Ferroelectric $\pi$-stacks of molecules with the energy gaps in the sunlight range

4 MB·

by  Paweł Masiak

Ferroelectricπ-stacksofmoleculeswiththeenergygapsinthesunlightrange
Paweł Masiak and Małgorzata Wierzbowska
Institute of Physics, Polish Academy of Sciences
Aleja Lotnikow 32/46, PL-02668 Warsaw, Poland
Ferroelectricπ-stackedmolecularwiresforsolarcellapplicationsaretheoreticallydesigned,insuchaway
thattheirenergygapsfallwithinvisibleandinfraredrangeoftheSunradiation. Bandengineeringistailored
byamodificationofthenumberofthearomaticringsandviaachoiceofthenumberandkindofthedipole
groups. Theelectronicstructuresofmolecularwiresandthechemicalcharacteroftheelectron-holepairare
analyzedwithinthedensityfunctionaltheory(DFT)frameworkandthehybridDFTapproachbymeansofthe
B3LYPscheme. Moreover,itisfoundthatoneoftheadvantageouspropertiesofthesesystems-namelythe
7 separate-pathelectronandholetransport-reportedearlier,stillholdsforthelargermolecules,duetothedipole
1 selectionrulesfortheelectron-holegeneration,whichdonotallowthelowestopticaltransitionsbetweenthe
0
stateslocalizedatthesamepartofthemolecule.
2

n
a INTRODUCTION
J

3
TheabilitytoabsorbawiderangeofSunspectrumandconvertthisenergyintothevoltagebetweentheelectrodesisakeyfactor
1
oftheefficientsolarbattery. Therefore, theopticallyactivematerialsideallyshouldbethecompositematerialsofsmall-, middle-

] andwide-bandgapsemiconductors,inordertocoverthewholeradiationrangefromthesoftultaviolet(350nm)tothefarinfrared
ci ofasunset(1400nm). Thispossibilityisofferedbythemultilayersofplanarmoleculesorarraysofmolecularwires.
s Recently,theso-calledcovalentorganicframeworks(COF)attractanattentionduetotheirspecialoptical,transport,andcatalytic
-
l properties,aswellaseasyfabrication[1–4]. Fromapointofviewofthephotovoltaics,stacksoftheCOFsaresimilartothebulk
r
t orintegratedheterojunctions[4,5]. Byachangeoftheplanarbondsbetweenthemoleculesfromthecovalenttohydrogenbonds,
m
onecanrestricttheelectronictransporttothedirectionacrossthelayers,i.e. alongthestacks,whiletheelectronictransportwithin
t. theplanesshallbesuppressed. Thisisadvantageousforthesolarbatteries,wheretheplanarcurrentwouldcauseonlyadissipation
a
of an energy. Therefore, in the previous works [6, 7], we studied the layers of molecules with the COOH terminal groups as the
m
connectingpartsforbuildingthenetworks. TheCOOHgrouppossessesalsoasmalldipolemoment.
- Theferroelectricallyorderedmolecules,composedofbenzeneringsandtwodipolegroups(COOHandCH CN),arrangedinthe
d 2
n π-typestacksoflayersorthemolecularwires,showmanyappealingeffects[6,7]. Inparticular,theenergylevelsofthesubsequent
o layers (or molecules in a stack) are aligned in a cascade, and this holds for the valence and conduction band as well [6–8]. Each
c layerissimultaneouslyadonorandacceptorofelectronsandholes,dependingonadirectionofthecarriermotion[6]. Theexcitons
[
insuchlayersarelocalizedandhavethecharge-transfercharacterfromthedipolegrouptothearomaticcentralring. Theelectric

1 field generated by the ferroelectrically ordered dipole groups leads to a polarization which is induced at electrodes. This effect
v for the graphene sheets, chosen as the electrodes, causes a change of the work function by ±1.5 eV for the anode and cathode,
8 respectively[6]. Moreover,theelectronsandholesmoveacrosssuchπ-stacksalongdifferentpaths:theelectronsthroughthecentral
4
ringsandholesbetweenthedipolegroups[7]. Thecarriermobilities,obtainedwiththerelaxationtimeestimatedduetotheelastic
7
3 scatteringandionicintrusions,arehigherthanthoseintheorganometalhalideperovskites[7,9,10]. Foralltheabovereasons,itis
0 interestingtoinvestigatefurtherpropertiesoftheferroelectricmolecularlayersandstacks,inordertobringthesesystemscloserto
1. theexperimentalandindustrialinterest[11].
0 Inthistheoreticalwork,wefocusontheruleswhichgovernthebandgapchange.Theenergygapshouldfallintoaninterestingfor
7 usrangeoftheSunradiation. Recently,asimilarsystem(tothecasesinvestigatedbyus)hasbeentheoreticallyandexperimentally
1
investigated, namely 2D imine polymer [12]. The authors revealed that a bandgap tunning by expanding a conjugation of the
:
v backboneofthearomaticdiaminesispossibleinthismaterial[12]. Itisalsowellknownthatthebandgapdecreaseswithasizeofa
i system[13,14]. However,withoutcalculations,theexactvalueoftheenergygapisdifficulttopredict,aswellasitsdependenceon
X
asymmetryandtheedgetermination[14,15].
r
a Wehavebegunourstudybychoosingatypeofmolecules,whichcouldbemostpromisingforourpurpose. Fig. 1presentssome
of the molecules which are analyzed in this work. The collection of the geometries of all other studied systems, not presented in
figureshere, isincludedinthesupportinginformation. Wehavechosenthreedipolegroups: COOH,CH CN,CH CF , andtheir
2 2 3
combinationsinvariousrepetitions. Thesizeofthemesogenicaromaticpartwasenlargedlinearly. Thenumberofthebenzene-type
ringsisgiveninournotationbyanintegernumberfollowingthe”b”letter.
