Theoretical study of perfluorinated oligothiophenes: electronic and structural properties

Theoretical study of perfluorinated oligothiophenes: electronic and structural properties

Polymer 45 (2004) 6391–6397 www.elsevier.com/locate/polymer Theoretical study of perfluorinated oligothiophenes: electronic and structural properties...

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Polymer 45 (2004) 6391–6397 www.elsevier.com/locate/polymer

Theoretical study of perfluorinated oligothiophenes: electronic and structural properties A. Raya*, M.A. Mora Departamento de Quı´mica, Universidad Auto´noma Metropolitana, Campus Iztapalapa, Av. San Rafael Atlixco No. 186, Col. Vicentina, Iztapalapa, Apdo. Postal 55-534, 09340 Me´xico, D.F. Me´xico. Received 8 April 2004; received in revised form 25 June 2004; accepted 25 June 2004

Abstract A quantum-chemical study at the Hartree–Fock, (HF), second order Møeller–Plesset perturbation theory, (MP2), and density functional theory, (DFT), levels was performed on perfluorinated oligothiophenes with the aim to predict the potential utility of these materials in the development of electronic devices based on organic n-type semiconductors. The electronic properties analyzed, such as ionization potential, HOMO–LUMO energy difference and electron affinities suggest that perfluorinated oligothiophenes are more difficult to oxidize, and have a larger band gap in comparison with their non-substituted parent compounds. Structural changes on bond lengths and bond angles between perfluorinated and non-substituted oligothiophenes were also observed. Thus, the incorporation of fluorine atoms into oligomers structure could be an effective way to design materials with n-type conductivity. q 2004 Elsevier Ltd. All rights reserved. Keywords: Ab initio; Electronic structure; Oligothiophenes

1. Introduction In the field of the conducting polymers, a-conjugated oligo- and poly-thiophene derivatives are a representative class of environmentally and thermally stable materials, and many applications have been found for them. Among these applications are nonlinear optical devices, polymer LEDs, electrical conductors, artificial muscles, photoresists, antistatic coatings, sensors, batteries, electromagnetic shielding material, solar cells, electrodes and optical devices [1]. The experimental search of new oligo- and poly-thiophenes has led to interesting new materials with promising technological applications, as field-effect transistors (FETs) for example [2]. In a FET device, the semiconductor layer supports a channel of holes (p-type) or electrons (n-type) between the source and drain electrodes. The most important

* Corresponding author. Current address: Departamento de Ciencias Ba´sicas e Ingenierı´as, Universidad del Caribe, 77500 Cancu´n Q. Roo, Me´xico. Tel.: C52-99-8881-4424; fax: C52-99-8881-4400 x 160. E-mail address: [email protected] (A. Raya). 0032-3861/$ - see front matter q 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.polymer.2004.06.054

characteristics for a FET semiconductor are high charge carrier mobility, high current modulation, stability, and processability [2d]. Particularly, the a-oligothiophenes (anT) are active p-channel materials, and FETs based on asexithiophene (a-6T) derivatives present high field-effect mobility [2]. Until now, many materials have been synthesized for applications as p-type channels with excellent results, but only few organic n-type semiconductors that can be used in FETs are known, however these suffer from low electron mobility, poor stability in air and/or demanding processing conditions [3–5]. Experimentally, the introduction of halogens into the polymer backbone has been an effective way to improve some properties. In particular, the substitution with fluorine has pronounced effects [6–8]. For example, the high stability of poly-tetrafluoroethylene (Teflon) is due to the high strengths of the C–F bonds and the shielding of the polymer backbone by the fluorine atoms, which prevents chemical attack. In the poly(3,4-difluoropyrrole) case, a very good stability of the film against oxidative degradation is observed and attributed to the fluorine presence into the polymer backbone [8].

