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Synthetic Metals 159 (2009) 2081–2085

Contents lists available at ScienceDirect

Synthetic Metals

journa l homepage: www.e lsev ier .com/ locate /synmet

lectronic structures of neutral, cationic and dicationic states of the lowand gap polymers. Polythieno[3,4-b]benzene, a case study

anuel Garcia, Estrella Ramos, Patricia Guadarrama, Serguei Fomine ∗

nstituto de Investigaciones en Materiales, Universidad Nacional Autónoma de México, Apartado Postal 70-360, CU, Coyoacán, Mexico DF 04510, Mexico

r t i c l e i n f o

rticle history:eceived 29 June 2009eceived in revised form 20 July 2009ccepted 22 July 2009

a b s t r a c t

The electronic structures of neutral cationic and dicationic states of oligothieno[3,4-b]benzene contain-ing up to 20 repeating units have been studied using broken symmetry B3LYP/3-21G* method. The modelpredicts that short oligomers (up to decamers) have closed shell aromatic ground state, while the ground

vailable online 20 August 2009

eywords:ow band gap conjugated polymersroken symmetry DFTITN

state of longer oligomers possesses multireference character and cannot be described within a frameworkof one determinant methods. It has been found that the ground state has significant contributions fromtriplet state. The S0 → S1 energy calculated for longest of polythieno[3,4-b]benzene (PITN) oligomer con-taining 20 repeating units is in excellent agreement with experiment. Unlike polythiophene where theground state of dications is open shell polaron pair state dicationic ground state of calculated oligomers isclosed shell bipolaronic state (at least up to oligomers containing 20 repeating units) which was confirmed

by stability calculations.

. Introduction

Much effort has been devoted over the past two decades to thereparation of novel organic conjugated polymers having low bandaps without the need of doping [1]. Polythieno[3,4-b]benzenePITN) is the first prepared derivative of polythiophene having aow band gap (about 1.0 eV) without doping (Fig. 1) [2].

Brédas et al. reported that fusion of a benzene and thiophenencreased the quinoid contribution to the electronic structure, byestabilizing the HOMO and stabilizing the LUMO, thus decreasinghe band gap [3]. There have been various experimental [2,4] andheoretical [3,5] studies of PITN. The principal aim of these stud-es was to establish whether the ground state of PITN is aromaticr quinoid. The previous studies showed that the band gap of theuinoid form is in better agreement with experimental data thanhe aromatic one [6]. Quinoid structure can be forced by replacinghe terminal capping CH with a capping CH2 group. Even though theand gap of the quinoid form is close to the experiment, the quinoidontribution may be overestimated by using capping CH2 groups.hus, it has been shown [7] that good agreement for the band gap ofITN was obtained with CH as the terminal capping group. There-

ore, previous theoretical studies where a methylene was used aserminal capping group probably exaggerated the quinoid charac-er of PITN. Such a contradiction between available data could beconsequence of the fact that the low band gap polymers in gen-

∗ Corresponding author.E-mail address: fomine@servidor.unam.mx (S. Fomine).

379-6779/$ – see front matter © 2009 Elsevier B.V. All rights reserved.oi:10.1016/j.synthmet.2009.07.030

© 2009 Elsevier B.V. All rights reserved.

eral and PITN in particular has multireference character of theirground states making restricted HF or DFT used so far inappropri-ate for the correct description of PITN ground state structure. Thus,it has been shown that the ground state of various oligoacenes [8]and thieno[3,4-f]isothianaphthene [9] which can be considered asmodels of low band gap polymers is diradicalic. In case of PITN,diradicalic state corresponds to quinoid structure while closed shellsolution implies aromatic polymer chain. Because of the multiref-erence character of biradical, one can expect that only a methodincluding both static and dynamic electron correlation effects candescribe singlet biradicals properly. However, it has been shownthat unrestricted DFT (UDFT) performs surprisingly well in the caseof singlet biradicals [10]. UDFT results obtained for the ground stateof oligoacenes were in excellent agreement with CASSCF calcu-lations [8]. UDFT leads to symmetry breaking of the Kohn-Shamground state of singlet biradical because of a mixing of the groundstate with the lowest triplet state. Therefore, UDFT is an adequatetool to explore the electronic structure of the low band gap poly-mers where the ground state can have a significant admixture fromthe lowest triplet state. The aim of this study is to explore the natureof the electronic structure of PITN using broken symmetry, UDFT.