Firstly, weinvestigated aneffect ofa numberof the aromaticrings and numberof dipolegroups on asize of theenergy gap; it
means,thedifferencebetweentheenergeticpositionsofthelowestunoccupedandthehighestoccupiedmolecularorbital(LUMO-
HOMO).Secondly,wecheckedaneffectofmixingvariouschemicalgroupsastheterminaldipolesinonemolecule. Weestimated
also an effect of the π-stacking. Finally, we analyzed how the molecular modiffications - which were done in order to tailor the
bandgapsize-affecttheexciton(electron-hole)characterandtheseparationofthechargecarrierpaths.
2
b1(COOH) b1(CH CN) b1(CH CF ) b1(COOH,CH CN)
3 2 3 2 3 3 2 3
b5(CH CN) b9(COOH)
2 10 4
b17(COOH)
8
FIG.1: Atomicstructuresofsomeofthestudiedmoleculesandtheirshortnames.
THEORETICALMETHODS
The molecular calculations have been performed with the Gaussian code [16], using the correlation-consistent valence double-
zeta atomic basis set with polarization function cc-pVDZ [17]. Molecular geometries were optimized with the hybrid-functional
methodintheB3LYPflavor[18],whichmixesthedensityfunctionaltheory(DFT)[19]intheBLYP[20,21]parametrizationwith
theHartree-Fockexactexchangein80%and20%,respectively. Theoptimizedatomicstructureswereusedtobuildthemolecular
wires.
Further calculations for the molecules and 1D structures have been performed with the Quantum ESPRESSO suite of codes
[22]. This package is based on the plane-wave basis set and the pseudopotentials for the core electrons. The normconserving
pseudopotentialswereusedwiththeenergycutofffortheplane-wavessetto35Ry.Moreover,someoftheresults,suchasoptimized
intermoleculardistances,werecheckedtobethesameasusingthelargerenergycutoffof45Ry. Theintermoleculardistanceswere
obtained within the local density approximation (LDA), since it is known to give better geometries than the generalized gradient
approximation(GGA).TheLDA-optimizedseparationsbetweenmoleculesinthestackwerethenusedfortheB3LYPcalculations
for the molecular wires. The uniform Monkhorst-Pack k-points mesh in the Brillouin zone [23] was chosen for 1×1×10 for the
wires. FortheB3LYPscheme,weusedthemeshes1×1×9and1×1×3forthek-andq-pointgrids,respectively.
Inordertoobtainthebandstructuresprojectedontothelocalgroupsofatoms,weemployedthewannier90package[24],which
interpolatesbandsusingthemaximally-localizedWannierfunctions[25,26]. Thesametoolhasbeenusedforthecalculationsof
thedipolemoment,whichcanbeobtainedfromthepositionsofthemaximally-localizedWanniercenters,r ,usingtheformula[27]
n
(cid:88) (cid:88)
d = Z R − r (1)
a a n
a n
whereZ andR aretheatomicpseudopotentialchargeanditsposition,correspondingly,andindexesaandnrunoverthenumber
a a
ofatomsandWannierfunctions,respectively.
RESULTS
Dipolemoment
There are a number of important implications of using the dipole groups: i) the hydrogen bonds via the COOH groups within
theplanesrestricttheelectronictransportanddissipationofenergyinthedirectionsperpendiculartothephotovoltaicpath, ii)the
3
polarization generated across the solar device orders the energy levels in a cascade [6], iii) the electronic transport along the π-
stacksisrestrictedtotheπ-conjugatedringsfortheelectrons, andholesmovebetweenthedipolegroups[7], iv)anadsorptionof
the optically active molecules at the surfaces of the transparent conductive oxides, used as the electrodes, leads to the high power
conversionwhenitisrealizedwiththeCOOHgroup[28]. Therefore,itisusefulltoexaminevariousdipolegroupsfortheirimpact
on the energy gaps. In table 1, the dipole moments in the direction parallel to the photovoltaic transport for all studied groups
attachedtoonearomaticringarecollected.
TABLEI:Dipolemoment(inDebye)ofbenzenewithchosenpolargroups-acomponentperpendiculartothearomaticring(D )-
z
obtainedfromtheLDAcalculationsandtheWannier-functionsspreadsaccordingtoEq. 1.
Molecule D
z
b1(COOH) -0.07
1
b1(CH CN) -0.59
2 1
b1(CH CF ) -0.35
2 3 1
b1(COOH,CH CN) -2.06
2 3
LUMO-HOMOenergydifferences
A collection of molecules with various lengths of the aromatic chains is gathered in Fig. 2. The energy gaps are presented on
a scale of the Sun radiation activity from the soft ultraviolet (350 nm) to the far infrared of a cloudy sky (1400 nm). The impact
ofvariousdipolegroupsontheLUMO-HOMOenergydifferencedoesnotchangewiththegrouptypes,whentheyareattachedto
thelongchains(abovefivebenzenerings). Moreover,increasinganumberofthedipolegroupsdoesnotchangetheenergygapfor
thelongermolecules. Duetothelackofthiseffect,wecanfocusonthetransportpropertieswhenadesignofthedipolegroupsis
considered.
