Cation Engineering for Resonant Energy Level Alignment in Two-dimensional Lead Halide Perovskites - Marchal et al. - Unknown - Unknown

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SUPPORTINGINFORMATIONCationEngineeringforResonantEnergyLevelAlignmentinTwo-dimensionalLeadHalidePerovskitesNadègeMarchal,1,2EdoardoMosconi,1,*GonzaloGarcía-Espejo,3TahaniM.Almutairi,4ClaudioQuarti,5DavidBeljonne,2FilippoDeAngelis1,6,7*1ComputationalLaboratoryforHybrid/OrganicPhotovoltaics(CLHYO),IstitutoCNRdiScienzeeTecnologieChimiche“GiulioNatta”(CNR-SCITEC),ViaElcediSotto8,06123Perugia,Italy.2LaboratoryforChemistryofNovelMaterials,UniversityofMons,PlaceduParc,20,B-7000Mons,Belgium.3DepartamentodeQuímicaFísica,InstitutoUniversitariodeInvestigaciónenQuímicaFinayNanoquímica,IUQFN,UniversidaddeCórdoba,CampusdeRabanales,EdificioMarieCurie,E-14071Córdoba,Spain.dChemistryDepartment,CollegeofScience,KingSaudUniversity,Riyadh11451,SaudiArabia.5Univ.Rennes,ENSCR,INSARennes,CNRS,ISCR(InstitutdesSciencesChimiquesdeRennes),UMR6226,RennesF-35000,France.6CompuNet,IstitutoItalianodiTecnologia,ViaMorego30,16163Genova,Italy.7DepartmentofChemistry,BiologyandBiotechnology,UniversityofPerugia,ViaElcediSotto8,06123Perugia,Italy.

1TableS1.CalculatedHOMOandLUMOenergies(eV)inpolarsolventfortheinvestigatedmoleculesalongwiththeN-NdistanceinÅ.HighlightedinredarethefinalselectedtargetA-sitecationswiththelabelsusedthroughoutthiswork.Forsystems[1]-[4]PbI4theN-Ndistancewithinthecationsembeddedintheperovskite(inparenthesis)andtheshortestinterlayerI-Idistancefromtheinorganicperovskitesublatticearealsoreported.I-IVol.N-NA-sitedi-cationsHLdist.dist.3Å12,2-(ethylenedioxy)bis(ethylammonium))7.92-7.830.644.59252.84(8.28)22,2’-(1,4-phenylene)bis(ethan-1-aminium)10.544.10-6.82-0.52281.778.69(8.78)33,3’-dimethoxy-[1,1-biphenyl]-4,4’-diaminium10.056.93-6.75-2.01359.77(9.94)4(1E,3E)-hexa-1,3,5-triene-1,6-diaminium8.75-6.97-2.54202.82(8.55)5.115Buta-1,3-diyne-1,4-diaminium-8.80-2.286.60142.516Hexane-1,6-diaminium-9.390.558.92202.827(1E)-buta-1,3-diene-1,4-diaminium-7.96-2.406.27159.968hexa-2,4-diyne-1,6-diaminium-7.72-1.958.35195.44

29Naphtalene-2,7-diaminium-7.04-2.247.43244.5910Naphtalene-2,6-diaminium-7.02-2.307.94242.8811(2E,4E)-hexa-2,4-diene-1,6-diaminium-6.75-1.528.69211.79123,3’-carbonyldibenzenaminium-7.61-2.6610.50313.2113[1,1’-biphenyl]-3,3’-diaminium-7.04-1.997.32283.9014[1,1’-biphenyl]-3,3’-diaminium-7.04-1.978.74284.3715Octa-2,4,6-triyne-1,8-diaminium-7.26-2.5010.85195.4416[1,1’-biphenyl]-4,4’-diaminium-7.04-2.0410.08285.44173,4’-carbonyldibenzenaminium-7.55-2.6010.50313.68