2. Computational details

All calculations were carried out using Gaussian 03 [11]. Tounderstand the evolution of electronic structure of PITN with poly-merization degree (n), thieno[3,4-b]benzene and the oligomerswith n from 2 to 20 were fully optimized without any symme-try restrictions using B3LYP hybrid functional as implemented in

2082 M. Garcia et al. / Synthetic Metals 159 (2009) 2081–2085

GsitlpusTfsilbpta

e3e[ttwtmara

3

3

scts

TO(

Fig. 1. Aromatic (A) and quinoid (Q) resonant structures of PITN.

aussian 03 suit of programs in combination with 3-21G* basiset. Initially built C2h structures were altered in up–down fash-on to allow non-planar structure since plane conformation is nothe lowest energy structure of PITN [7]. It has been shown ear-ier that B3LYP functional performs well for long oligothiopheneolycations [12]. In case of neutral molecules both restricted andnrestricted formalism were used for singlet state while for triplettate UDFT was applied. Only UDFT was used for dicationic states.o break spatial symmetry guess(mix, always) keyword was usedor UDFT calculations of singlets to ensure that the lowest energytate was found. In case of neutral and dicationic oligomers, stabil-ty calculations were performed for all oligomers to ensure that theowest energy electronic state is found. Some of calculations haveeen repeated at BHandHLYP/3-31G* level of theory for comparisonurpose. This model leads to strong spin contamination (S2 = 3 forriplets and more than 2 for open shell singlets and cation radicals)nd could be not as reliable as B3LYP/3-21G* model.

The first excitation energies were estimated for the low-st energy structure of each oligomer at TD-BHandHLYP/6-1G*//B3LYP/3-21G* level. This level of theory reproduces very wellxperimental band gap determined for polythiophene (2.1–2.2 eV)13]. Calculated S0 → S1 energies for polythiophene oligomer con-aining 40 repeating units was found to be of 2.23 eV according tohis model. Mono- and dicationic states of all studied moleculesere fully optimized at UDFT level without any symmetry restric-

ions (both singlet and triplet states) using geometries of neutralolecules as starting geometries. Studied oligomers are denoted

s ITNn. Mono- and diionized oligomers are referred to as + and ++,espectively. S, OSS and T correspond to singlet, open shell singletnd triplet states, respectively.

. Results and discussion

.1. Neutral oligomers

Table 1 shows relative energies of closed shell singlet (S), openhell singlet (OSS) and triplet (T) states for different oligomers. Itan be seen that for ITN1–ITN10, OSS solution is collapsed to S solu-ion and for these oligomers the lowest energy state is closed shellinglet. The inter-ring bond lengths are close to 1.44 Å, (Fig. 2), close

able 1pen (OSS)–closed (S) shell singlet (�oss–s) and OSS–triplet (T) (�oss–t) energy gaps

kcal/mol). The expectation value of the S2 operator for OSS 〈S2〉s and T states 〈S2〉t .

Oligomer �oss-s �oss-t 〈S2〉s 〈S2〉t

ITN1 0.00 −45.16 0.00 2.02ITN2 0.00 −27.20 0.00 2.03ITN4 0.00 −14.73 0.00 2.07ITN6 0.00 −9.14 0.00 2.10ITN8 0.00 −5.41 0.00 2.13ITN10 0.00 −2.41 0.00 2.15ITN12 −0.49 −0.13 1.19 2.16ITN14 −3.05 −0.04 1.18 2.17ITN16 −11.30 −0.01 1.18 2.17ITN20 −12.09 0.00 1.18 2.17

Fig. 2. Inter-ring bond lengths in lowest energy state of ITNn oligomers.

to found experimentally for hexamer of thiophene [16], character-istic of aromatic structure.

Triplet state is higher in energy compared to singlet one forITN1–ITN10 oligomers. Therefore, short ITNn oligomers have closedshell singlet aromatic ground state. This hypothesis is also con-firmed by CASSCF(8,8) calculations where oligomers ITN1–ITN10have less than 0.4 electron outside the closed shell bonding orbitals.

