J. Phys. Chem. C 2007, 111, 4823-4830
4823
Comparative Theoretical Study of Heterocyclic Conducting Oligomers: Neutral and Oxidized Forms Jordi Casanovas*,† and Carlos Alema´ n*,‡ Departament de Quı´mica, Escola Polite` cnica Superior, UniVersitat de Lleida, c/ Jaume II Number 69, Lleida E-25001, Spain, and Departament d’Enginyeria Quı´mica, ETSEIB, UniVersitat Polite` cnica de Catalunya, AVda. Diagonal 647, Barcelona E-08028, Spain ReceiVed: July 13, 2006; In Final Form: January 29, 2007
The structural and electronic properties of pyrrole-, thiophene-, phosphole-, 3,4-ethylenedioxythiophene-, and 3,4-ethylenedithiafurane-containing oligomers have been studied using density functional theory with the B3PW91 functional and the 6-31+G(d, p) basis set. Calculations were performed on systems containing two, four, six, and eight monomers, with the results being extrapolated to infinite chain length polymers. The study on neutral oligomers indicated that polyphosphole presents the lowest energy gap (1.17 eV) and, in addition, it can be oxidized and reduced easily, that is, it is p- and n-dopable. The energy gaps estimated for poly(3,4-ethylenedioxythiophene) and poly(3,4-ethylenedithiafurane) are lower than those predicted for polythiophene and polypyrrole. On the other hand, calculations on two positively charged oligomers showed that the triplet electronic state is favored with respect to the singlet state when the number of monomers is long enough: the exact number of monomers required to satisfy this condition depends on the chemical nature of the system. Thus, dicationic pyrrole-, thiophene-, phosphole-, 3,4-ethylenedioxythiophene-, and 3,4-ethylenedithiafurane-containing oligomers with more than 8, 8, 11, 9 and 9 monomers, respectively, form a biradical with two separated polarons.
Introduction During the past two decades, conducting heterocyclic polymers have been extensively studied and developed for many commercial applications because of their attractive electrical and optical properties.1-6 The electronic, optical, magnetic, and structural properties of these π-conjugated compounds, which can be synthesized by chemical and electrochemical polymerization, have been controlled and modulated by the addition of suitable functional groups to their backbones. Polypyrrole (PPy) and polythiophene (PTh) are probably the most thoroughly investigated parent π-conjugated polymers because of their remarkable properties, as well as their excellent environmental stability. Among their derivatives, poly(3,4ethylenedioxythiophene) (PEDOT) has been found to be the most useful because of its interesting properties.7-13 Specifically, the electrical conductivity of PEDOT is higher than that of PTh, and in addition, it is considered to be the most-stable conducting polymer currently available. Moreover, the interchange of the sulfur and oxygen atoms in the PEDOT structure gives rise to poly(3,4-ethylenedithiafurane) (PEDTF), whose electronic properties are expected to be similar to those of PEDOT.14 On the other hand, less work has been done on polyphosphole (PPh), the phosphorus analogue of PPy, this deficiency being mainly the result of chemical difficulties in its synthesis.15 In spite of this, it was recently suggested that the band gap of PPh should be narrower than that of PPy and PTh. Quantum chemical calculations on small oligomers have been demonstrated to be very useful for the study of the structural * To whom correspondence should be addressed. E-mail: jcasanovas@ quimica.udl.es (J.C.);
[email protected] (C.A.). † Universitat de Lleida. ‡ Universitat Polite ` cnica de Catalunya.
and electronic properties of conducting polymers.16,17 Accordingly, a very large number of computational studies using such theoretical procedures have been reported during the past decade. However, a detailed inspection of these works reveals that usually their results cannot be compared directly, and therefore, only general and qualitative trends can be extracted. This should be mainly attributed to three reasons: (i) different approaches, the levels of theory, or both were employed for the calculations, that is, semiempirical, ab initio, or density functional theory (DFT) methods, band theory, basis set, etc.; (ii) the studies were performed on oligomers of different lengths; and (iii) different redox states were considered, that is, doped or undoped states, and within the former, different electronic states. Although some systematic theoretical studies about the electronic properties of conducting heterocyclic oligomers have been recently reported,17a,b no attempt has been made to investigate the properties of PPy, PTh, PPh, PEDOT, and PEDTF, which are among the most useful and representative π-conjugated materials, using identical and comparable conditions. As a consequence, a complete understanding of the structural and electronic peculiarities that control the electrical and optical properties of these important conducting polymers has not been achieved yet. In this work, we present a comparative quantum mechanical study based on DFT calculations of oligomers that mimic the above-mentioned polymers. For this purpose, we determined the following structural and electronic properties: bond-length alternation pattern, preferences for aromatic or quinoid-like structures, ionization potential (IP), electron affinity (EA), and energy gap (g) of neutral oligomers containing n monomers, that is, n-Py, n-Th, n-Ph, n-EDOT, and n-EDTF with n ) 2, 4, 6, and 8 (Scheme 1). The results have allowed the estimation of the properties of high molecular weight neutral polymers by extrapolation to infinite chain length.