318(E)-4,4’-(ethene-1,2-diyl)dibenzenaminium-6.38-2.2512.39327.3619Pyrene-1,6-diyldimethanamidium-6.07-2.4411.18377.1220(E)-4,4’-(ethene-1,2-diyl)bis(2-methoxybenzenaminium)-6.28-2.2112.36359.7721(4-(4-ammoniomethyl)benzamido)phenyl)dimethanaminium-6.40-1.7513.93379.4422((1H-1,2,3-triazole-1,4-diyl)bis(4,1-phenylene))dimethanaminium-6.39-1.6515.07405.4923(E)-(ethene-1,2-diylbis(4,1-phenylene))dimethanaminium-5.97-1.8814.25353.85

424(((1E,3E)-buta-1,3-diene-1,4-diyl)bis(4,1-phenylene))dimethanaminium-5.63-2.0716.69418.2525(((1E,1’E)-1,4-phenylenebis(ethene-2,1-diyl))bis(4,1-phenylene))dimethanaminium-5.50-2.1520.90504.99TableS2.CalculatedHOMOandLUMOenergies(eV)inpolarsolventfortheinvestigatedmono-cations.VaccumDMSOMONO-CATIONSHOMOLUMOHOMOLUMO(eV)(eV)(eV)(eV)NBT(Reference)(butan-1-aminium)-12.557-4.612-9.125+0.619Buta-1,3-diyn-1-aminium-11.730-5.513-7.951-1.537Hexilammonium(Reference)(hexan-1-aminium)-11.438-4.562-8.761+0.6204-carboxybutan-1-aminium-10.710-4.734-7.839+0.075(1E,3E)-penta-1,3-dien-1-aminium-10.354-5.311-6.701-1.465Hexa-2,4-diyn-1-aminium-10.193-5.128-6.997-1.381

5Octa-2,4,6-triyn-1-aminium-9.439-5.292-6.677-2.085(1E,3E,5E)-hepta-1,3,5-trien-1-aminium-9.185-5.274-6.031-1.887Pyrene-1-ylmethanamidium-8.487-4.914-5.782-2.094(E)-4-styrylbenzenaminium-8.405-4.827-5.944-1.947(E)-(4-(4-methylstyryl)phenyl)methanaminium-7.815-4.220-5.667-1.674(4-(4-(p-tolyl)-1H-1,2,3-triazol-1-yl)phenyl)methanaminium-7.774-4.502-6.045-1.554(4-(4-methylbenzamido)phenyl)methanaminium-7.762-4.467-6.011-1.566(4-((1E,3E)-4(p-tolyl)buta-1,3-dien-1-yl)phenyl)methanaminium-7.335-4.188-5.373-1.913

6(4-((E)-4-((E)-4-methystyryl)styryl)phenyl)methanaminium-6.848-4.149-5.307-2.037TableS3.Geometricaldistortioncalculatedasadeviationfromtheidealangleforeachoctahedraandtheiraverage.OctahedraSystemAngle1234AVG[1]PbI4I-Pb-I(180°)9.989.989.989.989.98I-Pb-I(90°)4.965.005.054.964.99Pb-I-Pb(180°)18.7018.7018.7018.7010.89[2]PbI4I-Pb-I(180°)24.9824.9324.9824.9324.95I-Pb-I(90°)11.5011.5011.5011.5011.50Pb-I-Pb(180°)23.8723.9023.8723.9023.89[3]PbI4I-Pb-I(180°)27.8023.6522.4021.4323.82I-Pb-I(90°)15.7710.7512.6912.3912.90Pb-I-Pb(180°)35.3526.9235.5032.7132.62[4]PbI4I-Pb-I(180°)13.8115.2113.8215.2114.51I-Pb-I(90°)8.079.758.079.768.91Pb-I-Pb(180°)24.4023.9524.4123.9624.18ForeachPbwehaveoneoctahedra.Eachperfectoctahedrahas3I-Pb-I=180°,12I-Pb-I=90°and6Pb-I-Pb=180°.InTableS4wereporttheaverageofthedeviationfromtheidealanglesofeachoctahedraandthetotalaverage.

