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Applied Surface Science
j o ur na l ho me pa g e :w w w . e l s e v i e r . c o m / l o c a t e / a p s u s c
Hybrid functional calculated optical and electronic structures of thin anatase TiO 2 nanowires with organic dye adsorbates
Hatice Ünal
a, Deniz Gunceler
b, O˘guz Gülseren
c, S¸ inasi Ellialtıo˘glu
d, Ersen Mete
a,∗aDepartmentofPhysics,BalıkesirUniversity,Balıkesir10145,Turkey
bDepartmentofPhysics,CornellUniversity,Ithaca,NY14853,USA
cDepartmentofPhysics,BilkentUniversity,Ankara06800,Turkey
dBasicSciences,TEDUniversity,Ankara06420,Turkey
a r t i c l e i n f o
Articlehistory:
Received25December2014 Receivedinrevisedform10April2015 Accepted11April2015
Availableonline20April2015
a b s t r a c t
TheelectronicandopticalpropertiesofthinanataseTiO2(101)and(001)nanowireshavebeeninves- tigatedusingthescreenedCoulombhybriddensityfunctionalcalculations.Forthebarenanowireswith sub-nanometerdiameters,thecalculatedbandgapsarelargerrelativetothebulkvaluesduetosize effects.Theroleoforganiclightharvestingsensitizersontheabsorptioncharacteristicsoftheanatase nanowireshasbeenexaminedusingthehybriddensityfunctionalmethodincorporatingpartialexact exchangewithrangeseparation.Forthelowestlyingexcitations,directionalchargeredistributionof tetrahydroquinoline(C2-1)dyeshowsaremarkablydifferentprofileincomparisontoasimplemolecule whichischosenasthecoumarinskeleton.ThebindingmodesandtheadsorptionenergiesofC2-1dye andcoumarincoreontheanatasenanowireshavebeenstudiedincludingnon-linearsolvationeffetcs.
Thecalculatedopticalandelectronicpropertiesofthenanowireswiththesetwodifferenttypesofsen- sitizershavebeeninterpretedintermsoftheirelectron–holegeneration,chargecarrierinjectionand recombinationcharacteristics.
©2015ElsevierB.V.Allrightsreserved.
1. Introduction
Thewide-bandgapsemiconductortitaniumdioxide(TiO2)has attractedattentionsincethediscoveryofitsremarkablephotocat- alyticactivityunderUVirradiation[1,2].TiO2canbefunctionalized foroperationundervisiblelightilluminationbyimpuritydopants orbysensitizingmolecularadsorbates.Thelatteris particularly importantindyesensitizedsolarcell(DSSC)applicationswhere nanoporousTiO2 filmisusedastheanodeelectrode[3].Titania surfacesoffergoodadsorptioncharacteristicsandcaneasilybecov- eredwithamonolayerofalightharvestingdye.Theoperational systemsitsinanorganicsolventelectrolytewitharedoxsystem likeiodide/triiodidecouple.Photoexcitationofthemoleculeleads toelectron–holegenerationandsubsequentchargeinjectiontothe conductionband(CB)oftheoxidewhichactsasacurrentcollec- tor.Then, anelectronisdonatedfromtheelectrolytetorestore thegroundstateofthedye.Ontheotherhand,thechargecarrier transferthroughputislimitedduetorecombinationrate.There- fore,thesurfaceareaoftheoxideandthechoiceofthedyebecomes importantintheoverallcellefficiency.
∗ Correspondingauthor.Tel.:+905335733595.
E-mailaddress:emete@balikesir.edu.tr(E.Mete).
Thecrystalstructuresoftitaniaoccurmainlyinanatase,rutile andbrookitephasesinnature.Underambientconditionsandin itsbulkform,rutileisthemoststablepolymorph.Theopticalgaps aremeasuredas∼3.2eVforanatase[4]andas∼3.0eVforrutile [5].The anatasephase especiallyits (001) surfaceis knownto exhibithigherphotocatalyticactivityinmanysituations[6].More- over,TiO2nanomaterialswithgrainsizessmallerthan14nmare foundtobeinanataseformratherthaninrutilestructure[7,8].
Electronically,thin anatasenanowires exhibit differentfeatures relativetoothernanoparticulatetitaniaelectrodes.Inparticular, theincreasein thecorrespondingbandgapsandphotocatalytic oxidationpowersbecomemoreapparentasthenanowirediam- eterstendtobesmallerthan2nmduetotheconfinementeffect [9–11].