10.1021/jp0644210 CCC: $37.00 © 2007 American Chemical Society Published on Web 03/08/2007
4824 J. Phys. Chem. C, Vol. 111, No. 12, 2007 SCHEME 1: Chemical Structure of the Compounds under Study
On the other hand, as is obvious, the exploration of the doped states is essential within the context of conducting polymers. However, the information about the charged-doped states is frequently very scarce. In this work, we have considered the two positively charged states of the oligomers mentioned above, that is, the p-doped n-Py+2, n-Th+2, n-Ph+2, n-EDOT+2, and n-EDTF+2 with n ) 2, 4, 6, and 8. Furthermore, the monocations n-Py+1, n-Th+1, and n-Ph+1 with n ) 4, 6, and 8 have been analyzed to illustrate the differences between the one and two positively charged states. The overall results have contributed to a deeper insight into the structure-property relationships and, in particular, into the electrical properties of PPy, PTh, PPh, PEDOT, and PEDTF. Methods Geometry optimizations of neutral and cationic oligomers were carried out considering antiplanar conformations, that is, all the interring dihedral angles X-C-C-X (Scheme 1) were kept fixed at 180°because this is the expected conformation in the solid state. Calculations were performed using Becke’s threeparameter hybrid functional18 combined with Perdew and Wang’s correlation functional,19 B3PW91; the 6-31+G(d, p)20 basis set was employed in all cases. Recent studies showed that this methodology is able to provide a good description of heterocyclic oligomers like those studied in this work.14b,17c,d The restricted formalism was considered for calculations on the neutral oligomers (closed-shell systems). For dicationic oligomers, which were computed in both the singlet and triplet electronic states, the unrestricted DFT formalism UB3PW91 was used. It should be emphasized that, although these calculations require a huge amount of computational resources, they are essential to properly describe the fact that an isolated oligomer chain carrying two positive charges can form either a bipolaron or a pair of polarons.21 The UB3PW91/6-31+G(d, p) level of calculation was also employed for the monocations in the doublet electronic state. It is noteworthy that the number of possible oligophosphole diasteroisomers rapidly increases with the chain length because of the pyramidal nature of the tricoordinated phosphorus atom. However, in this work, we only considered the alternated and nonalternated conformations, abbreviated alt and non-alt, respectively. These arrangements are illustrated for 4-Ph in Scheme 2. In an early study,22 Bre´das found a direct relation between the electrical properties of heterocyclic polymers and the
Casanovas and Alema´n SCHEME 3: Aromatic (left) and Quinoid (right) Forms of Heterocylic Polymers
aromatic or quinoid character of their backbone (Scheme 3). Thus, there is a competition between the π-electron delocalization within the rings and the π-conjugation along the polymer backbone,23 the electrical conductivity being expected to increase with the quinoid character In this work, the structural information extracted from the optimized oligomers has been related with their aromatic or quinoid character. For this purpose, we examined the C-C bond-length alternation patterns along the π-system of the backbone and, in particular, the interring distances d. Furthermore, we evaluated the aromaticity of the cycles using two different but complementary criteria. The first is the Julg parameter (JP),24 a geometric criterion used to measure the deviations of the individual C-C bond lengths (ri) from the mean C-C bond distance (r) in the diene unit of the cycles
JP ) 1 -
225 3
3
( ) ri
1∑ r i)1
2
(1)
The second is a magnetic criterion based on the nucleusindependent chemical shift (NICS) approach.25 This consists of the calculation and reversion of the sign of the magnetic isotropic shielding at the center of the five-membered rings, that is, the nonweighted mean of the heavy atom coordinates. For this purpose, the NMR shielding tensors were evaluated at the B3LYP/6-311G(d) level18,26 using the gauge-independent atomic orbital (GIAO) method.27 The choice of this methodology is justified by our previous experience in computing chemical shifts of organic compounds.28 The IPs of neutral oligomers were calculated using Koopman’s theorem,29 that is, relating the IP to the negative energy of its HOMO (highest-occupied