M odeling Photovoltaic Perform ances of BTBPD-PC61BM System via Density Functional Theory Calculations

Ci-in ZhoZhi-hu TngXio-hu GuoHong-gung GeJin-qiMWen-ling Wng

a.Shaanxi Key Laboratory of Catalysis,School of Chem ical and Environmental Science,Shaanxi University of Technology,Hanzhong 723001,China

b.Key Laboratory forMacromolecular Science of ShaanxiProvince,School ofChem istry and Chem ical Engineering,ShaanxiNormal University,Xi’an 710062,China

M odeling Photovoltaic Perform ances of BTBPD-PC61BM System via Density Functional Theory Calculations

Cai-bin Zhaoa?,Zhi-hua Tanga,Xiao-hua Guoa,Hong-guang Gea?,Jian-qiMaa,Wen-liang Wangb

a.Shaanxi Key Laboratory of Catalysis,School of Chem ical and Environmental Science,Shaanxi University of Technology,Hanzhong 723001,China

b.Key Laboratory forMacromolecular Science of ShaanxiProvince,School ofChem istry and Chem ical Engineering,ShaanxiNormal University,Xi’an 710062,China

Designing and fabricating high-performance photovoltaic devices have rem ained a m ajor challenge in organic solar cell technologies.In this work,the photovoltaic performances of BTBPD-PC61BM system were theoretically investigated by means of density functional theory calculations coup led w ith the M arcus charge transfer m odel in order to seek novel photovoltaic system s.M oreover,the hole-transfer properties of BTBPD thin-fi lm were also studied by an amorphouscellw ith 100BTBPDmolecules.Results revealed that the BTBPDPC61BM system possessed a m idd le-sized open-circuit voltage of 0.70 V,large short-circuit current density of 16.874 m A/cm2,large fi ll factor of 0.846,and high power conversion efficiency of 10%.W ith the Marcusmodel,the charge-dissociation rate constant was predicted to be as fast as 3.079×1013s?1in the BTBPD-PC61BM interface,which was as 3?5 orders ofm agnitude large as the decay(radiative and non-radiative)rate constant(108?1010s?1), indicating very high charge-dissociation effi ciency(～100%)in the BTBPD-PC61BM system. Furthermore,by themolecular dynam ics simulation,the holemobility for BTBPD thin-fi lm was predicted to be as high as 3.970×10?3cm2V?1s?1,which can be attributed to its tight packing in solid state.

BTBPD,PC61BM,Photovoltaic performances,Density functional theory

I.INTRODUCTION

In the past 100 years,w ith the overconsum ption for fossil energies(coal,petroleum,and natural gas),environmentalpollution problem shave received w idespread attention,and actively exp loring for the clean and renewable energy has being become a hot and focus issue [1,2].Asone of themost prom ising long-term solutions for the clean and renewable energy,free-metal photovoltaic technology has attracted intense interests in recent years due to its num erous advantages com pared to the commercial inorganic photovoltaic technology,such as low manufacturing cost,flexibility,ease of solvent processing,and large-area capability[3?6].Previous studies indicated that the high-performance donorm aterials should meet the follow ing requirements:(i)narrow optical band gap,(ii)low-lying highest occupied m olecular orbital(HOMO)level,and(iii)high hole carrier m obility[7?9].Unfortunately,electron-donating materials that simultaneously satisfy those three demands are still scarce up to date.

Recently,Caiet al.synthesized a novel small molecule material(BTBPD)w ith the donor-acceptordonor(D-A-D)character,and found that the thin-fi lm field effect transistor fabricated w ith BTBPD had high hole mobility under natural ambient conditions[10]. M ore interestingly,BTBPD also exhibited the prom inent capture to solar radiation,and its strongest absorption peak was found to red-shift to 696 nm in solid state.In a word,all properties suggest that BTBPD should be an excellent electron donor candidate.In this work,taking BTBPD as donor and[6,6]-phenyl-C61-butyric acid methyl ester(PC61BM)as acceptor, we carried out a systematic theoretical study on the photovoltaic properties for BTBPD-PC61BM system by means of quantum chem istry and molecular dynam ics calculationscoup led w ith the incoherent chargehopping model in order to seek novel high-perform ance photovoltaic system s.In this work,our m ain ob jectives are to theoretically exp lore the app licability of BTBPD as an electron-donating material and estimate the photovoltaic performancesof BTBPD-PC61BM system.Theoretical calculations clearly show that BTBPD,as expected,is an excellent electron donormaterial,and the power conversion effi ciency(PCE)of BTBPD-PC61BM system theoretically reaches up to 10%.