Itisawellknownfact,thattheenergygapsobtainedwiththedensityfunctionaltheory-bothinthelocaldensityapproximation
(LDA) and the generalized gradient approximation (GGA) - are underestimated, while the energy gaps from a pure Hartree-Fock
methodarelargelyoverestimated. Thus,weusedthehybrid-functionalschemebymeansoftheB3LYPfunctionalwhichcontains
20%oftheexactexchange.Thepresentedseriesoftheenergiescouldbeanapproximationoftheopticalgaps-whenjustatendency
of the size and chemical group effect on the gaps is studied. The experimental data are usually closer to the combined GW+BSE
approachtakingintoaccountboththequasi-particleandtheexcitonicbindingenergyeffects[29,30]. However,fromthepresented
5 X = COOH Y = CH CN
2
Z = CH CF
2 3
4 b λ = 350 nm
] 2
V X b
e 4 2X
[ 3 8
rgy gap 2 4b5X6b5Z8b5X10b5Y b9Z b9Y b17 b17
Ene 1 b5X b5X 10 14 18Z 22Y
0 λ = 1400 nm 10 14 4b9X8b9X 14b9X22b9X b17X b17X b17X b17X
4 8 22 38
FIG.2: TheLUMO-HOMOenergiesoftheisolatedmoleculeswithvariablenumberofbenzeneringsandthreedipolegroups:
COOH(blackcircles),CH CN(redsquares),CH CF (bluetriangles)-obtainedwiththeB3LYPmethod. Thesolarspectrum
2 2 3
rangeismarkedinyellow. AllcalculationshavebeenperformedwiththeGaussiancode.
4
data,itisobviousthatarealizationofthehighlyefficient-fromthelight-absorptionpointofview-matricesofmolecularstacksis
possible.Especially,ifonecombinesthelayerswithcolumnsofvariousmolecules,whichhavedifferentsizeanddifferentabsorption
profiles.
Impactoftheπ-stackingfortheenergygaps
Theabsorptionefficiencyiscorrelatedwiththethicknessofthephotoactivelayer(Beer-LambertLaw),whichcannotbetoosmall
makingthematerialtobetransparent[31]. Hence,all2Dstructuresforthesolarcellsshouldbeexaminedfortheirpropertiesacross
thelayers. Stackingcausesthebanddispersionsinthedirectionperpendiculartotheslab. Thisbandwidthbroadening,inturn,acts
fortheclosureoftheenergygap. InTable2,wepresentaneffectofthewireformationonthebandgap,andcomparetheLDAand
B3LYPcomputationalmethodsforchosensystems.
TABLEII:Energygaps(ineV)oftheisolatedmoleculesandmolecularwires,obtainedwiththeLDAandB3LYPmethods. The
lastcolumndisplaystheintermoleculardistances(inÅ)inthewires(Dist.) -obtainedwiththeLDAschemeandusedalsoforthe
B3LYPcalculations. AllcalculationshavebeenperformedwiththeQEcode.
molecule E (isolated) E (wire) ∆E (wire-isolated) Dist.(wire)
gap gap gap
LDA B3LYP LDA B3LYP LDA B3LYP LDA
benzene 5.119 6.717 4.026 5.452 -1.093 -1.265 3.8
b1(COOH) 4.204 6.199 4.037 6.016 -0.167 -0.183 5.1
3
b1(COOH) 3.956 5.875 3.857 5.813 -0.099 -0.062 5.1
6
b1(CH CN) 4.293 6.074 3.986 5.692 -0.307 -0.382 4.4
2 3
b1(COOH,CH CN) 3.611 5.503 2.963 5.050 -0.648 -0.452 4.6
2 3
b1(CH CF ) 4.759 6.359 4.607 6.119 -0.152 -0.239 5.2
2 3 3
b1(COOH,CH CF ) 4.084 5.958 3.946 5.871 -0.138 -0.087 5.2
2 3 3
b1(COOH,CH CN,CH CF ) 4.249 6.196 4.025 5.989 -0.224 -0.207 5.0
2 2 3 1
b5(COOH) 0.822 1.783 0.738 1.670 -0.084 -0.113 5.1
4
ThelastcolumninTable2displaystheintermoleculardistancesobtainedwiththeLDAmethod. Theseparationofbenzenes,by
3.8Å,isnotmuchlargerthanthatofthegraphenemultilayers,whichisaround3.4Å[32]. Themostdistantaremoleculeswiththe
CH CF groups,of5.2Å. Thisisduetothefactthattheyarethelargestofallatomicgroupsattachedtotheringsstudiedhere,and
2 3
theFatomsdonotattracttheHatomsatthebottomoftheupperneighbor. TheCOOHgroupsarethesmallesthere,butseparations
ofthemoleculesterminatedbythemarealsolarge-of5.1Å-becausetheoxygenatomsfromtheneighboringringsrepeleachother.
TheCH CNgroups,althoughtheyarealsoquitelarge,attracteachotherbetweentheneighboringrings. ThisisbecauseNandC
2
tendto”exchange”hydrogen,andthiseffectleadstothesmallestintermoleculardistances,of4.6Å. Theseparationsofmolecules
inawireruleaneffectofthebandgapsizeinthestack;thiseffectisthestrongestforthebenzenewiresandmoleculescontainingthe
CH CNgroups.Itisinterestingtonote,thatanadditionofCOOHtotheringswithotherdipolegroupsweakensaneffectofstacking
2
onthebandgap. Thisholdsevenatthesameintermoleculardistance(seeforinstanceb1(CH CF ) andb1(COOH,CH CF ) ,or
2 3 3 2 3 3
b1(COOH) andb1(COOH) inTable2). Theoriginofthiseffectwillbemoreclearinthenextsubsection.