molecular orbital), which according to Janak’s theorem can be applied to DFT calculations.30 Similarly, the EAs were evaluated from the LUMO (lowest-unoccupied molecular orbital) energies. As is well established, Koopman’s theorem is limited in its use for the DFT methods. So, we should take these IP and EA values as simple estimations. The π-π* lowest-electron transition energies (g) were obtained as the difference between the HOMO and LUMO energies. Thus, Levy and Nagy evidenced that g can be rightly approximated using this procedure in DFT calculations.31 Finally, the IP, EA, and g values were obtained for the polymers by plotting the results of oligomers against the inverse of the chain lengths (1/n) and extrapolating to infinity. All calculations were carried out using the Gaussian 98 and Gaussian 03 suites of programs.32 Results and Discussion Neutral Polymers. n-Py, n-Th, n-Ph, n-EDOT, and n-EDTF oligomers with n ) 2, 4, 6, and 8 were constructed, and their
SCHEME 2: Two Conformations of 4-Ph: alt (left) and non-alt (right)
Heterocyclic Conducting Oligomers
J. Phys. Chem. C, Vol. 111, No. 12, 2007 4825
Figure 1. C-C bond distances along the conjugated π-system of 8-Py, 8-Th, 8-Ph (non-alt conformation), 8-EDOT, and 8-EDTF.
TABLE 1: Julg Parameters (plain) and NICS Values (italic) Obtained for 8-Py, 8-Th, 8-Ph (non-alt conformation), 8-EDOT, and 8-EDTF cycle 1 8-Py 8-Th 8-Ph 8-EDOT 8-EDTF
0.966 0.946 0.847 0.929 0.883
cycle 2 -12.75 -11.47 -3.92 -15.36
0.985 0.976 0.930 0.973 0.944
geometries were subsequently optimized. An inspection of the energies of the optimized structures indicates that n-Py, n-Th, n-Ph, and n-EDOT gain stability with the length of the oligomer up to n ) 6; the additional stabilization when n changes from 6 to 8 with respect to that obtained when n varied from 4 to 6 was almost negligible. In contrast, no additional stabilization was obtained for 6-EDTF with respect to the energy gain achieved with 4-EDTF. This result, which is consistent with previous observations,14 reflects the existence of the unfavorable interactions between the i and i + 2 EDTF units. Such contacts become more repulsive when the length of the chain increases; their minimization is a difficult task because the EDTF rings are forced to be coplanar, that is, the antiplanar conformation (θ ) 180°) was imposed. For the n-Ph oligomers, non-alt was the most stable conformation in all cases. Thus, the stability of the alt conformation decreases when the size of the molecule increases, that is, the relative energy of the latter conformation increases about ∼1.1 kcal/mol every two Ph rings. A puckered geometry was found for the Ph rings of all the oligomers, which is in agreement with the experimental observations33 and time-dependent DFT calculations34 on 4-Ph, as well as with a previous DFT study on 6-Ph.35 Moreover, the tricoordinated phosphorus atoms showed a pyramidal geometry (the sum of the valence angles around this atom in the non-alt conformation of 8-Ph ranges from 289.4 to 291.9°), with the hydrogen atoms almost perpendicular to the heterocycles, that is, the improper dihedral defined by the two H-P-C planes is about 99.5° in the central rings of 8-Ph. The C-C bond lengths in the π-system of 8-Py, 8-Th, 8-Ph (non-alt conformation), 8-EDOT, and 8-EDTF are depicted in Figure 1. As a general trend, the geometric structure of the oligomers shows a clear benzenoid character. However, the
cycle 3 -11.08 -9.24 -2.50 -14.34
0.986 0.979 0.943 0.977 0.950
cycle 4 -11.03 -9.22 -2.43 -14.18
0.986 0.980 0.947 0.978 0.951
-11.02 -9.20 -2.41 -14.15
degree of C-C bond alternation in the cycles grows in the following order: 8-Py < 8-Th < 8-EDOT < 8-EDTF < 8-Ph, which indicates the decrease of resonance within the rings. The lowest-aromatic character of 8-Ph is explained by the fact that the phosphorus lone pair has high s-character, whereas one p atomic orbital is involved in the bond to hydrogen. As a consequence, the hydrogen is almost perpendicular to the plane of Ph ring, and the interaction between the lone pair and the π-system is small. On the other hand, the interring bond length increases in the inverse order, that is, d(8-Ph) < d(8-EDTF) < d(8-EDOT) < d(8-Th) < d(8-Py); this distance ranges from 1.429 to 1.442 Å in the central cycles of 8-Ph and 8-Py, respectively. These observations suggest that PPh has the most pronounced π-electron conjugation along the molecular