Theprogressinthesynthesisofquasi-one-dimensionaloxide nanostructures opens up new possibilities to fabricate techno- logicallyattractiveapplications.Recently,titania nanowiresand nanorods become candidate building blocks of highly ordered architecturesforsolarcells[12].Theyofferlargesurface-to-volume ratioswhichalsoenhancen-typeconductivityproperties[13–15].
In addition,this is seen asan importantfactor in reducing the charge carrierrecombinationrates. Therefore,theuseof quasi- one-dimensionaltitaniaasthecurrentcollectorcomponentisa promisingwaytoimprovecellefficiencies.
http://dx.doi.org/10.1016/j.apsusc.2015.04.086 0169-4332/©2015ElsevierB.V.Allrightsreserved.
Organic photosensitizers have becomea good alternative to metaldrivencommercialdyes notonlybecausetheyarecheap, environmentallyfriendlyandeasytoisolatebutalsobecausetheir electronicandanchoringcharacteristicscanbemodifiedthrough variouslyfunctionalattachablemoieties.Recently,aclassofnovel organicsensitizersbased ontetrahydroquinoline moiety asthe electrondonorgrouphavebeenproposedtoachievephotoinduced intramolecular charge transfer [16]. For instance,-conjugated electrondonoracceptor (D--A)typeC2-1 dyehasthehighest conversionefficiencyof4.5%withinthisfamily[17].
Theoretical prediction of molecular and material properties havebeenfocusedbymanyresearcherstounderstandandimprove functionaldyesensitizersadsorbedontheoxide[18–24].Tetrahy- droquinolinebasedD--AtypedyesonTiO2(101)surfacehave beenstudiedusingstandarddensityfunctionalslabcalculations wheretwo-dimensionalperiodicitywasadopted[25,26].In this work,weexaminedthebandgapfeaturesofthinanatase(101) and(001)nanowiremodelsusingtherangeseparatedhybridden- sityfunctionaltheorycalculations.Then,weconsideredisolated C2-1(C21H20N2SO2)chargetransferdyeonthesenanowiresfor theiradsorptiongeometriesandtheirbindingenergiesinthesolu- tionusinganonlinearsolvationmodel.Wehavealsoinvestigated theelectronicpropertiesoftheresultingcombinedphysicalsystem suchasthedensitiesofstates,thechargedensitiesofthefrontier statesandtheabsorptionspectra.Inordertomakeacomparison withasimpleskeletonmolecule,wehavechosenthecoumarincore (C9H6O2)andrepeatedthesamecomputationssystematicallyfor thecoumarinonthethinanatase(001)and(101)nanowiresusing thehybridmethodbeyondthestandardDFT.Infact,coumarindyes withvariousanchoringgroupshasbeenextensivelystudiedinthe literaturebytheoreticalworks[27–39,41,40,42,43].
2. Computationaldetails
Weperformedperiodictotalenergydensityfunctionaltheory calculationsusingtheimplementationofthescreenedCoulomb hybridexchange-correlationscheme,HSE[44–46],intheVienna ab-initio simulation package (VASP) [47]. Single particle states wereexpandedintermsofplanewavesuptoakineticenergycut- offof400eVusingtheprojector-augmentedwaves(PAW)method [48,49].Brillouinzoneintegrationswerecarriedoutoverak-point samplingtogetwell-convergedvalues.
ThestandardDFTexchange-correlationfunctionalslikePBE[51]
suffersfromthelackofproperself-interactioncancellation(SIC)as intheHartree–Fockapproximationtotheinteractingmanypar- ticleproblem.Ingeneral,inthehybridapproaches,thenonlocal exactexchangeenergyispartiallyadmixedwiththesemilocalPBE exchangeenergyinordertoimprovethedescriptionofthelocal- izedstatessuchasthed-orbitalsoftheTiO2.Since,thebottomof theconductionband(CB)oftitaniaiscomposedof3d-stateshaving t2gsymmetry,hybridDFTmethodssignificantlyhealthebandgap underestimationofthestandardexchange-correlationschemes.
