,JilinUniversity,(3,6-dimethyl-dipyrido[3,2-f:2′,3′-h]-quinoxaline)asN∧Nli-Changchun130023,P.R.ChinagandinthetetrahedralCu(I)complex.TherelationshipsofkISCYuan-NanChen−LaboratoryofTheoreticaland>kSandk≫kT+kTandthes-shapedcurveofTADFrRISCrnrComputationalChemistry,InstituteofTheoreticalChemistry,lifetimeversustemperatureshowthattheshort-livedS1stateJilinUniversity,Changchun130023,P.R.Chinaparticipatesintheradiativetransition.ItisalsonecessarytopayLuShen−LaboratoryofTheoreticalandComputationalattentiontotheintensityratioofTADFandphosphorescence.Chemistry,InstituteofTheoreticalChemistry,JilinUniversity,AffectedbythestrongSOCeffect,theemissionofcomplex1inChangchun130023,P.R.Chinathesolidat300Kisamixtureof10%phosphorescenceand90%Yun-LiZhang−LaboratoryofTheoreticalandComputationalTADF,whilethatof2isalmostallTADF(98.3%).ThemixedChemistry,InstituteofTheoreticalChemistry,JilinUniversity,emissionofTADFandphosphorescenceincomplex1callsourChangchun130023,P.R.China2242https://dx.doi.org/10.1021/acs.jpclett.1c00119J.Phys.Chem.Lett.2021,12,2232−2244

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