3 6
ComparisonoftheLDAandB3LYPapproachesfortheisolatedmoleculesandwires,usually,exhibitsabitstrongereffectofthe
stackingonthebandgapforthehybrid-functionalscheme. AlsotheoriginofthiseffectissimilartothatofanadditionofCOOH,
and relies on the order of the energy levels. Because the experimental results for the band gaps of the molecules studied here do
notexistyet, itisnoteasytodeterminehowgoodistheB3LYPmethodinthiscase. However, onecouldexpectthatthismethod
willworksimilarasinthecaseofbenzene. InordertoevaluateeffectivenessoftheB3LYPmethodusedinourstudy,wecompared
energiesforbenzenecalculatedbydifferenttheoreticalmethodswithexperimentalresult. Theenergygapofthebenzenemolecule
(isolated)of6.72eVbymeansoftheB3LYPshouldbecomparedwiththevaluefromtheGWapproach,of10.5eV[33],because
both approaches do not take into account the excitonic effects. However, the measured optical gap is around 3.6 eV [34], due to
theeffectoflargeexcitonbindingenergyinsmallmolecules. Thisexcitoniceffectcanbetheoreticallyobtainedfromthedifference
ofthegapsobtainedwiththeGWandtheGW+BSE(BSEmeansBethe-Salpeterequation). Forbenzene,theGW+BSEbandgap
is around 3.1 eV [30]. Although the B3LYP scheme is much simpler then the GW and GW+BSE methods, and designed for the
fundamental gap only, its results are closer to the optical absorption than these of the GW aproach. Therefore, we expect that the
energygapsobtainedbyuswiththeB3LYPmethodshowthesametrendsinaseriesofsimilarmolecules-whichdifferonlywitha
sizeornumberortypeofthedipolegroups-astheopticalmeasurements.
5
Orderoftheenergylevels
The characters of the highest occupied and lowest unoccupied states determine the excitonic radius and binding energy, the
oscillatorstrengthoftheabsorptionoflight,aswellastheelectronictransportproperties.
a)12 b) c) 10
NO b1(XY)3 BLYP 20 b1(XZ)3 BLYP b1YZ BLYP
Density of states [arb. units] 48 CC ((rdiinpgo)le) XY YX YX Density of states [arb. units]11055 XZ XZ ZX FOCC ((rdiinpgo)le) Density of states [arb. units] 2468 Y FNCC ((rdiinpgoZ)le)
0 0 0
-6 -4 -2 0 2 4 6 -6 -4 -2 0 2 4 6 -6 -4 -2 0 2 4 6
Energy - E [eV] Energy - E [eV] Energy - E [eV]
F F F
d) e) f)
Density of states [arb. units]1248 OCC ((rdiinpgo)le) XbX1X3X BLYP Density of states [arb. units]11055 NCC ((rdiinpgo)le) Yb1YY3 Y BLYP Density of states [arb. units]1210055 FCC ((rdiinpgo)le)Zb1ZZ3 Z BLYP
0 0 0
-6 -4 -2 0 2 4 6 -6 -4 -2 0 2 4 6 -6 -4 -2 0 2 4 6
Energy - E [eV] Energy - E [eV] Energy - E [eV]
F F F
g)10 h) i) 20
Density of states [arb. units] 2468 FNOCC ((rdiinpgo)blXe1)XYZZY BLYP Density of states [arb. units] 2468 FNOCC ((rdiinpgo)le) bX1XYZZ Y B3LYP Density of states [arb. units]11055 XX OCC ((rdiinpgoslb)e)5X4 BLXXYP
0 0 0
-6 -4 -2 0 2 4 6 -4 -2 0 2 4 6 -6 -4 -2 0 2 4 6
Energy - E [eV] Energy - E [eV] Energy - E [eV]
F F F
j) 20 k)20 l) 40
b5XY BLYP b5XY BLYP b5Y BLYP
4 1 1 2 10
Density of states [arb. units]11055 XX NOCC ((rdiinpgYosl)e) XX Density of states [arb. units]11055 Y NOCC ((rdiinpgosXl)e) Y Density of states [arb. units]123000 YY NCCYY ((rdiinpgosl)e)YY YY YY
0 0 0
-6 -4 -2 0 2 4 6 -6 -4 -2 0 2 4 6 -6 -4 -2 0 2 4 6
Energy - E [eV] Energy - E [eV] Energy - E [eV]
F F F
m)30 n)40 o)30
Density of states [arb. units]121200555 NOCC ((rdiinpgosl)e) XXbYY5X4Y6YY BLYYYP XX Density of states [arb. units]123000 OCC ((rdiinpgosl)e) XX XX bXX5X1XX4 XXBLXXYPXX Density of states [arb. units]121200555 NOCC ((rdiinpgosl)e) YYbXX5XXX10YXX4 BXXLYXXPYY
0 0 0
-6 -4 -2 0 2 4 6 -6 -4 -2 0 2 4 6 -6 -4 -2 0 2 4 6
Energy - E [eV] Energy - E [eV] Energy - E [eV]
F F F
FIG.3: Densityofstates(DOS)projectedattheatomsofmolecules;thesystemsandmethodsaredenotedwithinthepanels;bn
meansachainofnbenzenerings,X=COOH,Y=CH CN,Z=CH CF .