TherangeseparatedhybridHSEfunctionaltreatstheexchange energyascomposedoflong-range(LR)andshort-range(SR)parts,
EXHSE=aEHFX,SR(ω)+(1−a)EPBEX ,SR(ω)+EPBEX ,LR(ω)
whereaisthemixingfactor[50]andω istherangeseparation parameter[44–46].Thecorrelationenergyistakenfromstandard PBEcorrelationenergy[51].Inourcalculationsweusedamixing factorofa=0.22toreproducetheexperimentalbulkbandgapof anataseas3.20eV.
Solvation effects have been included at the hybrid HSE exchange-correlationfunctionallevel forC2-1andcoumarinon theanatase nanowiresconsidered in this work. We performed
calculationsfor chloroform andwater environment viapolariz- ablecontinuummodel(PCM)includingboththenewnon-linear anditslinearcounterpartasimplementedintheopen-sourcecode JDFTx[52–55].Thesolventenvironmentisreproducedbyadielec- tricmediumsurroundingthesolutedyemolecule.Thedielectric functionofthesoluteturnsonaroundacriticaldensityvaluewhich
Fig.1.Thechargedensitydistributionplotsofthehighestoccupied statesof coumarin+001nw(a),C2-1+001nw(c),andofthelowestunoccupiedstatesof coumarin+001nw(b),C2-1+001nw(d)calculatedusingtheHSEfunctional.Inthis ball-stickrepresentation,thered,light-blue,brown,grey,yellowandwhitecolors areusedforO,Ti,C,N,SandHatoms,respectively.(Forinterpretationoftherefer- encestocolorinthisfigurelegend,thereaderisreferredtothewebversionofthe article.)
isusedtomodelthecavityaroundthesoluteandparametrizedto reproduceexperimentalsolvationenergies[53,54].
Theanatase001nwand 101nwmodelstructuresarecleaved fromthebulk phaseasshownin Figs.1and2.Bothnanowires withandwithoutC2-1and coumarinmoleculesareconsidered inlargeperiodictetragonalsupercells.Thenanowireshaveperi- odicityinonedimension.Avacuumseparationofatleast20 ˚Ais adoptedaroundthenanowirein ordertoavoid anyunphysical interactionwithitsperiodicimagesinthedirectionsperpendic- ulartothenanowireaxis.Wealsousedlargerperiodicityalongthe nanowireaxisinordertoconsiderthedyemoleculesasisolated onthe(001)and(101)facets.Weconstructedseveralprobable initialadsorptiongeometries.Theatomicpositionswerefullyopti- mizedusingtheconjugate-gradientsalgorithmbyminimizingthe Hellmann–Feynmanforcesoneachatomuntilathresholdvalueof 0.01eV/ ˚Aisreachedtostoptheself-consistentcycles.Therelaxed nanowiremodelskeeptheanataseformwithoutamajorstructural distortion[56].
Wecalculatedtheabsorptionspectrabyconsideringthetran- sitionsfromtheoccupiedtotheunoccupiedstateswithinthefirst Brillouinzone[57].Theimaginarypartofthefrequency depen- dentdielectricfunctionε2(ω)canbeexpandedasasumoversingle particlestatesdeterminedbytheself-consistentHSEcalculations.
Fig.2.Thechargedensitydistributionplotsofthehighestoccupied statesof coumarin+101nw(a),C2-1+101nw(c),andofthelowestunoccupiedstatesof coumarin+101nw(b),C2-1+101nw(d)calculatedusingtheHSEfunctional.
3. Resultsanddiscussion
Thin 001nw and 101nw models have been considered in periodicsupercellswithlargevacuumseparations.Theiratomic positionshavebeenrelaxedusingtheHSEexchange-correlation functional. We didnot fix anyof the ionic cores to theirbulk positionsinanyofthegeometryoptimizationcalculationsinthis work.AlthoughtheHSE-optimizedatomicstructuresofthebare nanowires are notshown, theydidnot have any majorrecon- structionfromtheirinitialgeometriessimilartothoseobtained previously[56].ThesurfaceTi Obond lengthsbecomeslightly largerthanthe bulkvalueof 1.95 ˚A.Thisdifferencegets much smallertowardthecenterofthenanowires.Therefore,both001nw and101nwmodelsmaintaintheanatasestructure.
We haveconsideredanumber ofprobableinitialadsorption configurationsforC2-1moleculeonbothofthenanowiremodels.