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Because of the structure plays a dominant role in the physical properties of conducting polymers, the synthesis is a critical subject in the development of organic n-type semiconductors; in this sense the molecular design of materials through quantum mechanical calculations is an useful alternative that could provide valuable information respect to the synthetic conditions, physical–chemical and structural information, and further technological applications of them. One aim addressed in this work is to analyze some electronic and structural properties of perfluorinated oligothiophenes, in order to explore the possibility that these materials could be considered as candidates for n-type semiconductors. To achieve a detailed description, we have obtained the geometries of minimum energy and the electronic structure of perfluorinated and non-substituted oligothiophenes up to hexamer at the HF, MP2 and density functional levels of theory. In Section 2, we describe the methodology employed in this work. Section 3 presents a discussion of the electronic and structural properties obtained, including the comparative analysis between perfluorinated and non-substituted oligothiophenes and with the available experimental data. Also, ionization potentials, HOMO–LUMO energy difference and structural parameters are discussed with respect to the chain growth; from the calculated electronic properties for the oligomeric molecules, we could infer polymer properties. To the best of our knowledge, experimentally only the perfluorinated oligothiophenes, with one and six rings, had yet been reported. Therefore, systematic quantum mechanical studies like this could be useful to predict electronic and structural properties for perfluorinated oligothiophenes that have not at present been synthesized.

2. Theoretical methodology The molecular structures of the compounds studied in this work were built according to the following sequence: initially, exploring the potential energy surface, the minimum energy structure of the perflorinated thiophene (PF-T) and thiophene (T) molecules were obtained. Then, two optimized molecules of PF-T or two optimized molecules of T were coupled to generate the respective dimers. The following structures were generated by consecutive addition of one optimized PF-T or T molecules to the most stable conformation of the dimer, trimer, tetramer or pentamer structure resulting in the previous step. The trans-planar conformation has been the molecular structure considered experimentally in the semiconductors field for both PF-6T and 6T oligomers, because it has been observed that in the solid state packing exists a reduction of the torsion angles between adjacent units without affect their electronic and optical properties. Also, in our discussion, only the fully optimized all-trans

conformations were considered. Geometry optimizations and electronic properties were obtained with the ab initio MP2, HF and density functional theory (DFT) methods using the computational package Gaussian 98 [9]. We have carried out the ab initio MP2 and HF geometrical optimization using the 6-31G(d) [10] basis set. DFT calculations were done using the hybrid functional B3LYP [9], in combination with a CEP-31G(d) split valence basis set that includes effective core pseudopotentials [11–13] and polarization functions on heavy atoms.

3. Results and discussion 3.1. Structural properties In a first step, the molecular structures of perfluorinated thiophene (PF-T) and thiophene (T) were optimized and utilized as starting monomers to build the corresponding oligomers of the perfluorinated and non-substituted oligothiophenes. The gas phase experimental geometries for perfluorinated oligothiophenes (PF-a-nT: nO1) and oligothiophenes (a-nT: nO2) are not available. Nevertheless, crystallographic data have been reported for some nonsubstituted oligothiophenes [14–16] and for PF-a-6T [17]. These experimental data are very useful in order to assess the impact of the fluorine substitution in the structural pattern of oligothiophenes and to compare the structural parameter trends obtained with the theoretical methods. Structural parameters obtained with HF and MP2 methods are realistic with respect to the experimental available information. The following discussion refers to our MP2 results, because at this level of theory the geometrical parameters calculated for bithiophene (2T) are in very good agreement with the corresponding X-ray diffraction values [18]. For the calculated bond lengths, the following general trends were observed: (1) for all the oligomers studied, PFa-nT and a-nT, the bonds of the inner thiophene rings are slightly shorter that the corresponding bonds of the terminal rings; (2) the C–C and CaC bond lengths are shorter in PFa-nT than in a-nT oligomers; (3) the C–S bond lengths are larger in PF-a-nT than in a-nT oligomers. Observations (2) and (3) are structural consequences of fluorine substitution on the electronic population of the carbon atoms to which they are bonded. One objective of this work is to assess the variation of selected parameters with the chain growth. The parameters selected for discussion are the Ca–Ca, Ca–Cb, Cb–Cb, and C–S bond lengths and the Ca–S–Ca bond angle of the inner and terminal rings. It is observed that for all the oligomers except hexamers, the optimized geometries concur that in the central fragment, the Ca–Ca and Cb–Cb bonds decrease upon chain growth, while the C–S and Ca–Cb increases slightly. Similarly, the central C–S–C angle increases when going from dimer to tetramer to hexamer. For hexamers the