2 2 3
In the previous work [7], we showed that one of the systems studied here, namely a wire of b1(COOH,CH CN) molecules,
2 3
possessesverylocalizedstateattheconductionbandminimum(CBM)andthevalencebandtop(VBT).Undertheappliedvoltage,
the electrons moved from the central aromatic ring of the molecule to the neighboring ring, while the holes hopped between the
6
dipolegroups. Thispropertymightreducearecombinationofcarriersandisverydesiredforsolarcelldevices[35]. Therefore,we
characterizethestatesaroundthebandgapforthewirescomposedofsomeoftheπ-stackedmolecules,studiedinthisworkfortheir
absorptionenergy. Plotsoftheprojecteddensityofstates(PDOS)forwiresofbenzeneandpentacenedecoratedwithvariousdipole
groupsarecollectedinFig. 3. Thechoiceforthesmallestmolecule(benzene)ismotivatedbyaneedofmakingacomparison(of
theresultsforthedecoratedbenzene)toourpreviousstudies[7],usingthehybrid-DFTmethod. Whilethepentacenemoleculehas
beenchosen,sinceitpossessesthegapinthesunlightrange-andinthesametimevaryingatypeandanarrangementofthedipole
groups. We varied the type and the arrangement of the dipole groups attached to these molecules in order to check the transport
properties. Asonewillseefurther,changingthemesogenicpartofthemoleculedoesnotaltertheconclusions.
All results are obtained with the BLYP functional, except for only one case - namely b1(COOH,CH CN,CH CF ) - for which
2 2 3
the PDOS is calculated also with the B3LYP method. Figs. 3(g) and 3(h) compare these two methods and lead to the following
conclusions: 1)Theordersoftheenergybandsarethesame-specifically, theO-projectedstatesareclosetotheFermilevel, and
N-projectedDOSisdeeperintheenergy,whiletheC-ringPDOSisbetweentheO-andN-projectedstates. 2)Theonlydifference
isforthewidthoftheenergybandlocalizedattheC-ring-itismorenarrowintheB3LYPcaseandleadstothehighervalueofthe
PDOSattheedgeofthevalenceband. Sinceusingthemorecompuationallyexpensivemethoddoesnotchangetheconclusions,we
continuewiththeDFTapproachforthePDOSanalysis.
WhentheCOOHorCH CNdipolegroupsareattachedtoasinglebenzenering,thehighestoccupiedlevelsarecomposedofthe
2
stateslocalizedatdipolesandpartiallyonthecentralaromaticring,whilethelowestunoccupiedstatesarebuiltmainlyoftheC-ring
localizedorbitals. TheoxygenorbitalsareclosertotheFermilevelthanstatesoftheNorigin. Thefluorinestatesarethedeepest
intheenergyofallstudieddipolegroups. Moreover,ifonlyCH CF groupsareattachedtobenzenethenbothholesandelectrons
2 3
arepredictedtomovethroughthecentralring,whichisaveryunwantedsituation. SummarizingresultsinFigs. 3(a)-(h): thebest
spaceseparationsofthecarrierpathsareforCH CNandCOOH.Combinationsofthesegroupsworkaswell. TheCOOHgroupis
2
usedasaconnectingpartfortheplanarstructures,asstudiedinthepreviouswork[6]. Ithasbeendemonstrated[28],thatusingthe
COOHgroupforadepositionoftheopticalmaterialatthetransparentelectrodesinthesolarcelldevicesonecanobtainthehighest
photovoltaicconversionofallexperimentallytestedcontacts. Thus,onlycombinationsoftheCOOHandCH CNdipolesattached
2
topentacenemoleculesarestudiedfurther,becausetheyrepresentthegroupofmoleculeswhichhavetheenergygapsfallingwithin
aconsideredrangeoftheSunspectrum.
InFigs. 3(i)-(o),foreachstudiedcase,thehighestoccupiedstatesofthedipole-grouporiginareseparatedfromtheFermilevel
by at least one band. It seems that the carriers separation, found for the decorated benzene in our previous studies [7], may not
work very well for larger molecules. However, the PDOS for the dipole localized states is very high, which might cause that the
oscillator strength for the absorption is larger than that for the band positioned at the Fermi-level. The calculations of the optical
propertiesbymeansoftheGW+BSEaproacharenecessaryforafullinsight. Ontheotherhand,whenonebuildstheplanarsystems
withπ-stacking,andaddstheelectrodes,andappliesthevoltage-whichleadstotheStarkshiftoftheenergylevels-thenthehole
transportbetweenthedipolegroupsomittingthecentralaromaticframemightbeplausible.
aDensity of states [arb. units]) 11055 NCC ((rdiinpgosl)e) YYb2Y4 BYLYYP bDensity of states [arb. units])1210055 YY NN YY NNCCN2 (((rdb-iirbnpigdo2sgl)Yee))4 BLYP cDensity of states [arb. units]) 1210055 NCCC (((rdaicinpegotysl)ele)ne) YAYc-Abc2YYY4 BLYP
0 0 0
-6 -4 -2 0 2 4 6 -6 -4 -2 0 2 4 6 -6 -4 -2 0 2 4 6
Energy - E [eV] Energy - E [eV] Energy - E [eV]
F F F
d)20 e) f)
NC (rings) b2"Y4 BLYP OC (rings) b7’X6 BLYP NC (rings) b7’Y6 BLYP
Density of states [arb. units]11055 C (dipole) YY YY Density of states [arb. units]1200 C (dipole) XX XX XX Density of states [arb. units]1200 C (dipole) YY YY YY
0 0 0
-6 -4 -2 0 2 4 6 -6 -4 -2 0 2 4 6 -6 -4 -2 0 2 4 6
Energy - E [eV] Energy - E [eV] Energy - E [eV]
F F F
FIG.4: Densityofstates(DOS)projectedattheatomsofmolecules;thesystemsandmethodsaredenotedwithinthepanels;bn
meansanumberofbenzenerings,X=COOH,Y=CH CN,Acistheacetylenebridge-C≡C-. The”prime”and”bis”denote
2
differentwaysofconnectingthearomaticringsorshapesofthearomaticmolecularcores.
