Theoretical Study of Long Oligothiophene Polycations as a Model for

10662

J. Phys. Chem. C 2007, 111, 10662-10672

Theoretical Study of Long Oligothiophene Polycations as a Model for Doped Polythiophene Sanjio S. Zade and Michael Bendikov* Department of Organic Chemistry, Weizmann Institute of Science, RehoVot, 76100 Israel ReceiVed: February 14, 2007; In Final Form: May 2, 2007

We investigated the different electronic states of oligothiophene polycations such as tri-, tetra-, hexa-, and octacations (nT3+, nT4+, nT6+, and nT8+) at the B3LYP/6-31G(d) level. 10-, 20-, 30-, and 50-mers of oligothiophene polycations were studied. This is the first time oligothiophene polycations have been studied using density functional theory (DFT). For relatively short (10- or 20-mer) oligothiophene polycations, the ground states are most likely the doublet for trications and the singlet for tetra-, hexa-, and octacations, while longer oligomer polycations (such as the 50-mer) exhibit degeneracy between different spin states. Using bond length alternation, charge distribution, and relative energies data, we showed that the electronic structure of sufficiently long tri- and tetracations (such as the 20- and 30-mer) and hexa- and octacations (such as the 50-mer) appears similar to that of the dications, with the oligothiophene chain separated into well-defined regions of cation radicals (polarons). Charge separation requires a chain length of at least about five thiophene rings per unit charge. Interestingly, one molecule of dopant per five thiophene rings is the typical doping level for polythiophene. Isodesmic reactions were used to assess the stability of oligothiophene polycations in the gas phase.

Introduction Polythiophenes, which are the best studied conducting polymers, have already found significant commercial applications.1 Oligo- and polythiophenes are widely used as organic electronic materials in applications such as field effect transistors (FETs),2 light-emitting diodes (LEDs)3, and photovoltaic cells.4 The mechanism of conductivity in these polymers is one of the most important questions in the field of organic electronics.5-8 Despite considerable efforts, one of the most basic questions for understanding conductivity in doped polythiophenes remains whether bipolarons (localized dicationic species) or polaron pairs (polarons or radical cation species) serve as the charge carriers in doped polythiophenes.6c,d,7,9-13 Understanding whether spinless bipolarons or spin-carrying polaron pairs are responsible for charge transport and conductivity in oligo- and polythiophenes is crucial for the design of oligo- and polythiophene based organic semiconductor devices. Most studies agree that bipolarons are the major charge carriers in polythiophene at high doping levels.9,14 The early polaron model based on Su-Schrieffer-Heeger (SSH) calculations predicts bipolaron formation in the absence of extrinsic effects such as solvent, counterions, and interchain interactions.6a However, some recent studies suggested that mostly polarons (and not bipolarons) are formed in doped polythiophenes and in long oligothiophenes.7,15 Recently, it was suggested that differences in the nature of the dopant can change the polaronbipolaron equilibrium.16 A DFT study by Gao et al.17 showed that the closed-shell bipolaron structure is more stable for the short oligothiophene dications, while the open-shell two-polaron structure is proposed as the ground state for longer oligomers, starting from the sexithiophene dication. This was rationalized as a polaron pair ground state already for the octathiophene dication.17 In a * To whom correspondence should be addressed. Tel: +972-8-9346028. Fax: +972-8-9344142. E-mail: [email protected].