Starting from ITN12 the lowest energy solution becomes openshell singlet (Table 1). S–OSS gap constantly increases from ITN12to ITN20 reaching more than (12 kcal/mol) for ITN20. As seenfrom Fig. 2, beginning from ITN12 the inter-ring bond lengths instudied oligomer continuously decrease reaching 1.37–1.38 Å forthe central rings of ITN16 and ITN20, showing increasing quinoidcontribution to the ground state structure. In case of BHandHLYP/3-21G* model OSS state becomes the lowest energy state alreadyfor ITN6. It has been observed [8] that the stability of OSS statein conjugated systems increases with amount of Hartree-Fock (HF)exchange in functional. Since BHandHLYP has 50% of HF exchangeand B3LYP only 20%, BHandHLYP stabilizes OSS to a greater extentthan B3LYP does. However, qualitatively both functional show sim-ilar trends.

To estimate the contribution of quinoid structure to each cal-culated oligomer we optimized closed shell singlet of ITN10 withterminal methylene capping group to force quinoid structure. Theinter-ring bond lengths for this structure were found to be of 1.37 Å.In pure aromatic structure (ITN1–ITN10) the inter-ring distance isof 1.43–1.44 Å. Therefore, for central rings of ITN16 and ITN20 thestructure is practically quinoid while for shorter oligomers and forouter rings of all oligomers there are contributions from both, aro-matic and quinoid structures. As seen from Fig. 2 there is a generaltrend of increasing quinoid structure contribution with the num-ber of the repeating units. Thus, calculations predict that the pointwhen the closed shell solution no longer becomes the lowest energysolution occurs for ITN12.

Fig. 3 shows inter-ring bond lengths for the triplet state ofoligomers. As seen, in triplet state all oligomers are forced to adoptquinoid structure.

Even for shortest oligomers the inter-ring bond lengths betweencentral rings are typical for quinoid structure. While the energydifference between S and OSS states increases with the numberof repeating units reaching (12.09 kcal/mol) for ITN20, the energydifference between OSS and T states decreases in the same direction

practically disappearing for ITN16. This is true for both B3LYP andBHandHLYP models. These results show that the ground state ofPITN is not a pure spin state and that there are contributions fromsinglet, and triplet states. Thus, S2 values for the ground states oflong oligomers in OSS state are slightly larger than one, implying

M. Garcia et al. / Synthetic Metals 159 (2009) 2081–2085 2083

Fig. 3. Inter-ring bond lengths in T state of ITNn oligomers.

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relaxation energies (�) are linearly related to the square root of thechain length for linear oligomers [18,19]. This is not the case for

ig. 4. Optimized geometry and the unpaired spin density distribution for ITN20nd ITN20+.

hat the ground state has more than 50% admixture from triplettate.

Fig. 4 shows optimized geometry and unpaired spin density dis-ribution for the ground state (OSS) in ITN20. The unpaired spinensity of ITN20 and other oligomers in their ground states isostly localized at the terminal units of an oligomer chain. There-

ore, the best description of the ground state structure of PITN thatan be done using unique resonant structure is a quinoid biradical.

The calculated S0 → S1 energies (Eg) for ITN oligomers werestimated using TD-DFT with both spin restricted and spin unre-tricted reference states (Table 2). As seen, TD-UDFT results for longligomers (ITN14, ITN16 and ITN20) are in excellent agreementith experiment 1.0–1.2 eV [2], while restricted method stronglynderestimates Eg due to overestimation of the ground statenergy. These data provide additional confirmation that restrictedFT describes incorrectly the ground state of PITN while UDFT gives

easonable description. Kwon and McKee [7] reported Eg for PITN

etermined by the extrapolation of excitation energies of aromaticITN oligomers calculated at TD-B3LYP/6-31G*//RB3LYP/6-31G*evel to be of 1.32 eV, which is relatively close to experimentalata of 1.0–1.2 eV. However, imposed symmetry restrictions and

able 2alculated S0 → S1 energies for ITNn oligomers (eV).