II.COMPUTATIONAL METHODS

To sim p lify calculations,the long-alkyl chain(2-ethylhexyl)in BTBPD was rep laced w ith the CH3,because it has been confi rmed that the substituted alkyl in organic com pounds has hardly any effect on their electronic structure and optical properties,and m erely prom otes solubility[11?13].A ll stable species were fully optim ized w ithout any symmetry constraints by means of density functional theory(DFT)calculations w ith the B3LYP hybrid functional[14]and the6-31G(d) basis set,w ith subsequent frequency calculations to confi rm that they were true m inima of potential energy surface.Based on the optim ized geom etries,the UV-Vis spectrum for BTBPD was simu lated w ith the time-dependent density functional theory(TD-DFT) [15,16]and the B3LYP/6-31G(d)scheme.In order to determ ine them ost reasonable geometry of BTBPDPC61BM com p lex,the detailed potential-surface scan was carried out between PC61BM and BTBPD w ith the CAM-B3LYP-D3(BJ)/6-31G(d)method[17,18]. As seen in FIG.S1(supp lementary m aterials),the BTBPD-PC61BM com p lex was found to be the m ost stable when the centroids distance of PC61BM and BTBPD is at 8.0?A,which is in good agreement w ith the recent studies[19,20].Then,in subsequent calculations,the centroids distance of PC61BM and BTBPD was invariably fixed at 8.0?A.In addition,in thiswork the influence ofmolecular orientation was also considered.As is shown in FIG.S2(supp lem entary m aterials),themolecular orientation affects a little on the BTBPD-PC61BM com plex.Based on optim ized structures for PC61BM,BTBPD,and BTBPD-PC61BM com p lex,total density of states(TDOS)and partial density of states(PDOS)were visualized w ith the Multiw fn 3.3.6 software developed by Luet al.[21,22].A ll quantum chem istry calculations were carried out w ith the Gaussian 09 software[23].

III.RESULTS AND DISCUSSION

A.Photovoltaic perform ances of BTBPD-PC61BM system

1.Electronic properties and open circuit-voltage

FIG.1 M olecular structures of BTBPD and PC61BM.

BTBPD and PC61BM molecular structures are depicted in FIG.1.The geom etric optim ization revealed that BTBPD m olecule has a near p lanar conform ation(FIG.S3 in supplementary materials),and the dihedral angle(α)between its adjacent units is close to 20?,which indicates its goodπ-conjugated character.FIG.2 shows the TDOS and PDOS of PC61BM, BTBPD,and BTBPD-PC61BM com plex.W ith the DOS,it is very easy to directly observe the contribution from each substituent to the frontier molecular orbital (FMO).As seen,in PC61BM molecule all density of HOMOs and LUMOs was found to concentrate on the C60sphere in theenergy range from?10.0 eV to 2.0 eV, and the contribution from the substituent(methyl-4-phenylbutanoate)is very small,m eaning the substituent only enhances the C60solubility,and hasa little influence on its electronic properties,which agreeswell w ith the previous experimental studies[24,25].Moreover,it can be noticed that CH3contributes very small to the HOMO and LUMO in BTBPD m olecule,verifying it is rational to rep lace 2-ethylhexylw ith CH3in the current work.Interestingly,the benzo[b]thiophene (BT)and bipyrrolylidene-2,2′(1H,1′H)-dione(BPD)in BTBPD molecule contribute very much to both the HOMO and the LUMO,denoting the HOMO and LUMO of BTBPD delocalize over them olecular skeleton,rather than centralize at a certain molecular fragment,which benefi ts the rapid charge-transfer between two molecules.As for BTBPD-PC61BM com p lex,the HOMO and the LUMO exhibit an obvious separation characteristic,and the HOMO com p letely locates on the BTBPD,while the LUMO mainly centuries on the PC61BM,which suggests the easy formation of BTBPD·+-PC61BM·?charge-separated state.According to the previous study,the open circuit-voltage for organic solar cells(OSCs),Voc,can be estimated w ith [26]:

FIG.2 Total density of states and partial density of states of(a)PC61BM,(b)BTBPD,and(c)PC61BM-BTBPD com p lex.

FIG.3 Predicted PCE for BTBPD-PC61BM cell w ith the Scharber diagram.

whereEHOMO(D)andELUMO(A)are the HOMO level of donor and the LUMO levelof PC61BM,eis the electron charge,and the value of 0.3 is an em pirical factor.Then,based on the experiment HOMO(?5.0 eV [10])for BTBPD and LUMO(?4.0 eV[27,28])for PC61BM,theVocwasestim ated to be as large as0.70 V for BTBPD-PC61BM system.M ore interestingly,the PCE of BTBPD-PC61BM system was predicted to be over 10%(FIG.3)by means of the Scharber diagram, indicating the BTBPD-PC61BM system is a prom ising OSC candidate.