separate study, for chains equal to or longer than the heptathiophene and octathiophene dications, at the BHandHLYP/ 3-21G* and ROHF/3-21G* levels, respectively, the triplet state is shown to be more stable than the corresponding singlet state.18 In our recent paper,12 the singlet and triplet states of oligothiophene dications (from the sexithiophene dication to the 50-mer oligothiophene dication, nT2+, n ) 6 to 50) were studied at the B3LYP/6-31G(d) level. We found that the singlet state dominates for short and medium size oligothiophene dications and, while the singlet and triplet states are degenerate for longer dications, the triplet state is never a pure ground state for oligothiophene dications. For short oligothiophene dications (e.g., 6T2+), the bipolaron state is the more important state, with only a small contribution made by the polaron pair state. For medium size oligothiophene dications (e.g., 14T2+), both the bipolaron state and the polaron pair state contribute to the electronic structure. Finally, in long oligothiophene dications, such as 30T2+ and 50T2+, the contribution from the polaron pair state becomes dominant, and these molecules can be considered as consisting of two independent cation radicals or a polaron pair. The major conclusions of that study regarding the relative energy of the singlet state vs the triplet state and regarding the relative stability of the bipolaron vs the polaron pair were also supported by CASSCF/6-31G(d) calculations, which further increased confidence in using the B3LYP/6-31G(d) level to study oligothiophene cations.12 Although significant work has been performed on oligothiophene radical cations and dications, we are aware of only one theoretical study performed on oligothiophene polycations. That was a theoretical study of oligothiophene tetracations using a semiempirical AM1 Hamiltonian and considering only the bipolaron state.19 However, the applicability of semiempirical methods to the task of distinguishing between bipolarons and polaron pairs is questionable. We are also unaware of any experimental studies of well-defined oligothiophene polycations.

10.1021/jp071277p CCC: $37.00 © 2007 American Chemical Society Published on Web 06/21/2007

Long Oligothiophene Polycations

J. Phys. Chem. C, Vol. 111, No. 28, 2007 10663

TABLE 1: Relative Energies (in kcal/mol) and S2 Valuesa for Different Spin States of the Tri-, Tetra-, Hexa-, and Octacations of 10T, 20T, 30T, and 50T at B3LYP/ 6-31G(d)b 10T Spin stateb

20T

30T

50T

relative energyc

S2 valuea

relative energyc

S2 valuea

relative energyc

S2 valuea

relative energyc

S2 valuea

0 8.4

1.17 (0.81) 3.78 (3.75)

0 1.1

trication 1.69 (0.99) 3.80 (3.75)

0 0.1

1.75 (0.94) 3.80 (3.75)

0 -0.3

1.74 (0.84) 3.77 (3.75)

0.04 0d 6.7

0.16 (0.02) d 2.06 (2.00)

5.0 0 1.5

1.65 (3.94) 2.76 (2.13)

23.1

6.03 (6.00)

4.4

6.06 (6.00)

8.0 0 3.3 0.4 1.0

1.93 (4.67) 2.50 (2.06) 2.97 (2.17) 6.06 (6.00)

7.7 0 1.7 0.04 -0.1

2.02 (4.48) 2.91 (2.08) 3.00 (2.11) 6.05 (6.00)

U S

0 21.7

hexacation 1.41 (3.75) 12.05 (12.00)

0 5.7

2.38 (7.70) 12.07 (12.00)

0 1.1

2.89(8.91) 12.09 (12.00 )

U N

0 52.6

octacation 1.07 (2.11) 20.05 (20.00)

0 23.7

2.19 (7.80) 20.07 (20.00)

0 5.5

3.51 (11.80 ) 20.11 (20.00 )

D Q

tetracation R U T UT QP

a 2 S values after annihilation of the first spin contaminant are given in parentheses. b D, doublet; Q, quartet; R, spin-restricted singlet; U, spinunrestricted singlet; T, triplet; UT, triplet calculated at UB3LYP/6-31G(d) using the guess)mix command; QP, quintet; S, septet; N, nonet. c For trications, the energies are given relative to the doublet, whereas for tetra-, hexa-, and octacations the energies are given relative to the spinunrestricted singlet. d Values from stability calculations using the RB3LYP/6-31G(d) optimized geometry; see ref 27.