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opposite trend is observed as we going from the center to the ends of the chain. Table 1 collects the calculated bond distances and bond angles for PF-a-4T and a-4T. The hexamer chemical structure and the atom numbering are shown in Fig. 1. This numbering is also followed in all the others studied compounds. Table 2 contains some optimized bond distances and bond angles for the PF-a-nT and a-nT even oligomers. For the C–S–C bond angle of PF-a-nT inner rings, the calculated value is 92 degrees while the value for the same angle located in terminal positions is 90 degrees. This slight decreasing is due to the presence of the fluorine atoms; that is, terminal rings are substituted with three fluorine atoms, while the central ones only possess two. It is worth mention that at Hartree–Fock level, our calculated bond lengths values for the PF-a-6T and a-6T molecular structures are within 1.42 and 1.5% of the corresponding X-ray data, respectively [16,17]. The optimized PF-a-6T structure is in good agreement with the diffraction X-ray data [17]. In the structural data obtained experimentally for the PF-a-6T crystal, the C–S bond lengths are shorter than in the a-6T crystal while the same C–S bond distance calculated for PF-a-6T is slightly larger than the corresponding calculated for a-6T. This finding may be explained based on the fact that our calculations were carried out for an isolated molecule in gas phase. 3.2. Electronic properties Electrical and optical properties of conducting polymers, and many technological applications are directly related with the electronic structure of these materials and, in particular, with the energy gap between the valence and conduction bands (band gap) [1]. On the other hand, the electronic properties are dependent on the molecular structure. So, quantum mechanical calculations may be very useful, since it is possible characterize the electronic structure of pure or doped conducting polymers to obtain relationships between electronic and geometric structures. Experimentally, energy gaps may be obtained either from electronic absorption or emission spectra or

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considering the redox potential difference in cyclic voltammetry experiments [17]. In both cases, the energy gap values are proportional to the energy difference between the highest occupied and the lowest unoccupied molecular orbitals, HOMO–LUMO. From a theoretical point of view, one method of estimating excitation energy is to compute it as the HOMO–LUMO energy difference [19]. This estimation is known as the frozen orbital approach. For all the molecules studied here, the energy gap values calculated at the MP2 and HF levels overestimates, in average, 2.6 times the experimental ones. It is already known that in the theoretical framework of Hartree–Fock theory, the frozen orbital approach gives an overestimation for the gaps of finite and infinite systems because the LUMO energy calculated for the neutral systems corresponds to the electronic affinity of the anion more than that of the neutral system [20]. In spite of this deficiency, it remains an attractive approach to obtain energy gaps for complex systems. Plotting the energy gaps estimated with the methods MP2 and HF for the a-nT oligomers versus the experimental ones it is observed a good linear correspondence between theoretical and experimental values with a 0.998 correlation coefficient. The straight lines properties were used as scaling parameters in order to correct the calculated band gaps and to extrapolate our results to predict band gaps that have not as yet been experimentally determined. In recent work [21], energy gaps of substituted oligothiophenes were evaluated in this way; and the energy gaps reported were in good agreement with the experiment. For PF-a-nT oligomers, we only know the experimental band gap value of PF-a-6T; therefore, the scaling parameters obtained for a-nT were used. Applying this approach, we have obtained a PF-a-6T band gap (2.99 eV) that only differs by 0.05 eV from the experimental value [17]; for the a-6T oligomer (2.89 eV), the scaled value is 0.04 eV larger than the experimental one. It is remarkable that the experimental band gaps difference observed between the PF-a-6T and a-6T is about 0.09 eV, while the difference obtained from our HF scaled band gaps is 0.10 eV. Experimental band gap values were determined

Table 1 ˚ ) and bond angles (degrees) calculated for PF-4T and 4T oligomers at MP2/6-31G(d) level Optimized bond distances (A Bond

S(10)–C(6) S(10)–C(9) C(4)–C(6) C(9)–C(11) C(1)–C(2) C(3)–C(4) C(6)–C(7) C(8)–C(9) C(2)–C(3) C(7)–C(8)

Oligomer

Bond angle

PF-a-4T

a-4T

1.743 1.745 1.437 1.434 1.368 1.379 1.382 1.383 1.413 1.401

1.738 1.739 1.445 1.441 1.377 1.388 1.389 1.390 1.414 1.406

C(1)–S(5)–C(4) C(2)–C(3)–C(4) S(5)–C(4)–C(3) S(5)–C(4)–C(6) C(4)–C(6)–C(7) C(6)–S(10)–C(9) S(10)–C(6)–C(4) C(6)–C(7)–C(8) S(10)–C(9)–C(11) S(15)–C(11)–C(9)