2.Charge binding energy and optical absorption properties

As is well-known,the charge binding energy(Eb) is one of the most parameters in photovoltaic devices, which is directly related to the charge separation.UsuallyEbis taken as the difference between the transport gap(Et)and the optical band gap(Eopt).The former is the diff erence between the adiabatic ionization potential(EAIP)and electron affi nity(EAEA)of donor in the solid state,while the latter is taken as the fi rst-singlet em ission energy(Em).Then,theEbcan be calculated as the follow ing expression[29]:

As seen in Eq.(2),to calculateEb,theEAIPandEAEAofdonor in solid state fi rstly should be calculated.Here,theEAIP/EAEAof solid BTBPD was estim ated via the scheme reported by Schwennet al.[30],which hasbeen verified to be an excellent selection that estimates the electronic properties of organic m aterials in the solid state.Table I shows calculatedEAIPandEAEAvalues for BTBPD in gas phase and solid statew ith two different DFT methods.It can be noted thatEbestimated by two m ethods is as large as 1.596 and 1.733 eV in gas phase,which ismuch larger com pared w ith those measured values of 0.2?1.0 eV in many organic materials[31],which can be attributed to the solid stacking eff ect.Com paring the results in gas phase to the ones in solid state,it can be noticed that in gas phaseEAIPis larger,whileEAEAis smaller,which is sim ilar to the measured and theoretical results in acenes[32].According to the calculatedEAIP,EAEA,andEmfor the solid BTBPD,theEbwas estim ated to be about 0.594 eV. The precious study showed that the exciton is unstablewhenEb

TABLE I CalculatedEAIP,EAEA,andEbvalues in the gas and solid state for BTBPD w ith two diff erent DFT methods.

As is known to all,the good harvest for solar radiation isessential for effi cient dye sensitizers,which determ ines the short-circuit current densityJscof DSC de-vices to some extent.To exp lore reliab le DFT m ethods estim ating op tical absorption properties for BTBPD,a set of popular DFT methods were tested.As seen in Table II,com pared w ith the experimental value,the B3LYP hybrid functional can estim ate accurately the excited energy of BTBPD,and the derivation between the theoretical and experimental values is only about 3.0 nm(about 0.008 eV).Moreover,it can be noticed that the strongest absorp tion in UV-Vis spectrum for the BTBPD molecule can be assigned to theπ-π?type, and dom inated com pletely by the electron transition of HOMO→LUMO(～100%).In addition,as observed in FIG.4,the TD-B3LYP/6-31G(d)method can reproduce well the UV-Vis spectrum of BTBPD m olecule in solid state,which confi rm s again themethod reliability used in this work.Since the HOMO and LUMO for BTBPD distribute the whole m olecule skeleton(FIG. S4 in supplementary materials),the lowest-excited singlet is a typically local excited state,and no obvious charge is transferred in light absorption process.

TABLE II Calculated excited energies(λmax),molar absorption coeffi cients(ε),oscillator strengths(f),and main configuration for BTBPD w ith diff erent DFT m ethods coup led w ith the 6-31G(d,p)basis set.

FIG.4 Simu lated and experim ental absorp tion spectra for BTBPD in solid state.

3.Short-circuit current densityJsc,fi ll factorFF,and PCEη

Short-circuit current densityJscis another key parameter that determ ines the PCE ofOSC devices,which can be expressed as[34,35]:

FIG.5 PredictedJscandηλfor BTBPD-PC61BM cell.

whereS(λ)is incident photon-to-current conversion efficiency at a fixed wavelength,eis the unit charge, andηEQE(λ)is the external quantum effi ciency.TheηEQE(λ)term can be described as the product ofηλ(light-harvesting effi ciency),ηCT(charge transfer efficiency),andηcoll(charge collection effi ciency)[36],

whereηλcan be calculated asηλ=1?10?f,fis the oscillator strength.Then,to estimate themaximumJsc, we sent theηCT=1.0 and theηcoll=1.0.Our calculation showed thatfisabout 1.3963 at the lowest-excited singlet state for BTBPD,then yielding theηλ=0.752. FIG.5 shows that the simulatedηλandJscw ith the above-mentioned parameters.As seen,theJscwas estimated to be ashigh as16.874m A/cm2for the BTBPDPC61BM system,which can be attributed to its strong spectral response.In addition,it can be noticed that theηλis as large as 81.7%in visible region.Relatively, BTBPD has a weak cap ture for ultraviolet radiation (ηλ≈57%).For theFFcalculation,an approxim ate scheme can be expressed as[37,38],

whereνocis the dimensionless voltage,which can be estim ated w ith theVoc[39,40],