Oligomer TD-UBHandHLYP/6-31G* TD-BHandHLYP/6-31G*

ITN1 3.97 3.97ITN2 3.14 3.14ITN4 2.34 2.34ITN6 1.91 1.91ITN8 1.74 1.74ITN10 1.63 1.63ITN12 1.25 1.60ITN14 1.14 1.56ITN16 1.08 0.16ITN20 1.00 0.04

Fig. 5. Mulliken charge distribution in cation radicals.

relatively short oligomers (octamer was the longest oligomer usedfor the extrapolation) definitely affected the results. As seen fromTable 2, linear extrapolation [15] is not possible for restricted solu-tion; since there is an abrupt decrease in the Eg for long ITN16 andITN20 oligomers.

3.2. Cations

The ionization of PITN leads to the formation of a polaron cation.It is known that a single polaron cation in polythiophene is local-ized at the center of polymer chain causing local deformation andincreasing the contribution of quinoid structure in the area of local-ization [14b,17]. The situation is very different for PITN cationradicals. Fig. 5 shows the Mulliken charge distribution in oligomericcation radicals of PITN.

As seen, the cation polaron is delocalized mostly at the ends ofoligomer chain. The charge decreases from the end to the centerof the oligomers and increases again to another end of oligomerchain. This conclusion confirms the unpaired spin density distribu-tion associated with polaron cation too (Fig. 4). As seen from Fig. 4,the unpaired spin density of ITN20+ is located at the ends of theoligomer chain, associated with positive charge. Table 3 shows ver-tical and adiabatic ionization potentials (IPv and IPa, respectively)of PITN oligomers as well as the corresponding relaxation ener-gies. It has been established that for polythiophene oligomers the

PITN oligomers. Their behavior resembles that found for oligoceneswhere saturation of the relaxation energy occurs due to polaronself-localization.

Table 3Vertical (IPv), adiabatic (IPa) ionization potentials and relaxation energies (�) of PITNoligomers, eV.

Oligomer IPv IPa �a

ITN1 7.42 7.32 0.10ITN2 6.49 6.27 0.22ITN4 5.75 5.48 0.27ITN6 5.38 5.10 0.28ITN8 5.20 4.87 0.33ITN10 5.08 4.71 0.37ITN12 4.62 4.59 0.03ITN14 4.59 4.57 0.02ITN16 4.57 4.54 0.03ITN20 4.53 4.50 0.03

a � = IPv − IPa.

2084 M. Garcia et al. / Synthetic Metals 159 (2009) 2081–2085

idPo

tsftcTSb

3

sttislscsttic

TOT

Fig. 6. Inter-ring bond lengths in cation radicals.

As seen, (Table 3) the relaxation energies first increased reach-ng a maximum for ITN10 and then abruptly drop for ITN12. Thisifference is due to the fact that the nature of the ground state inINT oligomers depends on the number of monomer units in theligomer.

Short neutral oligomers (n = 1–10) have aromatic structure ofheir ground states while the structure of longer oligomers demon-trate increasing quinoid contribution. On the other hand, as seenrom Fig. 6, the ground state of cation radicals has significant con-ribution from quinoid structure even for short oligomers, and thisontribution becomes even more important for larger oligomers.herefore, the geometry relaxation is larger for short oligomers.tarting from ITN12, the geometry of neutral and ionized speciesecomes very similar, thus decreasing the relaxation energy.

.3. Dications

Both DFT and CASSCF calculations demonstrated that the groundtate of long polythiophene dications is open shell with strong con-ribution from the polaron pair state [17], showing degeneracy ofhe open shell singlet and triplet states. It has been found thatn case of PITN dications the situation is very different. The unre-tricted solution is always collapsed to restricted one even for theargest ITN20++ dication and the closed shell singlet is the groundtate for dicationic state of PITN which is confirmed by stability cal-ulations for all dications at B3LYP/3-21G* level of theory. Table 4hows relative energy of singlet and triplet state for ITNn dica-ions. As seen, singlet state is always lower in energy, however,

he singlet–triplet gap grows smaller with the number of repeat-ng units which might be an indication that for very long chain OSSould be the ground state.

able 4SS–T energy gap (�s–t) (kcal/mol) and the expectation value of the S2 operator forstates 〈S2〉t .