7
Additionally,wecheckedafewmorepossibleconnectionsoftwoaromaticrings,through:(i)theacetylene(-Ac-),or(ii)nitrogen
(-N-)bridges,or(iii)-C-C-bond. ThePDOSofnaphthaleneandbi-phenylwithfourCH CNgroups,andsimilarsystemswiththe
2
abovebridges,arepresentedinFigs4(a)-(d). ThereisonlyalittleimprovementofthepositioningofthedipolegroupsinthePDOS,
anditiswhenthe-N-bridgeisused, withrespecttotheotherpossibilities. ThismeansthatafteranadditionofCOOH,thelight
holeswillmovebetweenthecarboxylgroupsandtheheavyholesbetweentheCH CNdipoles,ifmanyterminalgroupsareattached
2
to the edges. Figs 4(e)-(f) display the projected DOS for the decorated coronene molecule. They confirm earlier findings for the
lineararomaticmolecules.
Aspromisedearlierinthiswork,wecommentnowonthetwostackingeffectsmentionedintheprecedingsubsection.Thestrength
ofthebandgaploweringduetostackingisrelatedtothebandsbroadeningclosetotheFermilevel. This, inturn, isafunctionof
astrengthoftheinteractionbetweentheneighboringmolecules,andofcoursethedistancebetweenthem(theclosestneighboring
groupsofatomsaretheCH moietiesbelowthemolecularplaneandtheCNorCF topsofthedipolesbelow). Sinceadditionof
2 3
theCOOHgroupmovesthelevelsofotherdipolesdownintheenergy, thebandbroadeningofthesedeeperstatesdoesnotaffect
so much the energy gap. Therefore, addition of COOH weakens the effect of stacking on the gaps of molecules with CH CN or
2
CH CF dipoles. Inthesameway,theB3LYPmethod-whichlowersacontributionofthedipole-groupprojectedDOSattheFermi
2 3
levelwithrespecttotheBLYP-leadstoasmallerstackingeffectonthebandgap. Thelatesteffectisduetothefactthat,theC-ring
statesoftheneighboringmoleculesoriginatefromthegroupsofatoms,whicharemoredistantthantheneighboringdipolesinthe
stack.
Absorptionspectraofthreemoleculesinaseriesofthegrowingsizeofthemesogenicpart
Attheend,wecomparethetheoreticalabsorptionspectraforaseriesofthreemoleculeswithgrowingnumberofbenzenerings
in a chain, i.e. 2, 5 and 9, but having the same number and type of the dipole groups, namely four COOH moieties attached on
the both sides ofthe longer molecular axis, as in Fig. 1 for b9(COOH) (i.g. b9X4) andin Fig. 3(i) for b5X4. These spectra are
4
simulatedwiththeYambocode[36],usingitspossibilitytocalculatethedielectricfunction. Theresponsefunctionwasobtainedon
therandomphaseapproximationlevel. InFig. 5,boththeinteracting(Im ε)andnoninteracting(Im ε )dielectricfunctionsshow
0
theblueshiftofthedominantabsorptionpeakswiththegrowingmolecularsize.
The imaginary part of the noninteracting dielectric functions have the absorption edges at the energies which correspond to the
DFTenergygaps-whichare: 2.99eVforb2X , 0.84eVforb5X , and0.04eVforb9X . Measuredabsorbanceismoresimilar
4 4 4
withtheinteractingdielectricfunction,whichhastheprominentpeaksbetween2and4eVforb5X andb9X ,andbetween4and
4 4
6eVforb2X . TheGW+BSEspectrumwouldbeshiftedupduetothemany-bodyeffectsanddownduetotheexcitoniceffects.
4
Nevertheless,ourmainmessagethatitispossibletotunetheopticalspectraofthedipoledecoratedmoleculesintheπ-stacksisstill
valid.
b2X4
b5X4
ε b9X4
m
I
b2X4
b5X4
0
ε b9X4
m
I
0 1 2 3 4 5 6
Energy [eV]
FIG.5: Theimaginarypartoftheinteracting(toppanel)andnoninteracting(bottompanel)dielectricfunctionforthreechosen
molecules,obtainedwiththeYambocode.
8
The second optimistic message is connected to the transport properties, which are correlated with the oscillator strenth of the
dipole optical transitions and creation of the electron-hole pairs. As we see from the interacting dielectric function, the lowest
absorptionpeakismuchhigherintheenergythantheHOMO-LUMOgap. ThismeansthattheopticaltransitionsbetweentheDOS
peakswhicharethemostclosetotheFermilevel(onitsoccupiedandunoccupiedsides)arenotallowed. Thesepeakswereofthe
sameorigin,namelytheywerelocalizedatthecentralC-ringsandnotthedipolegroups. Instead,thehigherenergeticpositionsof
thefirstabroptionpeaksinthesemoleculessuggestthattheallowedtransitionsarebetweentheC-ringsanddipolegroups. Thisisa
wantedproperty,becausetheelectron-holepairswillbegeneratedonthespaciallydistantpartsofthemolecule. Thus,weretainthe
spaceseparationofthechargetransportforelectronsandholesagain,forthelargermoleculesthanbenzene.