wherekB,Tandqare Boltzmann constant,temperature(here,we setT=300 K),and elementary charge respectively,nis an ideality factor relating to an ideal (n=1)or non-ideal(n>1)diode[41],organic solar cells typically have ideality factors in the range of 1.5?2.0 due to their inherent disorder[42].According to the calculatedVoc(0.70 V)for the BTBPD-PC61BM system,theνocwas estim ated to be 27.08 atn=1.0 and 13.54 atn=2,then,theFFfor P61BM-BTBPD was predicted to be as high as 0.748(n=2.0)and 0.846 (n=1.0),in excellent agreem ent w ith m easured values in most OSC devices.According to the previous study, the PCE(η)of OSC devices can be estimated with the follow ing equation[43,44]

wherePmaxandPin(=100mW/cm2)are themaximum and incident power respectively.W ith the calculatedVoc,Jsc,andFF,the PCE of BTBPD-PC61BM system was predicted to be 8.83%(n=2.0)and 9.99%(n=1.0), which is slightly smaller than the value(>10%)estimated by the Scharber diagram.

B.Charge dissociation and recom bination rates

Generally,thecharge transfer in organic photoelectric m aterials obeys the incoherent charge-hopping m echanism,and the transfer rate constant between donor and acceptor,kDA,can be evaluated via the Marcusmodel [45,46],

whereλis the total reorganization energy,VDAis the eff ective charge transfer integralbetween donor and acceptor,?Gis theGibbs free energy changebetween the initial and final states,kBis Boltzm ann constant,his Planck constant,andTis the tem perature(here,we setT=300 K).

1.Gibbs free energy change in charge dissociation and recombination

As seen in Eq.(8),the Gibbs free energy change,?G, has a remarkable influence on thekDA.Generally,the?Gcan be estimated as the energy diff erence in the final and initial states,accounting for the Coulombic attraction between the two charges in charge-separated state.Thus,for the charge-dissociation,the?Gisw ritten as[47],

whereqDandqAare the atom ic charges on donor and acceptor in their relevant states w ith a separation distance,rDA.Theε0is the vacuum dielectric constant (8.854×10?12F/m),and theεsis the static dielectric constant ofm edium.Sim ilarly,the Gibbs free energy change(?Grec)in charge recombination can also be estimated w ith the expression sim ilar to Eq.(9)and Eq.(10).Here,theεsis estim ated w ith the Clausius-M ossotti equation[48],

whereVis the Connolly molecular volume,is the isotropic com ponent of molecular polarizability,,and theαiiis the diagonalmatrix elements of fi rst-order polarizability tensor.Calculations show that theεsis3.653 for BTBPD,which is in accord w ith themeasured values(ranging from 2.0 to 5.0[49, 50])in most organic m aterials.As for PC61BM,the experimentalεsvalue of 3.9[51]was used in thiswork. The totalεsof BTBPD-PC61BM system was taken as an average of their respective contributions.Our calculation showed that the?Gdisis about?0.316 eV, while the?Grecis smaller(?0.640 eV).As seen,the?Gdisand?Grecare consistently calculated to be negative,denoting that the charge-dissociation and chargerecombination arealways favorable in thermodynam ics. In addition,thesmaller?Grecindicated a larger driving force in charge-recombination process.

2.Reorganization energies in charge dissociation and recombination

Generally,in organic solids the total reorganization energy(λ)of electron transfer can be divided into two parts,namely the internal reorganization energy(λint)and theexternalone(λext).Theλintterm can be calculated w ith the adiabatic potentialenergy surface(PES) m ethod[52,53].In the case of charge dissociation,theλintis actually taken as an average of the follow ingλ1andλ2[54],

where(Q+)and(Q?)are the energies of donors in the lowest excited-statew ith the equilibrium geom etries of cationic and excited state respectively,(Q?) and(Q+)are the energies of donors in the cationic states w ith the equilibrium geometries of excited and cationic states respectively,(Q?)and(Q0)are the energies of acceptors in the neutral statesw ith the equilibrium geometries of anion and neutral states,respectively,and(Q0)/(Q?)are the energies of acceptors in the anionic states w ith the equilibrium geometries of neutral and anionic states.As seen in Table III,our calculation showed that theλint(λdis) is 0.191 eV in charge-dissociation process for BTBPDPC61BM,which rem arkably increases to 0.348 eV in the case of charge recombination.Com pared w ith theλint,theλextwas diffi cult to be accurately calculated. Here,we used the classical dielectric continuum model initially developed by M arcus for the electron-transfer reaction between spherical ions in solution to estim ate theλext.According to thismodel,theλextterm isgiven by[55],

whereεopis the optical dielectric constant ofmedium,RD(=6.41?A for BTBPD)andRA(=6.50?A for PC61BM)are the eff ective radii of donor and acceptor estimated as the radius of sphere having the sam e surface as the surface accessible area ofmolecule.TheqDandqAdenote the atom ic charges on the ions.Theεopwhich can be estim ated w ith the Lorentz-Lorenz equation[56,57],