Here, we report DFT studies of long oligothiophene polycations (up to 50-mers) which help to better understand the stability of a polaron pair vs a bipolaron and to better elucidate the conduction mechanism in polythiophenes. For the first time, we extend the study of charge carriers in oligothiophene to tri-, tetra-, hexa-, and octacations, considering different spin states and the interplay between polarons and polaron pairs and reveal similarities between oligothiophene polycations. Our calculations suggest that, while the singlet state is preferred for relatively short oligothiophene polycations, in long oligothiophene polycations all spin states are practically degenerate. We find that the preferred electronic state for long oligothiophene polycations is that of singlet polaron pairs. In sufficiently long oligothiophene polycations, a clear separation of the charge into welldefined cation radical (polaron pair) regions has been observed. Achieving charge separation requires the lengths of about five thiophene rings. Conducting polymers usually do not have high molecular weights.20 50T (Mw ) 4102) can be considered a realistic model for polythiophene.21 For oligothiophene polycations, our calculation corresponds to a doping level from 6% (in the case of 50T3+) to 40% (in the case of 10T4+ or 20T8+). In the case of high and medium doping levels, our results are applicable to experimentally studied doped polythiophenes, while in the case of low doping levels, our results are applicable to the initial doping of polythiophene. Theoretical Methods All calculations were carried out using the Gaussian 03 series of programs.22 Oligothiophenes are denoted by nT, where n represents the number of thiophene rings. The geometries of nT3+ and nT4+ (n ) 10, 20, 30, and 50) as well as nT6+ and nT8+ (n ) 20, 30, and 50) were fully optimized using a hybrid density functional, Becke’s three-parameter exchange functional combined with the LYP correlation functional (B3LYP), and with the 6-31G(d) basis set.23 No symmetry constraints were used. Mulliken population analysis was used to calculate the charges (summarized for thiophene rings) of the oligothiophene polycations at B3LYP/6-31G(d). We have shown previously that natural population analysis (NPA) predicts charges for oligothiophene dications that are similar to their Mulliken charges.12

Similarly to the situation with long oligothiophene dications, the restricted wave function is unstable for singlet oligothiophene polycations. We have also found wave function instability for triplet states of 30T4+ and 50T4+ which were optimized using default guess in Gaussian 03. Trications were calculated in the doublet and quintet states, and tetracations were calculated in spin-unrestricted and spin-restricted singlet states and in the triplet and quintet states. Hexa- and octacations were calculated in spin-unrestricted singlet states and also in septet and nonet states, respectively. In addition, we have optimized 30T4+ in spin-restricted singlet and quintet states and 30T6+ in spinrestricted singlet and septet states with the “pure” density functional (BLYP) at the BLYP/6-31G(d) level to compare the energies calculated using pure DFT with those yielded by the hybrid DFT method. Spin-unrestricted singlets were calculated using unrestricted broken-symmetry UDFT method. Guess)mix keyword was used to generate an appropriate guess for UDFT calculations of all spin-unrestricted singlets and for the triplet states of 30T4+ and 50T4+. The data for oligothiophene radical cations and dications that were used in the isodesmic equations were taken from ref 12. The following abbreviations for spin states are used: D,doublet; Q, quartet; R, spin-restricted singlet; U, spin-unrestricted singlet; T, triplet; UT, triplet calculated at UB3LYP/ 6-31G(d) using guess)mix command; QP, quintet; S, septet; and N, nonet. Recently, we tested the ability of the broken-symmetry UB3LYP/6-31G(d) level to appropriately describe oligothiophene dications by comparing the results to those obtained from CASSCF.12 We found qualitative agreement between the two methods with respect to the relative energies of singlet and triplet oligothiophene dications and regarding the electronic structure (polaron vs polaron pair) of the dications. We note that the applicability of DFT to the study of long conjugated systems is uncertain and, to the best of our knowledge, has never been investigated in detail, as it is not possible to perform benchmark calculations using high-level ab initio methods for long conjugated systems. However, we believe that DFT is the best practical theoretical level to study the systems considered in this paper. Recent discussion in the literature regarding the applicability of DFT as a tool for studying biradicals concluded that UDFT is the best method for studying large systems where

10664 J. Phys. Chem. C, Vol. 111, No. 28, 2007

Zade and Bendikov

Figure 1. Energies of (a) eq 1 (disproportionation of an oligothiophene trication) and (b) eq 2 (disproportionation of an oligothiophene tetracation) vs the inverse of chain length (extrapolated using a quadratic fit).