Oligomer PF-a-4T

a-4T

91.016 114.843 109.868 122.410 127.470 92.671 122.775 113.971 122.783 122.791

92.17 113.21 110.31 121.05 128.79 92.48 120.87 113.47 120.91 120.91

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Fig. 1. Atom labelling of the chemical structure of PF-a-6T.

from the PF-a-6T and a-6T absorption and emission spectra in CHCl3 [17]. A 0.09 V difference value is obtained when the potential differences between the first reduction and oxidation peaks from electrochemical measurements are taken. Scaled HF/6-31G(d) energy gaps are listed in Table 3 and these values are compared to UV spectroscopic potential peaks.

From Table 3, we can also see that PF-a-nT oligomers have larger band gaps than the corresponding a-nT oligomers. These results are in good agreement with the electrochemical characterization and experimental absorption spectra of the PF-a-6T and a-6T reported in reference [17]. Furthermore, it is worth mentioning that the band gap difference (0.09 eV) between the typical p-type

Table 2 ˚ ) calculated for perfluorinated and non-substituted a-oligothiophenes with nZ2,4,6. HF/6-31G(d) level. Selected bond angles Optimized bond distances (A (degrees) calculated with HF/6-31G(d) level method for perfluorinated and non-substituted a-oligothiophenes with nZ2,4,6 Dimers Bond S(5)–C(1) S(5)–C(4) S(10)–C(6) S(10)–C(9) S(15)–C(11) S(15)–C(14) C(4)–C(6) C(9)–C(11) C(14)–C(16) C(1)–C(2) C(3)–C(4) C(6)–C(7) C(8)–C(9) C(11)–C(12) C(13)–C(14) C(2)–C(3) C(7)–C(8) C(12)–C(13) Bond angle C(1)–S(5)–C(4) C(2)–C(3)–C(4) S(5)–C(4)–C(3) S(5)–C(4)–C(6) C(4)–C(6)–C(7) C(6)–S(10)–C(9) S(10)–C(6)–C(4) C(6)–C(7)–C(8) S(10)–C(9)–C(11) S(15)–C(11)–C(9) C(11)–S(15)– C(14) C(12)–C(13)– C(14) C(17)–C(16)– C(14) S(20)–C(16)– C(14)

PF-a-2T

Tetramers a-2T

PF-a-4T

Hexamers a-4T

1.728 1.756

1.726 1.741

1.727 1.757 1.745 1.747

1.725 1.742 1.742 1.742

1.459

1.464

1.457 1.456

1.462 1.460

1.331 1.342

1.343 1.352

1.332 1.343 1.344 1.345

1.344 1.353 1.351 1.352

1.429

1.433

1.428 1.419

1.433 1.428

90.72 115.10 109.70 122.31 127.98

91.62 113.38 110.54 121.16 128.31

90.70 115.06 109.70 122.31 127.67 92.39 122.68 114.20 122.62 122.62

91.61 113.35 110.56 121.15 128.51 92.00 120.98 113.50 120.99 121.00

PF-a-6T 1.727 1.757 1.745 1.747 1.746 1.746 1.457 1.456 1.456 1.332 1.343 1.344 1.345 1.345 1.345 1.428 1.419 1.418

a-6T 1.725 1.742 1.741 1.742 1.742 1.742 1.462 1.460 1.459 1.344 1.353 1.351 1.352 1.352 1.352 1.433 1.428 1.428

90.67 115.06 109.70 122.31 127.66 92.39 122.67 114.19 122.63 122.64 92.38

91.60 113.35 110.56 121.13 128.49 92.00 120.99 113.49 120.99 120.98 91.98

114.16

113.49

127.70

128.50

122.65

120.98

c

Energy gaps calculated at HF level were scaled according to equation: Escaled gap Z ðEgap K bÞ=m (scaling parameters: bZ2.352; mZ1.975). Experimental band gap of perfluorinated-a-oligothiophenes. Only PF-a-6T has been reported (see Ref. [17]). In parentheses is the corresponding non-substituted a-oligothiophene experimental band gap (values taken from Ref. [27]). a