chain. To gain a deeper insight into the π-electron conjugation in the heterocyclic system, we evaluated the JP and NICS values for each ring of the longest oligomers. JP provides geometric indication of the delocalization within the diene part of the ring, giving information about the aromaticity in the heterocyclic structure. Note that the π-conjugation along the cis-1,3-butadiene unit will be more pronounced when JP becomes closer to one. On the other hand, negative NICS values show the existence of aromaticity. Table 1 shows the JP and NICS values of the four cycles going from the edge to the middle of the oligomers with n ) 8. As a general trend, in the inner rings which are the most representative, the JPs are larger and the NICS values are less negative than in the outer rings. As can be seen, the JPs are in agreement with the bond length alternation pattern described above. Thus, the JP values grow following the sequence 8-Ph < 8-EDTF < 8-EDOT < 8-Th < 8-Py, which reflects the decreasing order of conjugation in the π-diene unit. The drastic reduction in the NICS values from 8-Py to 8-Ph in the
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TABLE 2: Ionization Potentials (IP), Electron Affinities (EA), and Band Gaps (Eg) Computed for n-Py, n-Th, n-Ph (non-alt conformation), n-EDOT, and n-EDTFa 2-Py 4-Py 6-Py 8-Py 2-Th 4-Th 6-Th 8-Th 2-Ph 4-Ph 6-Ph 8-Ph 2-EDOT 4-EDOT 6-EDOT 8-EDOT 2-EDTF 4-EDTF 6-EDTF 8-EDTF
IP
EA
g
g (exptl)
5.07 4.54 4.37 4.30 5.80 5.27 5.10 5.02 5.71 5.13 4.92 4.81 5.16 4.46 4.19 4.06 5.12 4.54 4.33 4.23
0.28 0.84 1.03 1.12 1.62 2.26 2.49 2.61 2.17 2.73 2.96 3.08 1.12 1.56 1.72 1.80 1.12 1.65 1.83 1.89
4.79 3.70 3.34 3.17 4.18 3.01 2.60 2.41 3.54 2.40 1.96 1.73 4.04 2.90 2.47 2.26 3.99 2.89 2.51 2.33
4.35, 4.49b
4.05-4.12c 3.16, 3.18d 2.41-2.88e
3.87, 3.89f
a
All values are in eV. b Ref 37. c Refs 37a and 38. d Ref 38. e Refs 38a, 38e, and 39. f Refs 13 and 40.
homologous n-Py, n-Th, and n-Ph series supports this view, whereas 8-EDOT also exhibits negative NICS values. Unfortunately, the computational demands of the NICS calculation in 8-EDTF were unreachable. These results confirm the weak aromatic character of the Ph ring in oligophospholes,36 especially with respect to that of oligopyrroles and oligothiophenes. The electronic properties, such as the polymer’s ability to be doped and the HOMO-LUMO gap, are expected to reflect the polymer backbone characteristics discussed above. Table 2 displays the IP, EA, and g values predicted for all the investigated oligomers with available experimental data13,37-40 being included for comparison. The five series of data show that, as is usual in π-conjugated systems, the HOMO energy increases and the LUMO energy decreases when the chain length increases. Consequently, EA increases with the size of the oligomer, while the IP and g values decrease. In the case of n-Ph, it is worth noting that, independent of n, g is about 0.04 eV lower for the alt conformation than for the non-alt one. From a quantitative point of view, the calculated g values are in excellent agreement with the experimental measures, especially when it is taken into account that the g values predicted for isolated chains in the gas phase are usually about 0.2 eV larger than those computed in condensed phase.41 This fact allows us to conclude that the theoretical level used in this work is accurate enough to be used as a prediction tool. With this objective in mind, we plotted the IPs, EAs, and g’s calculated for the different oligomers under study against their inverse chain length (1/n) in Figure 2. As can be seen, the linearity between the calculated properties and 1/n is excellent for all series of compounds. To predict the electronic properties of the polymers, this linear behavior was extrapolated to infinite chain length. The resulting IPs, EAs, and g’s are listed in Table 3, where available experimental data12,37,42-45 are also included. A comparison of the IPs and EAs shows that the heteroatom has strong influence on the ability of the polymer to be oxidized or reduced. Thus, the low IP and EA predicted for PPy agree with the experimental observation that this polymer can be p-doped but not n-doped.5 In contrast, the larger EA values of PTh explain its ability to be n-doped, even although the stability of the n-doped form is known to be poor.1,5 The IPs increase in the following order: PEDOT < PEDTF < PPy < PPh < PTh.