wherenis the refractive index,Vmis themolar volume (Vm=M/ρ,Mis the molar mass,andρis the density ofm aterial),Ris the molar refraction.Here,theρwas estimated w ith them olecular dynam icsm ethod, and the simulated detailwas shown in the supp lementary materials.Our results showed theεopandρfor BTBPD were equal to 2.960 and 1.312 g/cm3respectively.As for PC61BM,the experimental refractive index(n=1.866)is used to estimate to theεop,which is equal to 3.482 according to our estimation.W ith the above-m entioned param eters,theλextcan be conveniently obtained.At the case of BTBPD-PC61BM,theλextis equal to 0.103 eV.Summ ary,theλis 0.294 eV in charge-dissociation process for BTBPD-PC61BM system,which remarkably increases to 0.451 eV for the charge-recombination process.

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TABLE III Calculatedλdis,λrec,andλextvalues in the gas and solid state for BTBPD w ith two diff erent DFT m ethods.

3.Charge transfer integral in charge dissociation and recombination

As seen in Eq.(8),theVDAis an im portant param eter that determ ines thekDA,in this work,the directcoup ling(DC)method coup led w ith the PW 91PW 91/6-31G(d)schemewasused to estimateVDA[58,59],which have been illustrated to present themost accurateVDAvalue at the DFT level[60,61].In term s of the DC scheme,theVDAvalue of charge transfer can be calculated by the follow ing exp ression[62],

whereTD(i)A(j)is the charge transfer integral of theith molecular orbital of donor and thejth molecular orbital of acceptor,SD(i)A(j)is the spatial overlap integral of the above two m olecular orbitals,andeD(i)/eA(j)is the site energy.TD(i)A(j),SD(i)A(j),andeD(i)/eA(j)can be obtained from theandAmong them,ψD(i)is the HOMO(for charge-recombination)or LUMO(for charge-dissociation)of donor,ψA(j)is the LUMO of acceptor,andFKSis the Kohn-Sham matrix of donor-acceptor system.TheFKScan be obtained from

whereSis the intermolecular overlap matrix,Cis the m olecular orbital coeffi cient m atrix from the isolated monom er,andεis the orbital energy from onestep diagonalization w ithout iteration.Generally,theVDAin the charge-dissociation process is taken as the coup ling between the LUMO of donor and acceptor.However,since the LUMO+1 and LUMO+2 in PC61BM are degenerated energetically w ith its LUMO [63],theVDAbetween the LUMO of BTBPD and the LUMO+1/LUMO+2 of PC61BM was also computed.Finally,the averageVDAvalue((V1V2V3)1/3)was viewed as the totalVDAand then applied to estimate the charge-dissociation rate.As for the chargerecombination,the sam e treatm ent was done.Calculations show that theVDAin the charge dissociation for the BTBPD-PC61BM is?31.82 meV,which is equal to 20.37 meV for the charge-recombination process. Based on the calculatedλandVDAvalues,the chargedissociation(kdis)and charge-recombination(krec)rate constants were estimated to be as high as 3.079×1013and 4.808×1012s?1respectively in BTBPD-PC61BM com p lex.Recent studies illustrated that the decay rate constant(kd)ofexcited organicmolecules typically ranges 1.0×108s?1to 1.0×1010s?1[64].Our results showed that thekdisis larger than thekd3?5 orders ofm agnitude,which indicates high charge-dissociation effi ciency(～100%)in the BTBPD-PC61BM system. In addition,although thekrecis relatively large,the charge-recombination effi ciency is still very low.According to previous studies,the electron transferred onto PC61BM can be rapidly converted to the trip let state from the singlet state[63,64],which remarkably hinders from the recombination of free carriers.

C.Hole transfer rate and hole m obility in BTBPD thin-fi lm

As is known to all,the charge transport ability of donor remarkably aff ects the solar cell’s perform ance. Thus,it is essential to discuss charge transport properties of BTBPD thin-fi lm.Generally,the charge transport ability of organicmaterials can be chartered with its carriermobility,μ,which can be calculated bymeans of the Einstein-Sm oluchowski equation[67,68],

whereDis diff usion coeffi cient,eis elem entary charge,kBis Boltzmann constant,andTis absolute tem perature,respectively.TheDcan be estimated by means of the follow ing appropriate relation[69,70]:

wherenis the spatial dim ensionality,which is 3 in organic solids,diis the centroids distance of theith hopping dimer,kiis the charge transfer rate constant, andPiis the hopping probability,In this work,the chargem obility of BTBPD thin-fi lm wasevaluated bymeansof an amorphous cellw ith 100 BTBPD molecules built by means of the molecular dynam ics simulation.Table IV lists the calculated theλintterm w ith two different DFT methods.As seen,the CAMB3LYP/6-31G(d,p)schemepresentsquite largeλintvalues due to the long-range correlation eff ect.In addition,it can be noticed that theλintin solid state is obviously smaller than that in gas phase,denotingthat the solid stack to som e extent,lim its the structural relaxation of BTBPD molecule in charge transfer process.Since the donor materials in OSC devices usually keep in solid state under operating conditions, theλintestim ated in the solid state ism ore reasonable. To exp lore possible charge transfer dim ers,21 m olecular pairs w ith the relatively largeVDAvalues were abstracted from the optim ized amorphous cell,and their geometries,centroids distances,as well as estimatedVDAvalueswere shown in Table S1(supp lementarymaterials).Based on theλintthe solid state andVDAvalues,the hole carrier mobility,μh,was estimated to be ashigh as3.970×10?3cm2V?1s?1in the solid BTBPD, which is in excellent agreementw ith itsmeasured value (3.0×10?3?8.4×10?3cm2V?1s?1[10].According to the previous investigation,for high-performance OSC devices,theμhshould be not less than 10?3cm2V?1s?1[26].Our estimation showed as a potential donormaterialof OSC devices,the BTBPD can rapid ly transports holes.

TABLE IV Calcu latedλintfor BTBPD in solid and gas states w ith two diff erent DFT m ethods.

IV.CONCLUSION

In summary,BTBPD-PC61BM as a prom ising OSC system was theoretically studied bymeansof quantumchem ical and molecular dynam ics calculations.Results showed that BTBPD-PC61BM system possesses m idd le-sized open-circuit voltage(0.7 V),large shortcircuit current density(16.874m A/cm2),high fi ll factor (0.846),and high PCE(>10%).In addition,BTBPD was also revealed to possess the strong optical response, and suitable charge-binding energy(0.457 eV).Using the Marcus model,thekdiswas estimated to be as large as 3.079×1013s?1in the BTBPD-PC61BM blend,which indicated very high charge-dissociation effi ciency.Moreover,by means of an amorphous cell modelw ith 100 BTBPD molecules,the hole carriermobility of BTBPD thin fi lm was predicted to be as high as 3.970×10?3cm2V?1s?1.In brief,our calculation shows that BTBPD is a very potential donormaterial, and the BTBPD-PC61BM system isa high-performance OSC candidate.However,these results need to be verified by experim ents.

Supp lem en tary m aterial:Detailed potential-surface scan,optim ized BTBPD geom etry,calculated the lowest-excited energy for BTBPD,HOMO and LUMOof BTBPD,and detailed description for molecular dynam ics simulation are shown.

V.ACKNOW LEDGEM ENTS

This work was supported by the National Natural Science Foundation of China(No.21373132, No.21502109,No.21603133),the Education Department of Shaanxi Provincial Government Research Projects(No.16JK 1142,No.16JK 1134),and the Scientific Research Foundation of Shaanxi University of Technology for Recruited Talents(No.SLGKYQD2-13, No.SLGKYQD2-10,No.SLGQD14-10).

[1]A.M.Bagher,Sust.Energy.2,85(2014).

[2]O.Ellabbana,H.Abu-Rub,and F.B laab jerg,Renew. Sust.Energy.Rev.39,748(2014).

[3]A.Hagfeld t,G.Boschloo,L.Sun,L.K loo,and H.Pettersson,Chem.Rev.110,6595(2010).

[4]M.T.Spitler and B.A.Parkinson,Acc.Chem.Res. 42,2017(2009).

[5]S.Lew is,Science 315,798(2007).

[6]M.G r¨atzel,Acc.Chem.Res.42,1788(2009).

[7]J.Peet,M.L.Senatore,A.J.Heeger,and G.C.Bazan, Adv.Mater.21,1521(2009).

[8]M.C.Scharber,D.M hlbacher,M.Koppe,P.Denk,C. Waldauf,A.J.Heeger,and C.J.Brabec,Adv.Mater. 18,789(2006).

[9]P.Sista,H.Nguyen,J.M urphy,J.Hao,D.K.Dei,K. Palaniappan,J.Servello,R.S.Kularatne,B.E.Gnade, B.Xue,P.C.Dastoor,M.C.Biewer,and M.C.Stefan, Macromolecules 43,7875(2010).

[10]Z.Cai,Y.Guo,S.Yang,Q.Peng,H.Luo,Z.Liu,G. Zhang,Y.Liu,and D.Zhang,Chem.Mater.25,471 (2013).

[11]Y.Y i,V.Coropceanu,and J.L.Br′edas,J.M ater. Chem.21,1479(2011).

[12]T.Liu,J.S.Gao,B.H.X ia,X.Zhou,and H.X.Zhang, Polym er 48,502(2007).