7FigureS1.(a)PartialDensityofStates(PDOS)ofEDBEPbI4calculatedwithHSE06-SOClevel.Redlinerepresentstheinorganicpartwhilebluelinearerepresentingthecontributionoftheorganiccations.ThefulllinesrepresentthePDOSofthecompletesystem(OrganicandInorganicpartsinteracting)andthedashedlinesrepresenttheDOSoforganicandinorganicpartscalculatedseparated.(b)IsodensityplotofselectedwavefuctionsA,B,CandDasreferredbythegreyarrowsinpanel(a).

8FigureS2.(a)PartialDensityofStates(PDOS)of[4]PbI4calculatedwithHSE06-SOClevel.Redlinerepresentstheinorganicpartwhilebluelinearerepresentingthecontributionoftheorganiccations.ThefulllinesrepresentthePDOSofthecompletesystem(OrganicandInorganicpartsinteracting)andthedashedlinesrepresenttheDOSoforganicandinorganicpartscalculatedseparated.(b)IsodensityplotofselectedwavefuctionsA,B,CandDasreferredbythegreyarrowsinpanel(a).

9Correlationbetweenelectronicpropertiesand2Dspacing.Tofurtherunderstandanddemonstratethisstructuraleffectonthechargetransportpropertiesofthesematerials,wedecidedtoconductasystematictheoreticalstudyonstructure[1]PbI4increasinganddecreasingtheinterlayerdistancefrom-2Åto+2Åintheplane-stackingbcrystallographicdirectionofourcrystals(SchemeS1).Inthiscase,weproceededtoperformcalculationswithoutspacer,balancingthechargeinthecellwithaJelliummodel.SchemeS1.(a)SchemeoftheEDBEstructurewithoutcationsatdifferentinterlayerdistance:decreaseof2Å,initialdistanceandincreaseof2Åfromthelefttotheright(thetwoextremedistances);(b)Pictorialschemeoftheanglesrepresentingtheinorganicoctahedranetwork.Inparticular,weperformedaseriesofDFT-basedcalculations,atPBE+SOCleveloftheory,toobtainthebandgap,theenergylevelofthevalenceandconductionbandedge,thepartialdensityofstatesandtheelectron/holemassesonsystem[1]PbI4byvaryingtheinterlayersdistance,seeFigureS3.TableS4.Effectivemassesforholes(h)andelectrons(e)forthe[1]PbI4structurewithoutcationsandwithCs+atdifferentinterlayerdistances.NoCationCsDist.(Å)hehe3.080.848.080.7823.813.581.126.410.919.194.081.596.211.197.64.582.624.921.727.875.083.096.012.438.015.584.396.013.7110.186.086.185.625.6512.92

106.587.664.468.9316.03FigureS3.Effectoftheinterlayersdistanceonthebandgap(a),onthevalenceandconductionbandedges(VBE/CBE)levels(b),onthepartialdensityofstates(c)andontheholeeffectivemasses(d)forstructure[1]PbI4.Wealignedthebandedgestotheenergyofthe5dorbitalsofthePbforallthesystems,andthensetthezeroattheVBEoftheinitialsystem.Weframedtheoriginalinterlayerdistanceof[1]PbI4.Themotivationbehindtheanalysisoftheeffectofdistancebetweentheinorganiclayerswithoutcation(chargedsystem)andwithCs+istotrytoseparatethedifferenteffectthatcaninfluencetheobtainedresults.Inparticular,wearegoingtoisolatetheeffectofthedistancebetweenthelayersfromthepossibleoctahedradistortionoftheinorganiclatticeinducebythedifferentcations.