ThetailoxygenandtheOHgrouparefoundtobeactivelyinvolved intheadsorptionofthedyeontheoxidesurface(seeFigs.1and2).
C2-1moleculecanachieverelativelyhighadsorptionenergiesinits bidentatemodeaspresentedinTable1.Inthiscase,theOHgroup losesitshydrogentooneofthenearbysurfaceoxygensandthe remainingtwotailoxygensformtwoTi Obondswiththeanatase surface.Inthemonodentatebinding,however,C2-1formsonlyone Ti Obondthroughitstailoxygen.Thebidentatedye-surfacebond lengthsare∼2.0 ˚Awhichisclosetothebulkvalue.C2-1molecule slightlydistortsthenanowirestructureonlylocally.
Asareferenceminimalskeleton,weconsideredthecoumarin coreonthenanowiresurfaces.Inthis case,coumarinprefersto formasinglebondwitha5-foldcoordinatedsurfaceTiatomby aligningperpendiculartobothofthenanowiresasanenergetically favorablebindingconfiguration.TheTi Obondsbetweenthedye andthesurfacebecome2.18 ˚Aand2.21 ˚Aon101nwand001nw, respectively.Thedistortionofcoumarinonthenanowirestructure isevensmallerrelativetotheC2-1case.
TheC2-1complexisknowntohavephotoinducedintramolec- ularcharge transfer in thegas phase. On theother hand,both theHOMOand theLUMOcharge densitiesremain localizedon theentirecoumarincore.Therefore,theirchargeredistributions are remarkably different if they are considered tobe isolated.
Theirchargedensityrelocationcharacteristicsuponanexcitation becomesimportantwhenthesemoleculesareattachedtoanoxide surface.Inordertointerpretthechargeinjectionfeaturesofthese twodifferentdyeswecalculatedthechargedensitiesofhighest occupiedandlowestunoccupiedstatesofdye+nwcombinedsys- tems. Our HSE resultsare depictedin Fig. 1 for 001nwand in Fig.2for101nwcases.Thedonor-to-acceptorcharacterofC2-1dye, whichcanbeexplainedastheintramolecularchargetransferfrom thetetrahydroquinolinemoietytothe-conjugatedacidicpart,is significantlymodifiedwhenthemoleculeisadsorbedonthetita- niasurfaces.Thechargedensityofthehighestoccupiedstateof thecombinedsystemisdistributedovertheentiremoleculesim- ilartothecaseofcoumarinonthenanowires.Similarbehavioris seenonboth001nwand101w.However,thechargedensitydistri- butionsofthelowestlyingunoccupiedstatesofC2-1+001nwand coumarin+001nwareremarkablydifferent.Thiscanbeclearlyseen bycomparingthecorrespondingchargedensityplotsinFig.1band d.In thecase of101nw,both dyesexhibitsimilarchargeredis- tributionfeaturesbetweenthehighestoccupiedand thelowest unoccupiedstates.
ThebindingenergiesofC2-1andcoumarinonthe001nwand 101nwformonodentateandbidentateadsorptionmodesarecal- culated at the HSE level by the standard formulation used in similarsystemspreviously[18,19].Moreover,weincludedsolva- tioneffectsforthechloroformandwaterenvironmentsusingHSE functionaland anewnonlinearPCM.OurHSE+PCMresultsare presentedinTable1.MonodentatebondingofcoumarinandC2-1
Table1
Calculatedadsorptionenergiesofdyemoleculesonthinanatase(001)and(101)nanowirestructuresinvacuumandinsolutionusingHSEmethodandnonlinearPCM.
EnergyvaluesaregivenineV.
Dye @001nw @101nw
HSE HSE+PCM(CHCl3) HSE+PCM(H2O) HSE HSE+PCM(CHCl3) HSE+PCM(H2O)
Coumarin −0.63 −0.33 −0.07 −0.70 −0.58 −0.44
C2-1(monodentate) −0.73 −0.65 −0.11 −0.62 −0.43 −0.30
C2-1(bidentate) −1.25 −1.18 −0.52 −0.83 −0.70 −0.51
onboth(001and(101)surfacesshowsimilarlymoderateadsorp- tionenergiesinvacuumandalsointhesolution.Singlebondsare foundtobedrasticallyweakenedbythedielectricenvironmentof thestrongsolutionslikewater.Therefore,thesetypeofmonoden- tatebindingmodesarenotexpectedtobedurableandstablein theelectrolyteenvironment.Ontheotherhand,bidentatemodeof C2-1ontheoxidesurfacesgivesreasonablystrongbindingener- gies.Therefore,C2-1dyeformingtwoO-Tibondswiththesurface canevenbestableinanionicsolventlikewater.TheseHSE+PCM resultsshowthesignificanceofanchoringofthelightharvesting sensitizersforareliableDSSCoperation.