1 2 3 4 5 6

b

5.73 4.11 3.41 3.02 2.78 2.63 5.41 4.11 3.56 3.27 3.10 2.99

5.86 4.06 3.34 2.92 2.68 2.52

HF/6-31G(d) B3LYP/CEP-31G(d) HF/6-31G(d)a

5.23 4.08 3.42 3.15 3.00 2.89

a-Oligothiophenes Perfluorinated a-oligothiophenes n

Table 3 HOMO–LUMO energy gaps (in eV) calculated for perfluorinated and non-substituted a-oligothiophenes

B3LYP/CEP-31G(d)

Expb,c

– (5.23) – (4.05) – (3.49) – (3.16) – (2.99) 2.94 (2.85)

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semiconductor a-6T and PF-a-6T obtained by these authors was considered a primary factor in the expectation that PFa-6T acts as n-type semiconductor. In this work, the HF results yield band gap differences from 0.03 eV (dimers) to 0.14 eV (trimers). In Fig. 2, it is shown the behaviour of the HOMO and LUMO energies calculated at the HF and DFT levels of theory versus the reciprocal chain length. The fluorine substitution do not affect the usual behaviour observed in p systems, and the energy of the HOMO and LUMO orbitals shows a linear relationship with the inverse of the chain length. The introduction of fluorine atoms in the oligomer structures lowers the respective LUMO energies. For the hexamer the difference is 0.75 eV when the HF values are considered and 0.72 eV when estimated with the DFT approach. For the HOMO energy values, a similar trend is observed at both levels of theory. The result is a larger band gap for the perfluorinated oligomers when they are estimated through the frozen orbital approach. If the oligomers band gap is plotted versus the reciprocal chain length, a linear relationship is obtained with a 0.998 correlation coefficient for PF-a-nT oligomers and 0.994 for a-nT oligomers, when the HF method was employed. The energy gap behaviour for PF-a-nT oligomers is in agreement with the measured behaviour for a-nT oligomers. Recently, DFT has been used in order to obtain more realistic values for band gaps of conducting polymers. In particular, the band gap values calculated by means of

Fig. 2. (a) Scaled HF energy gaps (eV) of PF-a-nT and a-nT oligomers plotted versus reciprocal chain length. (b) DFT energy gaps (eV) of PF-anT and a-nT oligomers plotted against the inverse of the chain length. Solid line for perfluorinated oligomers and dashed line for non-substituted oligomers.

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hybrid functionals were in good agreement with the experimental ones [19,22]. In contrast with Hartree–Fock theory (where vertical ionization potentials are close to the experimental ones but electronic affinities obtained are poor), DFT hybrid methods underestimate the ionization potentials and electronic affinities by almost the same amount; so that, when a difference of these values is taken, a convenient cancellation of errors results [19]. Table 3 contains the HOMO–LUMO energy differences calculated with the HF/6-31G(d) and B3LYP/CEP-31G(d) methods. When the values calculated at the B3LYP/CEP31G(d) level are compared with those obtained experimentally for a-nT oligomers the correlation obtained indicates a very good correspondence between theory and experiment. This fact gives us confidence in the calculated band gap values that we are reporting here for PF-a-nT whose experimental band gaps have not been determined. The evolution of the energy gap as a function of the inverse chain length is also linear. The trend is similar to that observed at the HF level. Other relevant electronic properties of conducting polymers are the ionization potential, IP, and electron affinity, EA. IP is an electronic parameter that can be interpreted as a measure of the possibility of a polymer (or oligomer) to experience a p-type doping, while the electronic affinity indicates the possibility to experience a n-type doping [23]. At the HF level, it is known that the negative of the eiegenvalue of the HOMO correlates very well with the vertical ionization potentials (Koopmans’ theorem) [24]. Therefore, we have obtained the IPs using Koopmans’ theorem. On the other hand, there is a considerable controversy in the literature concerning the interpretation of DFT orbital energies. According with a Parr and Yang’s review [25], no simple physical meaning of Kohn–Sham orbital energies should be expected. In Table 4 negative HOMO energies at the HF/6-31G(d) and B3LYP/ CEP-31G(d) levels of theory are compared for PF-a-nT and a-nT. It is worth mentioning that IPs calculated with the HF method for thiophene (T) and bithiophene (a-2T) have a value of 8.94 and 7.77 eV, respectively, while the experimental values are 8.95 eV [26] and 7.63 eV [27], respectively. Theoretical IPs calculated as -3 HOMO with the