11Whiletheeffectonthebandgapisslightwhenweincreasetheinterlayerdistance,whichalreadyshowstheexistenceofaninteractionbetweentheinorganiclayersthatdiminishwhenwespacethem,thereisahugeeffectwheninorganiclayersgetcloser,goingtoavalueofbandgapclosetotheoneofa3Dperovskite(1.6eV).TheDOSoftheallseriesvaryingtheinterlayerdistancearealignedon5dorbitalsignaofPbspeciesandputthezeroinenergyattheVBEoftheinitialsystem,seeFigureS3b-c.WecanconcludefromthisanalysisthattheclosingofthebandgapismainlyduetoashiftoftheVBEtohigherenergywhenwedecreasetheinterlayerdistanceassociatedtoanincreaseoftheinteractionbetweentheoctahedraofthetwolayersviatheundercoordinatediodine.Finally,wemovetoanalyzetheinfluenceoftheinterlayerdistanceontheeffectivemasses,seeFigureS3dandTableS3.Inparticular,weobserveadecreaseoftheeffectivemassesoftheholeswhenwedecreasetheinterlayerdistance,andanincreaseofthesemasseswhentheinterlayerdistanceincrease.BandstructureanalysisFigureS4.(a)SchematicrepresentationoftheBrillouinzoneofspacegroupP21/c(14)fromBilbaoCrystallographicserver.PBE-SOCbandstructureof(b)[1]PbI4,(c)[2]PbI4,(d)[3]PbI4and(e)[4]PbI4.OntheY→Cdirection(highlightedinred)wasselectedforthecalculationoftheelectronandholemasses.ComputationalDetailsInthispaperweusedthreedifferentcodestosimulatetheperovskiteandtheisolatedcations.Inparticular,thecomputationalscreeningoftheisolatedorganiccationshavebeencarriedoutusingGaussian09programpackage1alongwithB3LYP2and6-31G*basisset.WechoicetheGaussiancodebecauseofismoresuitable,efficientandfasterfororganicnon-periodicsystemsandwecandirectlyobtaintheabsoluteestimationoftheHOMOandLUMOvalues.GeometryoptimizationwerecarriedoutinvacuofollowedbysinglepointcalculationinsolventusingtheC-PCMsolvation

12method.3Gaussian09singlepointcalculationatdifferentleveloftheorywherecarriedoutasreportedinTableS5bychangingthepercentageoftheexactexchange.ToalignandcorrelatetheGaussianresultswealsoperformedsinglepointcalculationwithQE,thatwasusedfortheperiodiccalculationoftheperovskitematerials,andwealsoperformedsinglepointwithVASPasfurthercheck.Inparticular,singlepointswithQEarecarriedoutwiththesameleveloftheoryadoptedforthe2Dsystems(HSE06withα=0.43),seebelow;singlepointwithVASParecarriedoutusingacutoffenergyfortheplanewavebasissetof500eValongwiththePAWpseudopotentials.Ontheotherhand,thecalculationonthe[A]PbI4materials,whereA=1-4werecarriedoutusingQuantumEspressoprogrampackage.4Inthiscasethechoiceofaplane-wavebasedcodeismandatorytoeasilyandefficientlysimulatetheelectronicpropertiesoftheperovskitematerials.Geometryoptimizationof[1]PbI4wherecarriedoutusingfixedexperimentalcellparameters5whilethegeometryoptimizationof[2-4]PbI4werecarriedoutrelaxingbothcellparametersandatomicpositionswithplanewavecutoffof25/200RyalongwithPBE6functionandultrasoftpseudopotentialwithelectronsfromI5s,5p;N,C,O2s,2p;H1s;Pb,6s,6p,5dshellsexplicitlyincludedincalculations.Thecalculationoftheformationenergieshasbeencarriedoutfollowingthisequation:ΔE=Eperov–(4*EPbI2+8*EI-+4*Emol)whereEperovisthetotalenergyofthefinalperovskitethatcontain4formulaunits;EPbI2istheenergyofthePbI72initsP3m1crystalphase;EI-istheenergyoftheisolatedI-anion;Emolistheenergyofisolatedcation.Allthesequantitiesarecalculatedwiththesameleveloftheoryofthegeometryoptimization.DOScalculationhasbeencarriedoutusingtheexactexchangethroughtheHSE06functional8(α=0.43),followingthepreviousapproach.9-10TheisolatedInorganic/OrganicseparatedcontributiontotheDOSarecalculatedstartingfromthewholesystem,removingtheinorganicorinorganicpartalternativelyandperformingasinglepointcalculationatthesameleveloftheory(HSE06,α=0.43).Thetotalchargewasalsocorrectedaccordingly.Hybridcalculations,spinorbitcouplingincluded,havebeencarriedoutattherelaxedPBEgeometriesusingnormconservingpseudopotentialwith22valenceelectronsforPbhasbeenused,byincludingthePb5sand5pstates,whichensuresanaccuratereproductionofMAPbI3bandgapandbandedgesagainstGWcalculations.11Fortheotherelements,pseudopotentialswiththesamenumberofvalenceelectronsasintheUScasehavebeenused.Toreducethecomputationaleffort,hybridSOCcalculationshavebeenperformedbyusingaplanewavecutoffof40Ry,withoutaffectingtheaccuracyofthecalculations.