CONCLUSIONS
Ouraimistotailorthebandgapinthemolecularπ-stacks,inordertoproposesystems-withferroelectricpropertiesinvestigated
earlier[6,7]-forthesolarcellapplications. Tunningtheopticalpropertiesispossiblebyvaryinganumberthebenzeneringsand
a choice of the dipole groups when the molecules are small. While in cases of larger molecules, with longer aromatic chains, the
band gaps are almost independent on the terminal groups. On the other hand, a choice of the dipole groups and their number are
criticalparametersfortheatomiclocalizationofthehighestoccupiedandlowestunoccupiedstates. Therefore,thecharacterofthe
photogeneratedelectron-holepairissensitivetothechemicalconnectionsbetweentheneighboringmoleculesinthestacksandthis,
inturn,determinesthetransportproperties[7].
Summarizing: thelinearchains,betweenfiveandnineofthearomaticrings,aregoodcanditesforbuildingblocksoftheorganic
nanostructesforphotovoltaicapplications,whentheyareterminatedwiththeCOOHandCH CNgroups. WhileusingtheCH CF
2 2 3
groupsdoesnotgivethedesiredproperties. Thedipoleselectionrulesfortheopticaltransitionsretainthecharge-pathsselectivity,
whichappearstobelostwhenlookingjustatthePDOS.
ACKNOWLEDGEMENT
ThisworkhasbeensupportedbyTheNationalScienceCentreofPoland(theProjectNo. 2013/11/B/ST3/04041). Calculations
have been performed in the Cyfronet Computer Centre using Prometheus computer which is a part of the PL-Grid Infrastructure,
andbypartintheInterdisciplinaryCentreofMathematicalandComputerModeling(ICM).
[1] CookTR,YangRY,StangPJ(2013)Metal-OrganicFrameworksandSelf-AssembledSupramolecularCoordinationComplexes: Comparing
andContrastingtheDesign,SynthesisandFunctionalityofMetal-OrganicMaterials.ChemRev113(1):734-777
[2] ChakrabartyR,MukherjeePS,StangPJ(2011)SupramolecularCoordination:Self-AssemblyofFiniteTwo-andThree-DimensionalEnsem-
bles.ChemRev111(11):6810-6918
[3] Medina DD, Rotter JM, Hu Y, Dogru M, Werner V, Auras F, Markiewicz JT, Knochel P, Bein T (2015) Room temperature synthesis of
covalent-organicframeworkfilmsthroughvapor-assistedconversion.JAmChemSoc137(3):1016-1019
[4] Calik M, Auras F, Salonen LM, Bader K, Grill I, Handloser M, Medina DD, Dogru M, Lo¨bermann F, Trauner D, Hartschuh A, Bein T
(2014) Extraction of photogenerated electrons and holes from a covalent organic framework integrated heterojunction. J Am Chem Soc
136(51):17802-17807
[5] XiaoZ,YuanY,YangB,VanDersliceJ,ChenJ,DyckO,DuscherG,HuangJ(2014)Universalformationofcompositionallygradedbulk
heterojunctionforefficiencyenhancementinorganicphotovoltaics.AdvMater26(19):3068-3075
[6] Wierzbowska M, Wawrzyniak-Adamczewska M (2016) Cascade donoracceptor organic ferroelectric layers, between graphene sheets, for
solarcellapplications.RSCAdv6,49988-49994
[7] Wawrzyniak-AdamczewskaM,WierzbowskaM(2016)Separate-PathElectronandHoleTransportAcross-StackedFerroelectricsforPhoto-
voltaicApplications.JPhysChemC120(14),7748-7756
[8] SobolewskiAL(2015)Organicphotovoltaicswithoutp-njunctions:acomputationalstudyofferroelectriccolumnarmolecularclusters.Phys
ChemChemPhys17(32):20580-20587
[9] MottaC,El-MellouhiF,SanvitoS(2015)Chargecarriermobilityinhybridhalideperovskites.SciRep5:12746(1)-12746(8)
[10] LeijtensT1,StranksSD,EperonGE,LindbladR,JohanssonEM,McPhersonIJ,RensmoH,BallJM,LeeMM,SnaithHJ(2014)Electronic
propertiesofmeso-superstructuredandplanarorganometalhalideperovskitefilms: chargetrapping,photodoping,andcarriermobility.ACS
Nano8(7):7147-7155
[11] ZhaoYS,FuH,PengA,MaY,XiaoD,YaoJ(2008)Low-DimensionalNanomaterialsBasedonSmallOrganicMolecules:Preparationand
OptoelectronicProperties.AdvMater20(15):2859-2876
9
[12] XuL,YuY,LinJ,ZhouX,TianWQ,NieckarzD,SzabelskiP,LeiS(2016)On-surfacesynthesisoftwo-dimensionaliminepolymerswitha
tunablebandgap:acombinedSTM,DFTandMonteCarloinvestigation.Nanoscale8(16):8568-8574
[13] DengJP,ChenWH,ChiuSP,LinCH,WangBC(2014)Edge-terminationandcore-modificationeffectsofhexagonalnanosheetgraphene.