[13]S.Goeb,A.De Nicola,and R.Ziessel,J.O rg.Chem. 70,1518(2005).

[14]A.D.Becke,J.Chem.Phys.98,5648(1993).

[15]E.Runge and E.K.U.G ross,Phys.Rev.Lett.52,997 (1984).

[16]R.Bauernschm itt and R.Ahlrichs,Chem.Phys.Lett. 256,454(1996).

[17]T.Yanai,D.P.Tew,and N.C.Handy,Chem.Phys. Lett.393,51(2004).

[18]K.Aidas,A.M?gelh?j,E.J.K.Nilsson,M.S.Johnson, K.V.M ikkelsen,O.Christiansen,P.S¨oderhjelm,and J.Kongsted,J.Chem.Phys.128,194503(2008).

[19]T.Liu and A.Troisi,J.Phys.Chem.C 115,2406 (2011).

[20]C.Zhao,Z.Wang,K.Zhou,H.Ge,Q.Zhang,L.Jin,W. W ang,and S.Y in,Acta Chim.Sinica 74,251(2016).

[21]T.Lu and F.Chen,J.Com p.Chem.33,580(2012).

[22]T.Lu and F.Chen,J.M ol.G raph.M odel.38,314 (2012).

[23]M.J.Frisch,G.W.Trucks,H.B.Schlegel,G.E. Scuseria,M.A.Robb,J.R.Cheesem an,G.Scalm ani, V.Barone,B.M ennucci,G.A.Petersson,H.Nakatsu ji,M.Caricato,X.Li,H.P.Hratchian,A.F.Izm ay lov,J.B loino,G.Zheng,J.L.Sonnenberg,M. Hada,M.Ehara,K.Toyota,R.Fukuda,J.Hasegawa, M.Ishida,T.Nakajim a,Y.Honda,O.K itao,H.Nakai, T.Vreven,J.J.A.M ontgom ery,J.E.Peralta,F. Ogliaro,M.Bearpark,J.J.Heyd,E.Brothers,K.N. Kudin,V.N.Staroverov,R.Kobayashi,J.Norm and, K.Raghavachari,A.Rendell,J.C.Burant,S.S.Iyengar,J.Tom asi,M.Cossi,N.Rega,J.M.M illam,M. K lene,J.E.Knox,J.B.Cross,V.Bakken,C.Adam o,J. Jaram illo,R.Gom perts,R.E.Stratm ann,O.Yazyev, A.J.Austin,R.Camm i,C.Pom elli,J.W.Ochterski, R.L.Martin,K.Morokuma,V.G.Zakrzewski,G.A. Voth,P.Salvador,J.J.Dannenberg,S.Dapprich,A. D.Daniels,O.Farkas,J.B.Foresman,J.V.Ortiz,J. Cioslowski,and D.J.Fox,Gaussian 09,Revision A.02, Wallingford,CT,USA:Gaussian Inc.(2009).

[24]L.Zheng,Q.Zhou,X.Deng,M.Yuan,G.Yu,and Y. Cao,J.Phys.Chem.B 108,11921(2004).

[25]X.Wang,Y.Guo,Y.Xiao,L.Zhang,G.Yu,and Y. Liu,J.M ater.Chem.19,3258(2009).

[26]M.C.Scharber,D.M hlbacher,M.Koppe,P.Denk,C. Waldauf,A.J.Heeger,and C.J.Brabec,Adv.Mater. 18,789(2006).

[27]J.C.Hummelen,B.W.Knight,F.LePeq,F.Wud l,J. Yao,and C.L.W ilkins,J.Org.Chem.60,532(1995).

[28]Z.Xu,L.M.Chen,M.H.Chen,G.Li,and Y.Yang, App l.Phys.Lett.95,013301(2009).

[29]P.K.Nayak and N.Periasam y,O rg.Electron.10,1396 (2009).

[30]P.E.Schwenn,P.L.Burn,and B.J.Powell,O rg.Electron.12,394(2011).

[31]B.P.Rand,J.Genoe,P.Herem ans,and Poortm ans,J. Prog.Photovolt:Res.App l.15,659(2007).

[32]J.E.Norton and J.L.Br′edas,J.Am.Chem.Soc.130, 12377(2008).

[33]Y.Li,T.Pullerits,M.Zhao,and M.Sun,J.Phys. Chem.C 115,21865(2011).

[34]P.Peum ans,A.Yakim ov,and S.R.Forrest,J.App l. Phys.93,3693(2003).

[35]N.B′erub′e,V.Gosselin,J.Gaudreau,and M.C?ot′e,J. Phys.Chem.C 117,7964(2013).

[36]X.Liu,W.Shen,R.He,Y.Luo,and M.Li,J.Phys. Chem.C 118,17266(2014).