Figure 2. Evolution of the IP (a), EA (b,) and g (c) values with the inverse chain length of the n-Py, n-Th, n-Ph (non-alt conformation), n-EDOT, and n-EDTF oligomers.
TABLE 3: Ionization Potentials (IP), Electron Affinities (EA), and Band Gaps (Eg) Extrapolated for PPy, PTh, PPh (non-alt conformation), PEDOT, and PEDTFa PPy PTh PPh PEDOT PEDTF
IP
EA
g
g (exptl)
4.03 4.75 4.52 3.71 3.94
1.41 2.93 3.36 2.02 2.17
2.62 1.82 1.17 1.69 1.77
2.85, 3.0b 2.0-2.3c 1.2-1.7d
a All values are in eV. b Refs 37b and 42. c Refs 1b and 43. d Refs 12, 44, and 45.
Because PTh, which shows the largest IP, is p-dopable, all the other polymers should be as well. Moreover, it is worth noting that the IPs obtained for PEDOT and PEDTF are so low that their neutral forms may be unstable, that is, they tend to oxidize. On the other hand, the EAs increase in the order PPy < PEDOT < PEDTF < PTh < PPh. Because the stability of the n-doped form of PTh is low, that of reduced PEDOT and PEDTF might be very poor also. Interestingly, the results predict that PPh can be easily oxidized and reduced. Accordingly, the electron/holeaccepting ability of PPh is more efficient than that of the other polymers studied in this work. Moreover, Table 3 reveals that PEDOT and PEDTF should have similar band gaps, whereas the lowest value clearly corresponds to PPh. p-Doped Polymers. As mentioned above, one of the most important features of π-conjugated polymers is their ability to conduct electricity in the p- and n-doped states (oxidized and
Heterocyclic Conducting Oligomers
J. Phys. Chem. C, Vol. 111, No. 12, 2007 4827
Figure 3. Triplet-singlet energy differences of n-Py+2, n-Th+2, n-Ph+2 (non-alt conformation), n-EDOT+2, and n-EDTF+2 as a function of the chain length.
reduced, respectively). To gain a comprehensive understanding of some doping effects, we analyzed the optimized geometries and the electronic properties of n-Py+2, n-Th+2, n-Ph+2, nEDOT+2, and n-EDTF+2 oligomers with n ) 2, 4, 6, and 8. Since oxidized oligomers carrying two charges may have either a singlet or a triplet ground state depending on their radical nature, we studied both electronic states. Moreover, both the alt and non-alt conformations of n-Ph+2 were considered, with non-alt being the most stable in all cases, that is, independently of n. The spin contamination was very low in all cases, that is, the highest overestimation was 2.3%. Figure 3 represents the energy of the triplet state relative to that of the singlet state for the five series of investigated oligomers. Results show that the singlet ground state is the most stable for short oligomers, even although the stability of the triplet increases with the chain length for all the oligomers. Accordingly, long oligomers prefer a triplet electronic ground state suggesting a diradical electronic structure with two unpaired electrons. Analysis of the energy profiles displayed in Figure 3 predicts that the lowest n value where the triplet state is stabilized with respect to the singlet one is 8 for n-Py and n-Th, 9 for n-EDOT and n-EDTF, and 11 for n-Ph. To provide a deeper insight into the structure of the triplet state, Figure 4a represents the C-C bond length alternation pattern of 8-Py+2 and 8-Th+2 in this electronic state. A comparison of Figures 1 and 4a reveals notable differences between these dicationic octamers in the triplet state and the neutral singlet counterparts. As a general trend, the two central rings of the charged octamers show a benzenoid character, whereas the structure becomes more quinoid toward the molecular ends with exception of the terminal rings. Accordingly, the three central interring bond distances (bonds 12, 16, and 20) are longer than the neighboring C-C interring bond lengths, while bonds 6, 10, 22, and 26 are the shortest bonds. Thus, the structure of the doubly oxidized oligomers looks like it is divided into two quinoid parts separated by aromatic rings in the middle of the chain. A similar tendency is reflected by the C-C bond length alternation patterns of 8-EDOT+2, 8-EDTF+2, and 8-Ph+2, which are displayed in Figure 4b. However, the biradical dication nature of the triplet state is not so clear for these oligomers. For instance, the benzenoid character of the two central rings is less pronounced than in 8-Py+2 and 8-Th+2. This is an expected result since, as was mentioned above, the singlet state is most favored for n-EDOT+2, n-EDTF+2, and n-Ph+2 with n being lower than 9, 9, and 11, respectively. This means that in
Figure 4. C-C bond distances along the conjugated π-system of (a) 8-Py+2 and 8-Th+2 in the triplet electronic state and (b) 8-Ph+2 (nonalt conformation), 8-EDOT+2, and 8-EDTF+2 in the triplet electronic state. The numbering of the bonds is identical to that in Figure 1.
oligomers with n ) 8, the reduction in the electrostatic repulsion produced by the two polarons is not enough to compensate for the energy required to create two well-defined structural defects in the polymer chain. The Mulliken population analysis was used to calculate the distribution of charges along the monomers of all the dicationic oligomers with n ) 8 in the triplet state (Figure 5a). On the other hand, to clarify the charge transport mechanism, we also evaluated the spin density per monomer in the same octamers (Figure 5b). As can be seen, both the charges and the spin densities are moved from the middle toward the chain ends. It could be argued that the UB3PW91 theoretical level is not able to provide a good description of these states because of the tendency of DFT methods to over-delocalize the charges. To check this aspect, we performed single-point UHF/6-31+G(d, p) calculations on the optimized structures; the results are displayed in Figure 6. As can be seen, the physical description provided by the UHF method for the triplet is very similar, from a qualitative point of view, to that obtained using DFT calculations. On the other hand, it should be noted that the distribution of charges of 8-EDOT+2 and 8-EDTF+2 present some deviation with respect to that of 8-Py+2, 8-Th+2, and 8-Ph+2. This discrepancy should be attributed to the electron-donation effects exerted by the oxygen and sulfur heteroatoms of 8-EDOT+2 and 8-EDTF+2, which are directly attached to the 3 and 4 positions of the backbone Th and furane rings, respectively. These findings are in contrast with some previous studies based on DFT calculations, which describe the two positive charges of n-Th+2 and n-EDOT+2 as uniformly distributed along the oligomer chains.46,47 The overall results allow us to conclude that the electronic structure of large dicationic oligomers corresponds to a triplet state carrying a pair of polarons diffused apart because of the Coulombic repulsion between the two charges, as is depicted in Scheme 4 for 8-Py+2 and 8-Th+2. This structure cannot be
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Figure 5. Mulliken charge (a) and spin density (b) per monomer calculated at the UB3PW91/6-31+G(d, p) level for 8-Py+2, 8-Th+2, 8-Ph+2 (non-alt conformation), 8-EDOT+2, and 8-EDTF+2 in the triplet electronic state.
Figure 6. Mulliken charge (a) and spin density (b) per monomer calculated at the UHF/6-31+G(d, p) level for 8-Py+2, 8-Th+2, 8-Ph+2 (non-alt conformation), 8-EDOT+2, and 8-EDTF+2 in the triplet electronic state.