Oligomer �s–t 〈S2〉t

ITN1++ −19.16 2.00ITN2++ −18.22 2.03ITN4++ −15.94 2.04ITN6++ −12.91 2.05ITN8++ −11.41 2.06ITN10++ −10.72 2.08ITN12++ −10.54 2.09ITN14++ −10.47 2.12ITN16++ −9.42 2.07ITN20++ −8.38 2.09

Fig. 7. Mulliken charge distribution in singlet (S) and triplet (T) states of ITN20++dication.

It is noteworthy that unlike neutral oligomers where singlet–triplet gap is practically disappeared already for ITN16, for dicationsthis gap is still significant even for ITN20++. CASSCF(8,8) calcu-lations performed for ITN10++ showed that the ground state ofdications is closed shell. Thus, the number of electrons outsideclosed shell bonding orbitals for ITN10++ is only 0.31, similar tothat found for short ITN oligomers (n = 1–10) with closed shell sin-glet ground state. Therefore, according to calculations it seems thatthe bipolaron and not the polaron pair is the ground state of iso-lated dicationic molecules of PITN. The stability calculations forBHandHLYYP/3-21G* model predicts that for IITN1++ to ITN10++oligomers closed shell solution is the ground state. However forITN12++, ITN14++, ITN16++ and ITN20++ dications OSS solution are0.001, 0.02, 0.05 and 0.11 kcal/mol lower in energy than the corre-sponding closed shell solution. S2 values found for these states areof 0.04, 0.16, 0.28 and 0.48, respectively. Since oligomers showingRHF → UHF instability are very large to be treated at CASSCF levelit is difficult to decide which method can be trusted. Calculationsperformed for acenes [8,20] show that broken symmetry UB3LYPresults are in good agreement with CASSCF; both methods pre-dict OSS character of the ground state for hexacene while shorteracenes are closed shell systems. On the other hand our calcula-tions show that BHandHLYP predicts OSS ground state already fortetracene. It seems that BHandHLYP functional overestimates sta-bility of OSS states. Therefore, B3LYP method should be consideredmore reliable compared to BHandHLYP.

Fig. 7 shows the Mulliken charge distribution in S and T statesof ITN20++ dication. In singlet (the lowest energy) state most of thecharge is located at terminal fragments, while in triplet state thereis additional maximum in the center corresponding to one of thepartially dissociated polarons in polaron pair.

In some cases for neutral molecules (Table 1) spin contamina-tion is notorious when using UDFT method, that could be a concern.However, while for UHF symmetry breaking and spin contamina-tion leads to the wrong wave function and a poor description ofthe corresponding molecule, the electron density is less sensitiveto spin contamination and, therefore, properties such as energy orgeometry calculated with the help of the electron density ratherthan the wave function can adopt reasonable values, as it has beenshown [10b].

Neither neutral nor charged state of PITN cannot be represented

by unique resonance structure, however, analyzing the charge andunpaired spin densities distribution in neutral, mono- and dica-tionic states of PITN oligomers it is possible to locate resonancestructures that make most important contributions to the corre-sponding ground states (Fig. 8).

M. Garcia et al. / Synthetic Metals 159 (2009) 2081–2085 2085

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Therefore, as seen from Fig. 8 the closed shell nature of PITNications is a consequence of open shell nature of neutral groundtate.

. Conclusions

The ground state of PITN, and probably of the low band gapolymers in general has a multireference character and cannote described correctly within a framework of one determinantethod. Therefore, neither aromatic nor quinoid structure repre-

ent perfect description of PITN ground state. However, quinoidtructure gives a reasonable description of PITN, especially forentral fragment of long oligomers. Only short oligomers can beescribed correctly using spin restricted methods and their struc-ure is definitely aromatic. Unlike polythiophene where dicationicround state is open shell polaron pair, PITN dicationic state androbably dicationic states of all low band gap polymers whereeutral ground state has multireference character is closed shellipolaronic state.

upporting information available

Optimized Cartesian coordinates, and electronic energies.

cknowledgments

This research was carried out with the support of GrantN100209 from PAPIIT. We acknowledge the support of DGSCA,NAM, for using supercomputer KanBalam. We are grateful to thenonymous reviewer for his truly helpful comments.

ppendix A. Supplementary data

Supplementary data associated with this article can be found, inhe online version, at doi:10.1016/j.synthmet.2009.07.030.

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