13TableS5.Theoreticalbenchmarkontheisolated[1],[2]and[3]moleculesatdifferentleveloftheoryanddifferentcodeattheB3LYP/6-31G*optimizedgeometryinVacuo.TheHOMOandLUMOenergiesarereportedalongwiththeBandGap.*Calculationcarriedoutassinglepointonthegeometryextractedbythe2Drelaxedperovskitesystems.Vac.Solv.EDBE1HOMOLUMOGapHOMOLUMOGapPBE-12.71-6.905.80-6.43-0.036.40B3LYP-14.10-6.267.84-7.830.648.47B3LYP-0.43-15.75-5.4010.35-9.491.5010.99G09HSE06-13.97-6.247.73-7.710.638.34HSE06-0.43-14.89-5.769.13-8.651.109.76HSE06-0.43*-14.64-5.998.65-8.510.879.37PBE-SOC-9.00-3.805.19QEHSE06SOC-0.43-11.00-3.008.00PBE0-SOC-10.54-2.997.55PBE-9.04-3.815.24PBE0-10.63-2.987.65VASPHSE06-10.23-3.316.92HSE060.43-11.11-2.998.132HOMOLUMOGapHOMOLUMOGapPBE-11.60-6.894.71-6.071.407.47B3LYP-12.34-6.286.07-6.82-0.526.30B3LYP0.43-15.11-6.948.17-7.780.288.06G09HSE06-12.21-6.275.95-6.72-0.795.93HSE060.43-12.66-5.906.76-7.18-0.446.73HSE060.43*-11.66-4.906.76-7.32-0.536.783HOMOLUMOGapHOMOLUMOGapPBE-11.58-8.293.29-5.99-2.663.33B3LYP-12.37-7.674.70-6.75-2.014.73B3LYP0.43-13.35-7.016.34-7.71-1.346.37G09HSE06-12.25-7.944.31-6.65-2.314.34HSE060.43-12.72-7.685.04-7.13-2.065.07HSE060.43*-13.00-7.785.23-7.36-2.125.24References:1.M.J.Frisch,G.W.T.,H.B.Schlegel,G.E.Scuseria,M.A.Robb,J.R.Cheeseman,G.Scalmani,V.Barone,B.Mennucci,G.A.Petersson,H.Nakatsuji,M.Caricato,X.Li,H.P.Hratchian,A.F.Izmaylov,J.Bloino,G.Zheng,J.L.Sonnenberg,M.Hada,M.Ehara,K.Toyota,R.Fukuda,J.Hasegawa,M.Ishida,T.Nakajima,Y.Honda,O.Kitao,H.Nakai,T.Vreven,J.A.Montgomery,Jr.,J.E.Peralta,F.Ogliaro,M.Bearpark,J.J.Heyd,E.Brothers,K.N.Kudin,V.N.Staroverov,R.Kobayashi,J.Normand,K.Raghavachari,A.Rendell,J.C.Burant,S.S.Iyengar,J.Tomasi,M.Cossi,N.Rega,J.M.Millam,M.Klene,J.E.Knox,J.B.Cross,V.Bakken,C.Adamo,J.Jaramillo,R.Gomperts,R.E.Stratmann,O.Yazyev,A.J.Austin,R.Cammi,C.Pomelli,J.W.Ochterski,R.L.Martin,K.Morokuma,V.G.Zakrzewski,G.A.Voth,P.Salvador,J.J.Dannenberg,S.Dapprich,A.D.Daniels,Ö.Farkas,J.B.Foresman,J.V.Ortiz,J.Cioslowski,andD.J.Fox,Gaussian,Inc.,WallingfordCT,2009.

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