detected in short oligomers because their length disfavors such configuration. However, when the number of monomers is long enough, the reduction of the Coulombic repulsion produced by separating the two positive polarons further apart outweighs the energy cost required for creating two structural defects on the chain, instead of the single deformation associated with a bipolaron. It should be mentioned that the preference for a pair of separated polarons, instead of a bipolaron, in large dicationic thiophene oligomers was already theoretically proposed by Tol,48 Geskin and Bre´das,21 and Gao et al.49 However, to our knowledge no previous study has been reported which suggested that this is also the electronic structure for n-Py+2, n-Ph+2, n-EDOT+2, or n-EDTF+2. Thus, previous works were mainly restricted to short dicationic Th-containing oligomers in the singlet state, which were calculated using a closed-shell quantum mechanical formalism. Finally, it is worth noting that, although the data represented in Figure 3 show a clear tendency, oligomers with more than
eight units should be considered to extrapolate these results to the p-doped polymers. To ascertain how many units are required to describe each polaronic defect, additional calculations on n-Py+1, n-Th+1, and n-Ph+1 with n ) 4, 6, and 8 were performed. Figure 7 displays the C-C bond distances along the conjugated π-system of some of these compounds. A comparison of the profiles of Figures 1 and 7 indicates that the positive charge mainly affects the geometry of the central 4 rings of 8-Py+1, 8-Th+1, and 8-Ph+1. Thus, Figure 7a shows a clear evolution toward the quinoid form, which takes place in the diene region of the heterocycles. Accordingly, bonds 10, 14, 18, and 22 of 8-Py+1 and 8-Th+1 are shorter than their respective two neighboring bonds. Moreover, bonds 12, 16, and 20 have more double-bond character than bonds 4, 8, 24, and 28: all interring bond distances are clearly shorter in the monocations than in their neutral counterparts. The same tendencies, although less pronounced, are observed for 8-Ph+1. On the other hand, the optimized structures of 6-Py+1, 6-Th+1, and 6-Ph+1 (Figure 7b) also show geometrical distortions in the
SCHEME 4: Possible Structure of 8-Py+2 (X ) NH) and 8-Th+2 (X ) S) in the Triplet Electronic Statea
a
The position of the unpaired electron is indicated by the arrows.
Heterocyclic Conducting Oligomers
J. Phys. Chem. C, Vol. 111, No. 12, 2007 4829 properties in Ph-containing polymers by selected chemical modifications. The band gaps extrapolated for PEDTF and, especially, PEDOT are lower than that of PTh, indicating better conducting properties. This fact is already known for EDOT derivatives, but no experimental measures related to the electric properties of oligomers or polymers based on EDTF have been reported yet. On the other hand, the energy, geometry, charge distribution, and spin pattern analysis of n-Py+2, n-Th+2, n-Ph+2, n-EDOT+2, and n-EDTF+2 oligomers suggests that, if they are long enough, the charge carriers may be two well-defined and separated polarons, that is, a biradical dication. This fact was only previously proposed for the n-Th oligomers. Acknowledgment. This work was supported by the MEC projects MAT2003-00251 and MAT2006-04029. Gratitude is expressed to the “Centre de Supercomputacio´ de Catalunya” (CESCA) and the Universitat de Lleida for computational facilities. References and Notes
Figure 7. C-C bond distances along the conjugated π-system of (a) 8-Py+1, 8-Th+1, and 8-Ph+1 (non-alt conformation) and (b) 6-Py+1, 6-Th+1, and 6-Ph+1 (non-alt conformation).
central four rings. As a consequence, it can be concluded that the minimum number of rings required to describe the charge distribution of n-Py+1, n-Th+1, and n-Ph+1 is six. These results are in good agreement with early works on Th-containing oligomers,50 which concluded that oligomers with more than 10-12 monomeric units are desirable to provide a realistic description of the dicationic p-doped polymers. Unfortunately, this task requires a huge amount of computational resources, being practically forbidden at present time, especially for EDOT and EDTF oligomers. However, it should be noted that if counterions were explicitly considered, the charge defects would be more localized and the number of required monomeric units would probably be less. Conclusions Geometric and electronic properties of neutral and p-doped n-Py, n-Th, n-Ph, n-EDOT, and n-EDTF oligomers with n ) 2, 4, 6 and 8 have been analyzed using (U)B3PW91/6-31+G(d, p) calculations. Although we have not considered the influence of the torsional disorder, the environment, and the intermolecular interactions, the results compare very well with the available experimental data allowing us extract some interesting conclusions and predictions. The results indicate that Ph oligomers are very good candidates to be used as building blocks for novel conducting or optical materials because of their narrow band gap and their ability to be oxidized and reduced. Specifically, the band gap extrapolated for PPh, 1.17 eV, is considerably lower than that of PPy and PTh, which are the most frequently studied conducting polymers. Furthermore, the phosphorus atom still retains its versatile reactivity, facilitating the tuning of the
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