Molecules19(2):2361-2373
[14] Hu W, Lin L, Yang C, Yang J (2014) Electronic structure and aromaticity of large-scale hexagonal graphene nanoflakes. J Chem Phys
141(21):214704(1)-214704(10)
[15] SinghSK,Neek-AmalM,PeetersFM(2014)Electronicpropertiesofgraphenenano-flakes:energygap,permanentdipole,terminationeffect,
andRamanspectroscopy.JChemPhys140(7):074304(1)-074304(9)
[16] FrischMJetal.(2013)Gaussian09,RevisionD.01.Gaussian,Inc.,WallingfordCT
[17] DunningJrTH(1989)GaussianBasisSetsforUseinCorrelatedMolecularCalculations.I.TheAtomsBoronThroughNeonandHydrogen.
JChemPhys90(2):1007-1023
[18] BeckeAD(1993)Density-functionalthermochemistry.III.Theroleofexactexchange.JChemPhys98(7):5648-5652
[19] KohnW,ShamLJ(1965)Self-ConsistentEquationsIncludingExchangeandCorrelationEffects.PhysRev.140(4A):A1133-A1138
[20] BeckeAD(1988)Density-functionalexchange-energyapproximationwithcorrectasymptoticbehavior.PhysRevA,38(6):3098-3100
[21] LeeC,YangW,ParrRG(1988)DevelopmentoftheColle-Salvetticorrelation-energyformulaintoafunctionaloftheelectrondensity.Phys
RevB37(2):785-789
[22] Giannozzi P, Baroni S, Bonini N, Calandra M, Car R, Cavvazzoni C, et al. (2009) QUANTUM ESPRESSO: a modular and open-source
softwareprojectforquantumsimulationsofmaterials.JPhysCondensMatter21(39):395502(1)-395502(19)
[23] MonkhorstHJ,PackJD(1976)SpecialpointsforBrillouin-zoneintegrations.PhysRevB13(12):5188-5192
[24] Mostofi AA, Yates JR, Lee YS, Souza I, Vanderbilt D, Marzari N (2008) wannier90: A tool for obtaining maximally-localised Wannier
functions.ComputPhysCommun178:685-699
[25] MarzariN,VanderbiltD(1997)MaximallylocalizedgeneralizedWannierfunctionsforcompositeenergybands.PhysRevB56(20):12847-
12865
[26] MarzariN,MostofiAA,YatesJR,SouzaI,VanderbiltD(2012)MaximallylocalizedWannierfunctions: Theoryandapplications.RevMod
Phys84(4):1419-1475
[27] RestaR(1994)Macroscopicpolarizationincrystallinedielectrics:thegeometricphaseapproach.RevModPhys66(3):899-915
[28] ManoharanS,AsiriAM,AnandanS(2016)Impactofanchoringgroupsforimprovingthebindingnatureoforganicdyestowardhighefficient
dyesensitizedsolarcells.SolarEnergy126:22-31
[29] vanSettenMJ,CarusoF,SharifzadehS,RenX,SchefflerM,LiuF,LischnerJ,LinL,DeslippeJR,LouieSG,YangC,WeigendF,Neaton
JB,EversF,RinkeP(2015)GW100:BenchmarkingG0W0forMolecularSystems.JChemTheoryComput11(12):5665-5687
[30] BlaseX,AttaccaliteC(2011)Charge-transferexcitationsinmoleculardonor-acceptorcomplexeswithinthemany-bodyBethe-Salpeterap-
proach.ApplPhysLett99(17):171909(1)-171909(3)
[31] Lee J-Y, Tsai M-C, Chen P-C, Chen T-T, Chan K-L, Lee C-Y, Lee R-K (2015) Thickness Effects on Light Absorption and Scattering for
NanoparticlesintheShapeofHollowSpheres.JPhysChemC119(46):25754-25760
[32] Borysiuk J, Sołtys J, Piechota J (2011) Stacking sequence dependence of graphene layers on SiC (0001) - Experimental and theoretical
investigation.JApplPhys109(9):093523(1)-093523(6)
[33] NeatonJB,HybertsenMS,LouieSG(2006)RenormalizationofMolecularElectronicLevelsatMetal-MoleculeInterfaces.PhysRevLett
97(21):216405(1)-216405(4)
[34] HanazakiIJ(1972)Vapor-phaseelectrondonor-acceptorcomplexesoftetracyanoethyleneandofsulfurdioxide.JPhysChem76(14):1982-
1989
[35] WehrenfennigC,EperonGE,JohnstonMB,SnaithHJ,HerzLM(2014)HighChargeCarrierMobilitiesandLifetimesinOrganoleadTrihalide
Perovskites.AdvMater26(10):1584-1589
[36] MariniA,HoganC,Gru¨ningM,VarsanoD(2009)YAMBO:anabinitiotoolforexcitedstatecalculations.CompPhysComm180:1392-1403
10
SUPPLEMENTARYINFORMATION
TABLEI:NumericaldatasetforFig. 2: theLUMO-HOMOenergies(ineV)oftheisolatedmoleculeswithvariablenumberof
benzeneringsandthreedipolegroups: X=COOH,Y=CH CN,Z=CH CF .
2 2 3
b2X b2X b5X b5Z b5X b5Y b5X b5X b9X b9X
4 8 4 6 8 10 10 14 4 8
4.384 4.099 1.783 1.745 1.770 1.766 1.748 1.677 0.820 0.814
b9Z b9Y b9X b9X b17X b17X b17Z b17X b17Y b17X
10 14 14 22 4 8 18 22 22 38
0.808 0.821 0.810 0.778 0.568 0.568 0.547 0.556 0.544 0.549