TheinclusionofthenonlinearPCMchangesthebindingenergies inthepositivedirection.Themainreasonisthatthedyemolecule andtheadsorptionsitesontheTiO2surfaceinteractwiththesol- ventverystrongly.Becausesuchaninteractionisnotpresentin vacuumcalculations,resultsgivemorenegativebindingenergies.
Sincewaterisamorepolarsolventthanchloroform,ithasahigher dielectricconstant.Hence,waterinteractsmorestronglywiththe adsorptionsites.ThereforecalculatedbindingenergiesinH2Oare morepositivethanthoseinCHCl3.
The geometry optimization by minimizing the Hellmann–
Feynman forces causes surface ionic cores to relax into their minimumenergypositions.Hence,possiblesurfacestatesarepas- sivatedyieldingacleanbandgap(Fig.3).TheHSEmethodgavethe bandgapsofbarenanowiresas4.06eVfor001nwand4.01eVfor 001nw.ThesearesignificantlylargerthanbothHSE-calculatedand experimentallymeasuredbulkvalueof3.20eV.Forthenanowire diametersaround1nm,HSEcalculationsindicateastrongquantum confinementeffect[56].Thiswideningofthegap,uponadsorption ofdyes,resultsinsomemolecularstatestofallintotheenergy gap,wheremostofthedeeperlyingoccupiedmolecularorbitals stay in the valence band as resonant states. Consequently, the
Fermienergyshiftsuptohigherenergiesleadingtoanenergy-gap narrowingwhichisanimportantfactorforphotovoltaicproper- ties.On theotherhand,thelowestlyingunoccupiedmolecular levelsofthedyesdelocalizeontheTi3dstatesinsidetheconduc- tionband(CB)ofthenanowires,aschannelsofexcitedelectron injectiontothenanowires.Thedensityofstates(DOS)ofthecom- bineddye+nanowiresystemshavealsobeenpresentedinFig.3 forcoumarin,andC2-1intwomodes,namelymono-andbidentate forms.Forbothofthenanowires,themolecularstatesofcoumarin appeararoundtheVBedgewhileoneofthemisisolatedfromthe rest.ForC2-1monodentatemode,essentiallythreefilledisolated statesfallintothebandgapofbothnanowiretypes.Ongoingfrom monodentateto bidentatebonding, anadditional isolatedstate appearsabovetheVB.Significantbandgapreductionisobtained inthecaseofC2-1bridgingin bidentateformonbothtypesof nanowires,whichmakesC2-1dyewithsuchbondingmoreimpor- tantforlightharvesting.
Aswediscussedwiththeelectronicstructure,appearanceof severalnewdyerelatedstateswithinthebandgapofnanowires might cause a redshift of the optical absorption of these dye- nanowirecompositesystemsifthetransitionsfromthesestates aresymmetryallowed,sotheymightbecomeactiveinthevisi- blepartofthespectrumwhichisverybeneficiaryforphotovoltaic applications.In order to investigate theoptical absorption, we havecalculatedthedipolematrixelementsbetweenoccupiedand emptystatesforeachcase,whichisessentiallytheimaginarypart ofthedielectricfunction,2(ω).Thecalculatedabsorptionspectra forcleananatasenanowirealongwiththoseforthecorrespond- ingdye-nanowirecompositesystemsaredepictedinFig.4(a)and (b)for(001)and(101)nanowires,respectively.Firstofall,when wecomparethecorrespondingopticalabsorptionspectraofthe differentnanowireandnw+dyesystems,generalfeaturesarevery
Fig.3.TheHSE-calculatedpartialandtotaldensitiesofstates(DOS)of(C2-1,coumarin)+nanowirecombinedsystemsforlowenergybindingmodes.Theresultsareshown for001nwontheleftandfor101nwontherightpanes.Themolecularcontributionsareindicatedasdark(red)shades.ThedottedlinesdenotetheFermienergiesandset atslightlyabovethehighestoccupiedstates.TheDOSstructuresarealignedwithrespecttothevalencebandmaximumofthebarecasesforeachtypeofnanowires.(For interpretationofthereferencestocolorinthisfigurelegend,thereaderisreferredtothewebversionofthearticle.)
