Low-Cost Computing of the Thermophysical Properties of Organic – Inorganic Halide Perovskites by Density Functional Theory Combined wit

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SupportingInformationLow-CostComputingoftheThermophysicalPropertiesofOrganic–InorganicHalidePerovskitesbyDensityFunctionalTheoryCombinedwiththeThree-DimensionalReferenceInteractionSiteMethodTomoyasuYokoyama1,2*,SatoruOhuchi1,TaisukeMatsui1,YukihiroKaneko1,Ta-kaoSasagawa21TechnologyDivision,PanasonicCorporation,3-1-1Yagumo-nakamachi,MoriguchiCity,Osaka570-8501,Japan2LaboratoryforMaterialsandStructures,TokyoInstituteofTechnology,4259Nagatsuta,Midori-ku,Yokohama,Kanagawa226-8503,JapanCorrespondingAuthor*TomoyasuYokoyama,yokoyama.tomoyasu@jp.panasonic.comS1

1DetailedCalculationMethodFortheDFT/3D-RISMapproach,theinteractionbetweentheorganicmoleculesandinorganiccagesisdescribedbyaclassicalforcefieldmodeledbytheLennard-Jones(LJ)potentialandpointcharges.Thus,itisnecessarytodeterminetheparametersoftheLJpotential(εαandσα).Wecomparedtwoforcefields,thegeneralAMBERforcefield(GAFF)andtheall-atomoptimizedpotentialsforliquidsimulations(OPLS-AA)forcefieldobtainedbytheACPYPEcode,andinvestigatedtheeffectoftheLJparametersonthepropertiesofcubicMAPbI3.TheresultsareshowninFiguresS1.Theelectronicdensityofstatesandbandstructuresobtainedusingthetwodifferentforcefieldsshowedlittledifferencewhenthelatticeconstantswerethesame.However,whentheGAFFandOPLS-AAforcefieldswereused,thelatticeconstantsoftheoptimizedMAPbI3were6.39and6.43Å,respectively,asshowninFigureS1(g).Thus,GAFFwasusedinthisworkbecausethelatticeconstantobtainedusingGAFFwasclosetotheexperimentalvalueofMAPbI3.S2

2(a)(b)gaffopls-aa0.020.020.00.0(e/bohr3)(e/bohr3)(c)(d)teteta1)ta1-)sf-.sf.o.fuo.fuyit1-MAPbIyit1-MAPbIsV3sVe3ne(ne(eDDEnergy(eV)Energy(eV)(e)(f)))VVe(e(yygrgreennEE(g).).f/uVem(ygreneltaoTexp.Latticeparameter(Å)S3

3FigureS1.RISMchargedensitydistributionoftheMAcationonthe(001)planeincubicMAPbI3obtainedbyDFT/3D-RISMusing(a)GAFFand(b)OPLS-AA.ElectronicdensityofstatesofcubicMAPbI3obtainedbyDFT/3D-RISMusing(c)GAFFand(d)OPLS-AA.BandstructuresofcubicMAPbI3obtainedbyDFT/3D-RISMusing(c)GAFFand(d)OPLS-AA.Theoriginoftheenergyissetatthevalencebandmaximum.Forcomparison,itwascalculatedintheunitcellwiththesamecubiclatticeconstant(6.31Å).TheRISMtemperaturewassetto330K.(e)TotalenergydependenceofthelatticeconstantofcubicMAPbI3obtainedbyDFT/3D-RISMusing(c)GAFFand(d)OPLS-AA.Theoriginoftheenergyissettotheminimumvalueoftheenergywhenthelatticeconstantischanged.Theexperimentallatticeconstantof6.31Åisalsoshown.(a)(b)(c)yyyrgrgrgen)en)en)emememltoltoltota/ata/ata/atoVtoVtoVeeeeeevvvti(mti(mti(mlalalaeeeRRRNumberofk-pointsineachdirectionEnergycutoffforwavefunctions(Ry)Energycutoffforchargedensity(Ry)S4

4FigureS2.Energydependenceofthe(a)numberofk-points,(b)energycutoffforthewavefunctions,and(c)energycutoffforthechargedensity.Theoriginoftheenergyissettotheminimumvalueoftheenergywhentheparameterischanged.(a)(b)0.020.0(/bohr3)FigureS3.Distributionsof(a)Cand(b)NincubicMAPbI3obtainedbyDFT/3D-RISM.S5

5(a)teta1)s-.f.fouyit1-PbI3-sVne(eDEnergy(eV)(b))Ve(Eg=1.20eVygrenEFigureS4.(a)Electronicdensityofstatesand(b)bandstructuresofcubicPbI3−obtainedbyDFT.Theoriginoftheenergyissettothevalencebandmaximum.S6

6(a)teta1)s-.f.fouyit1-CsPbI3sVne(eDEnergy(eV)(b))Ve(ygrenEFigureS5.(a)Electronicdensityofstatesand(b)bandstructuresofcubicCsPbI3obtainedbyDFT.Theoriginoftheenergyissettothevalencebandmaximum.)V(eyrgenEPbI3-S7

7FigureS6.HarmonicphonondispersionofcubicPbI3−obtainedbyDFT.(a)(b)T=300KT=100K(c)(d)0.010.0(e/bohr3)FigureS7.ThechangeoftheinorganicframeworkinthetetragonalMAPbI3aftertheatomicpositionrelaxationbyDFT/3D-RISMat(a)300Kand(b)100K,duetothereduced(enhanced)molecularrotation(interactions)withdecreasingtemperature.Theexperimentaldatawereusedforthea-andc-axislatticeconstants.TheRISMchargedensitydistributionoftheMAcationonthe(111)planeinthetetragonalMAPbI3obtainedbyDFT/3D-RISMat(c)300Kand(d)100K.S8