B3LYP/CEP-31G(d) method were found to be smaller than the available experimental values (Table 4). This deviation in IPs values has been related to the insufficient cancellation of the self-interaction error in the Hartree exchange term by terms of opposite sign in the hybrid exchange-correlation functional [28,29]. Fig. 3(a) and (b) shows the curves obtained when IPs and -3HOMO are plotted versus 1/n, respectively, calculated for PF-a-nT and a-nT oligomers. With both HF/6-31G(d) and B3LYP/CEP-31G(d) methods, linear relationships were obtained. Also, with both methods, it is possible observe that PF-a-nT have larger IPs than the nT oligomers. At HF level, IPs for PF-a-nT are within 1.0 eV of the corresponding non-substituted parent compounds; at DFT level, the PF-a-nT -3HOMO are within 0.82 eV of the corresponding non-substituted oligothiophenes. The observed behaviour indicates that PF-nT are more difficult to oxidize that the non-substituted oligothiophenes, which is in good agreement with the electrochemical characterization of PF-a-6T and a-6T oligomers. This result could be considered as another indication of the semiconductor character of PF-a-6T and a-6T. Experimentally, it has been shown that a-6T can be easily p-doped [2(c),30], while is expected that PF-a-6T could be n-doped [17].

4. Conclusions Structural and electronic properties of perfluorinated oligothiophenes (from monomer up to hexamer) were analyzed at the MP2, HF and DFT levels of theory. Structural parameters obtained with MP2 and HF methods for the PF-a-nT and a-nT molecular structures are in good agreement with the corresponding X-ray available data. At all levels of theory, the properties calculated for perfluorinated oligothiophenes were compared with respect to those estimated for the non-substituted parent compounds; the impact of fluorine substitution on electronic properties was observed in the band gap and ionization potentials values. Perfluorinated oligothiophenes have larger band gaps and vertical ionization potentials than the non-substituted oligothiophenes. These results could be an indicative of

Table 4 Calculated ionization potentials (in eV) for optimized perfluorinated and non-substituted a-oligothiophenes at HF and DFT levels of theory

1 2 3 4 5 6

Perfluorinated a-oligothiophenes

a-Oligothiophenes

HF/6-31G(d)

HF/6-31G(d)

9.74 8.70 8.26 8.03 7.90 7.81 a b

B3LYP/CEP-31G(d) 6.38 5.54 5.22 5.04 4.94 4.87

Experimental ionization potential for thiophene is 8.95 eV (see Ref. [26]). Experimental ionization potential for thiophene is a-2T is 7.63 eV (see Ref. [27]).

a

8.94 7.77b 7.30 7.06 6.95 6.85

B3LYP/CEP-31G(d) 5.86 4.06 3.34 2.92 2.68 2.52

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[3] [4] [5] [6] [7] [8] [9]

Fig. 3. (a) Ionization potential (eV) from HF calculations versus 1/n for PFa-nT and a-nT oligomers. (b) Reciprocal chain length dependence of 3HOMO at B3LYP/CEP-31G(d) level. Dashed line for perfluorinated oligomers and solid line for non-sustituted oligomers.

the semiconductor character type. The band gaps and vertical ionization potentials as a function of the reciprocal chain length for perfluorinated and non-substituted oligothiophenes shows a similar trend. The band gaps calculated with the B3LYP method are in good agreement with experimental gaps of non-substituted oligothiophenes. The scaling parameters for the HF calculations and the DFT results, allow us to know reliable values of band gaps for perfluorinated oligothiophenes that have not still been synthesized.

[10]

[11] [12] [13] [14] [15] [16] [17]

Acknowledgements

[18] [19]

A.R. and M.A.M. thanks CONACYT for support through a graduate scholarship and partial support, respectively. The authors are grateful to Drs Robin P. Sagar and Humberto Vazquez T. for their critical reading of the manuscript, and to referee for helpful suggestions.

[20] [21]

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