ε2(ω) (arb. units)
001nw
(a)
coumarin C2-1 mono.
C2-1 bi.
0 2 4 6 8 10
ε2(ω) (arb. units)
Energy (eV)
(b)
101nw coumarin C2-1 mono.
C2-1 bi.
Fig.4.Absorptionspectraofbareanddyeadsorbed001nw(a)and101nw(b)cases calculatedusingtheHSEhybridDFTmethod.
similarforboth(001)and(101)nanowires.Forbarenanowires, theabsorptionstartsafter4eV,whichcoincideswithenergyband gapof thenanowire,therefore we can saythat theabsorption edgeisfromthevalencebandedgetotheconductionbandedge.
However,whencoumarinisattachedtothenanowire,twonew states,oneveryclosethevalancebandedgeandtheotherisalmost 0.8eV above theedge, associated withthe dye appearswithin thebandgapofthenanowire.Thesearethereason ofthetwo peaksobservedneartheadsorptionedgeabsorptionspectrumof coumarin+nanowiresystem,otherwise thespectrumlooks very similartothebarenanowireone.InthecaseofC2-1dye,there areseveraldyeoriginatesstateswithinthebandgapforbothof theadsorptionmodes,monodentateandbidantate.Theabsorption spectraof bothofthemodesaresimilar.Comparedtothebare nanowirespectrum,therearetwonewpeaks,onearound2eVat themiddleofthebandgapandtheotheraround3eValmost1eV belowtheabsorptionedge(orequivalentlyconductionbandedge).
Formonodentatemode,thepeakat2eVissharpwhilethereare twopeaksaround3eV.However,forbidentate,wehavetwosplit peaksaround2eV,andoneverybroadpeakaround3eVinstead oftwopeaksof monodentatecase.Comparingthesepeakposi- tionswithDOSreportedinFig.3,wecanconcludethatthepeak around2eVisduetoatransitionfromdyeassociatedstateatthe Fermileveltotheconductionbandedge.Forbothdyetypesthe LUMOlevelsstronglyresonatewiththeCBwhentheyareattached tothesurfaceoftheoxidenanowire.Meanwhile,theHOMO-like levelsappearinthebandgapof TiO2 nanowires asisolatedand well-localizedstatesonthedye.Theassociatedchargedensitydis- tributionscanalsobeseeninFig.1.Briefly,thelowerlyingpeaks intheabsorptionspectraforthedye+nwcombinedsystems,are essentiallyduetothetransitionsfromthedye-relatedHOMO-like leveltothestatesatthebottomoftheconductionband.
4. Conclusions
We have investigated the band gap related properties and resultingabsorptionspectraofbarethinanatasenanowireswith diameters less than1nm.We used therange separatedhybrid HSEfunctionalwithinDFT.Forthesenanowires,theHSEapproach
estimatesreasonablylargerbandgapsinagreementwiththequan- tumconfinementeffect.Thesameleveloftheorywasappliedto examinetheadsorptionconfigurations,electronicstructuresand opticalprofilesofD--AtypeorganicC2-1photosensitizeronthe (001)and(101)facetsoftheoxidenanowires.Theintramolecu- larchargetransfercharacterofC2-1appearstobemodifiedonce theC2-1formsabidentatebondingwiththesurfaceoxygenson theanatasenanowires.TheC2-1+nwsystemshowssimilarspa- tialchargedensityfeatureswiththatofthecoumarin+nwforthe highest occupiedstatewhich is activelyinvolvedin thelowest lyingphotoexcitation.TheHSE+PCMincludingnonlineardielectric effectsshowsthatthebindingenergyofC2-1dyeremainsmod- erateinsolutionenvironment. Thismightbeseenasoneofthe explanationsofwhytheanchoringofsensitizermoleculesonthe oxidesurfaceisimportant.Thenumberofdyerelatedstatesabove theVBofthetitaniananowiresisassociatedwiththecomplex- ityofthemolecularstructure.Therefore,functionalmoeitiesare desirabletoabsorbalargerportionofthevisiblespectrum.Conse- quently,theuseofrangeseparatedhybriddensityfunctionalsisa promisingwaytodescribebandgaprelatedelectronicstructures fordyeandTiO2nanowiresystems.