[37]X.Guo,N.Zhou,S.Lou,J.Sm ith,D.T ice,J.Hennek, R.O rtiz,J.T.L.Navarrete,S.Li,J.Strzalka,L.Chen, R.P.H.Chang,A.Facchetti,and T.J.Marks,Nat. Photonics.7,825(2013).

[38]D.Gupta,S.M ukhopadhyay,and K.Narayan,Sol.Energy M ater.Sol.Cells.94,1309(2010).

[39]Y.Zhou,C.Fuentes-Hernandez,J.W.Shim,T.M. Khan,and B.K ippelen,Energy Environ.Sci.5,9827 (2012).

[40]X.Liu,C.Huang,W.Shen,R.He,and M.Li,J.M ol. M odel.22,15(2016).

[41]M.A.Green,Solid-State Electron.24,788(1981).

[42]B.K ippelen and J.L.Br′edas,Energy Environ.Sci.2, 251(2009).

[43]S.A rdo and G.J.Meyer,Chem.Soc.Rev.38,115 (2009).

[44]G.P.Smestad and M.Gr¨atzel,J.Chem.Educ.75,752 (1998).

[45]R.A.M arcus,Rev.M od.Phys.65,599(1993).

[46]R.A.M arcus,Ann.Rev.Phys.Chem.15,155(1964).

[47]V.Lem aur,M.Steel,D.Beljonne,J.L.B r′edas,and J. Cornil,J.Am.Chem.Soc.127,6077(2005).

[48]O.F.M ossotti,M em orie M at.Fis.M odena 24,49 (1985).

[49]D.Y.Zang,F.F.So,and S.R.Forrest,App l.Phys. Lett.59,823(1991).

[50]G.Brocks,J.van den Brink,and A.F.Morpurgo,Phys. Rev.Lett.93,146405(2004).

[51]V.D.M ihailetchi,J.K.J.van Duren,P.W.M.B lom, J.C.Humm elen,R.A.J.Janssen,J.M.K roon,M. T.Rispens,W.J.H.Verhees,and M.M.W ienk,Adv. Funct.M ater.13,43(2003).

[52]M.M alagoliand J.L.B r′edas,Chem.Phys.Lett.327, 13(2000).

[53]V.Lem aur,D.A.da Silva Filho,V.Coropceanu,M. Lehm ann,Y.Geerts,J.Piris,M.G.Debije,A.M.van de Craats,K.Senthilkumar,L.D.A.Siebbeles,J.M. W arm an,J.L.B r′edas,and J.Cornil,J.Am.Chem. Soc.126,3271(2004).

[54]M.X.Zhang,S.Chai,and G.J.Zhao,O rg.Electron. 13,215(2012).

[55]R.A.M arcus,J.Chem.Phys.43,679(1965).

[56]H.A.Lorentz,Ann.Phys.9,641(1880).

[57]L.Lorenz,Ann.Phys.11,70(1880).

[58]S.Yin,Y.Yi,Q.Li,G.Yu,Y.Liu,and Z.Shuai,J. Phys.Chem.A 110,7138(2006).

[59]A.Troisi and G.Orlandi,J.Phys.Chem.A 110,4065 (2006).

[60]Y.Song,C.Di,X.Yang,S.Li,W.Xu,Y.Liu,L. Yang,Z.Shuai,D.Zhang,and D.Zhu,J.Am.Chem. Soc.128,15940(2006).

[61]J.Huang and M.Kertesz,Chem.Phys.Lett.390,110 (2004).

[62]S.Yin,L.Li,Y.Yang,and J.R.Reimers,J.Phys. Chem.C 116,14826(2012).

[63]T.Liu and A.Troisi,Adv.M ater.25,1038(2013).

[64]A.Listorti,B.O’Regan,and J.R.Durrant,Chem. M ater.23,3381(2011).

[65]J.W.A rbogast,C.S.Foote,and M.Kao,J.Am.Chem. Soc.114,2277(1992).

[66]P.M.A llemand,C.K.Khemani,A.Koch,F.Wud l,K. Holczer,S.Donovan,G.G rner,and J.D.Thom pson, Science.253,301(1991).

[67]A.Einstein,Ann.Phys.17,549(1905).

[68]M.van Sm oluchow ski,Ann.Phys.21,756(1906).

[69]J.D.Huang,S.H.Wen,W.Q.Deng,and K.L.Han, J.Phys.Chem.B 115,2140(2011).

[70]Q.Peng,Y.Y i,Z.Shuai,and J.Shao,J.Am.Chem. Soc.129,9333(2007).

ceived on February 16,2017;Accepted on April 7,2017)

?Authors to whom correspondence shou ld be add ressed.E-m ail: zhaocb@snut.edu.cn,gehg@snut.edu.cn,Tel.:+86-916-2641660