Acknowledgments.
This work is supported by TÜB˙ITAK, The Scientific and TechnologicalResearchCouncilofTurkey(Grant#110T394).Com- putationalresourceswereprovidedbyULAKB˙IM,TurkishAcademic Network&InformationCenter.
References
[1]A.Fujishima,K.Honda,Nature(London)238(1972)37.
[2]A.Fujishima,X.T.Zhang,D.A.Tryk,Surf.Sci.Rep.63(2008)515.
[3]B.O’Regan,M.Grätzel,Nature353(1991)737.
[4]L.Kavan,M.Grätzel,S.E.Gilbert,C.Klemenz,H.J.Scheel,J.Am.Chem.Soc.118 (1996)6716.
[5]J.Pascaul,J.Camassel,H.Mathieu,Phys.Rev.Lett.39(1977)1490.
[6]U.Diebold,Surf.Sci.Rep.48(2003)53.
[7]G.Li,L.Li,J.Boerio-Goates,B.F.Woodfield,J.Am.Chem.Soc.127(2005)8659.
[8]A.S.Barnard,L.A.Curtiss,NanoLett.5(2005)1261.
[9]M.Jankulovska,T.Berger,T.Lana-Villarreal,R.Gómez,Electrochim.Acta62 (2012)172.
[10]L.Yuan,S.Meng,Y.Zhou,Z.Yue,J.Mater.Chem.A1(2013)2552.
[11]T.Berger,T.Lana-Villarreal,D.Monllor-Satoca,R.Gómez,J.Phys.Chem.C112 (2008)15920.
[12]D.C¸akır,O.Gülseren,Phys.Rev.B80(2009)125424.
[13]P.K.Naicker,P.T.Cummings,H.Zhang,J.F.Banfield,J.Phys.Chem.B109(2005) 15243–15249.
[14]A.Iacomino,G. Cantele,F. Trani,D. Ninno, J. Phys.Chem.C114 (2010) 12389–12400.
[15]V.C.Fuertes,C.F.A.Negre,M.B.Oviedo,F.P.Bonafé,F.Y.Oliva,C.G.Sánchez,J.
Phys.Condens.Matter25(2013)115304.
[16]R.Chen,X.Yang,H.Tian,X.Wang,A.Hagfeldt,L.Sun,Chem.Mater.19(2007) 4007–4015.
[17]R.Chen,X.Yang,H.Tian,L.Sun,J.Photochem.Photobiol.A:Chem.189(2007) 295–300.
[18]D.C¸akır,O.Gülseren,E.Mete,S¸Ellialtıo˘glu,Phys.Rev.B80(2009)035431.
[19]D.C¸akır,O.Gülseren, E.Mete,S¸Ellialtıo˘glu,J.Phys.Chem.C115(2011) 9220–9226.
[20]W.Stier,O.V.Prezhdo,J.Phys.Chem.B106(2002)8047–8054.
[21]K.Hara,T.Sato,R.Katoh,A.Furube,Y.Ohga,A.Shinpo,S.Suga,K.Sayama, H.Sugihara,H.Arakawa,J.Phys.Chem.B107(2003)597–606.
[22]J.BanuelosPrieto,F.LopezArbeloa,V.MartinezMartinez,I.LopezArbeloa, Chem.Phys.296(2004)13–22.
[23]L.Campbell,S.Mukamel,J.Chem.Phys.121(2004)12323.
[24]P.Persson,M.J.Lundqvist,R.Ernstorfer,W.A.GoddardIII,F.Willig,J.Chem.
TheoryComput.2(2006)441–451.
[25]C.-R.Zhang,L.Liu,J.-W.Zhe,N.-Z.Jin,Y.Ma,L.-H.Yuan,M.-L.Zhang,Y.-Z.Wu, Z.-J.Liu,H.-S.Chen,Int.J.Mol.Sci.14(2013)5461–5481.
[26]C.O’Rourke,D.R.Bowler,J.Phys.Chem.C114(2010)20240–20248.
[27]Z.-S.Wang,F.-Y.Li,C.-H.Huang,L.Wang,M.Wei,L.-P.Jin,N.-Q.Li,J.Phys.Chem.
B104(2000)9676.
[28]A.Ehret,L.Stuhl,M.T.Spitler,J.Phys.Chem.B105(2001)9960.
[29]Z.-S.Wang,F.-Y.Li,C.-H.Huang,J.Phys.Chem.B105(2001)9210.
[30]P.Wang,S.M.Zakeeruddin,R.Humphry-Baker,J.E.Moser,M.Grätzel,Adv.
Mater.15(2003)2101.
[31]P.Wang,S.M.Zakeeruddin,P.Comte,R.Charvet,R.Humphry-Baker,M.Grätzel, J.Phys.Chem.B107(2003)14336.
[32]T.Horiuchi,H.Miura,K.Sumioka,S.Uchida,J.Am.Chem.Soc.126(2004)12218.
[33]T.Kitamura, M.Ikeda, K.Shigaki,T.Inoue,N.A.Anderson,X.Ai,T. Lian, S.Yangagida,Chem.Mater.16(2004)1806.
[34]Z.-S.Wang,K.Sayama,H.Sugihara,J.Phys.Chem.B109(2005)22449.
[35]D.P.Hagberg,T.Edvinsson,T.Marinado,G.Boschloo,A.Hagfeldt,L.Sun,Chem.
Commun.2245(2006).
[36]S.-L.Li,K.-J.Jiang,K.-F.Shao,L.-M.Yang,Chem.Commun.2792(2006).
[37]Y.Chiba,A.Islam,Y.Watanabe,R.Komiya,N.Koide,L.Han,Jpn.J.Appl.Phys.
45(2006)L638.
[38]Z.-S.Wang,Y.Cui,K.Hara,Y.Dan-oh,C.Kasada,A.Shinpo,Adv.Mater.19(2007) 1138–1141.
[39]Y.Kurashige,T.Nakajima,S.Kurashige,K.Hirao,J.Phys.Chem.A111(2007) 5544–5548.
[40]J. Preat, P.-F. Loos,X. Assfeld, D. Jacquemin,E.A.Perpëte, J. Mol. Struct.
Theochem.808(2007)85–91.
[41]X.Zhang,J.-J.Zhang,Y.-Y.Xia,J.Photochem.Photobiol.A:Chem.194(2008) 167–172.
[42]R.Sanchez-de-Armas,M.A.SanMiguel,J.Oviedo,J.F.Sanz,Phys.Chem.Chem.
Phys.14(2012)225–233.
[43]C.I.Oprea,P.Panait,F.Cimpoesu,M.Ferbinteanu,M.A.Girtu,Materials6(2013) 2372–2392.
[44]J.Heyd,G.E.Scuseria,M.Ernzerhof,J.Chem.Phys.118(2003)8207.
[45]J.Heyd,G.E.Scuseria,M.Ernzerhof,J.Chem.Phys.124(2006)219906.
[46]J.Paier,M.Marsman,K.Hummer,G.Kress,I.C.Gerber,J.G.Angyan,J.Chem.
Phys.125(2006)249901.
[47]G.Kresse,J.Hafner,Phys.Rev.B47(1993)558.
[48]P.E.Blöchl,Phys.Rev.B50(1994)17953.
[49]G.Kresse,J.Joubert,Phys.Rev.B59(1999)1758.
[50]J.P.Perdew,M.Ernzerhof,K.Burke,J.Chem.Phys.105(1996)9982.
[51]J.P.Perdew,K.Burke,M.Ernzerhof,Phys.Rev.Lett.77(1996)3865.
[52]K.Letchworth-Weaver,T.A.Arias,Phys.Rev.B86(2012)075140.
[53]D.Gunceler,K.Letchworth-Weaver,R.Sundararaman,K.A.Schwarz,T.A.Arias, Model.Simul.Mater.Sci.Eng.21(2013)074005.
[54]D.Gunceler,T.A.Arias,preprintavailableatarXiv:1403.6465.
[55]R.Sundararaman,D.Gunceler,K.Letchworth-Weaver,T.A.Arias,JDFTx,2012 http://jdftx.sourceforge.net
[56]H. Ünal, O. Gülseren, S¸ Ellialtıo˘glu, E. Mete, Phys. Rev. B 89 (2014) 205127.
[57]M.Gajdoˇs,K.Hummer,G.Kresse,J.Furthmüller,F.Bechstedt,Phys.Rev.B73 (2006)045112.