Figure 2. Bond length alternation for (a) 10T3+, (b) 20T3+, (c) 30T3+, and (d) 50T3+ (dash-dotted vertical lines separate a unit charge and are based on Figure 3). The x-axis is the C-C bond number starting from one end of the conjugated chain through to the middle of that chain. A mirror image of the pattern shown in the figure is observed for the remaining half of each oligothiophene chain. The repeating sets of three linked points represent intraring C-C bonds (the second of these bonds is the middle ring C2-C3 bond), while every fourth point on the x-axis corresponds to an interring C-C bond. The points are linked solely as a visual aid.

high-level ab initio calculations are impractical.24 For a more detailed discussion, see ref 25. Results and Discussion To thoroughly understand the nature of the charge carriers in doped conjugated polymers, we have calculated the tri- and tetracations for 10T, 20T, 30T, and 50T as well as hexa- and octacations for 20T, 30T, and 50T at B3LYP/6-31G(d) (Table 1).27 The complete set of spin states was considered for tri- and

tetracations (doublet and quartet for trications; singlet, triplet, and quintet for tetracations) while only the unrestricted singlet and high spin states were considered for hexa- and octacations (the singlet and septet states for hexacations and the singlet and nonet states for octacations). Some S2 values are higher than expected for the corresponding spin states. In the case of trications, the S2 values for the quartet state are around 3.773.80, which is very close to the expected value of 3.75, thus the calculation for the quartet can be considered reliable.



Figure 3. Charge distribution for (a) 10T3+, (b) 20T3+, (c) 30T3+, and (d) 50T3+ (dash-dotted vertical lines separate a unit charge).

However, in the case of the doublet state of 30T3+, the S2 value reaches 1.75 before annihilation of the first spin contaminant, and 0.94 after annihilation, instead of the expected value of 0.75. Thus, the calculation for the doublet is affected by considerable mixing with higher spin states (apparently, the quartet). In the case of other polycations, this phenomenon is even more pronounced. We have found that the wave function is unstable for the optimized structure of the triplet state of 30T4+ and 50T4+ (which probably has an electronic configuration of all paired electrons except for two which are spin-up). Using the guess)mix command leads to another triplet electronic configuration which can probably be described as having four unpaired electrons (three spin-up and one spin-down). For the triplet state (obtained using the guess)mix command) of 50T4+ (marked as UT in Table 1), S2 before annihilation is 3.0, while it is close to the expected value of 2.0 after spin annihilation. Thus, apparently, the quintet state is mixed into the calculations for triplets. In the case of the singlet state of 30T4+, the S2 values after spin annihilation reach the value of 4.67. This makes the results for singlet state tetracations unreliable, and therefore, they are given in Table 1 for comparison purposes only and should not be treated quantitatively. Nevertheless, we will later bring evidence that UB3LYP wave functions for an open-shell singlet describe polaron lengths in doped oligothiophenes correctly (see the Polaron Lengths in Doped Oligothiophenes section). The calculation for the quintet state of tetracations results in S2 values very close to the expected value of 6.0. Similarly, in the case of hexa- and octacations, the S2 values for the singlet increase from 20T to 50T and reach as high as 3.51 and 11.80 (before and after annihilation, respectively), for the unrestricted singlet

state of 50T8+. This indicates that the singlet configuration is not pure, but rather is heavily contaminated by higher states, and consequently, the energies of the high spin states are not expected to be much higher than that of the singlet. Higher spin states, that is, the septet for hexacations and the nonet for octacations, exhibit S2 values close to the expected values of 12 and 20, respectively. In agreement with our expectations from the S2 values for longer oligothiophene polycations (such as 50Tn+), all the spin states we considered are nearly degenerate (Table 1). Indeed, for 10T3+, the quintet state is 8.4 kcal/mol higher than the doublet state, but the two states become degenerate for 30T3+ and 50T3+. For oligothiophene tetracations, the difference between a quintet and spin-unrestricted singlet state is 23.1 kcal/ mol for 10T4+, but again, the two states become degenerate for 50T4+. A similar picture is observed for hexa- and octacations. However, even for 50T8+, the unrestricted singlet state is 5.5 kcal/mol lower in energy than the nonet state, while this difference is much larger (52.6 kcal/mol) for 20T8+. Thus, in sufficiently long oligothiophene octacations, the two spin states will be nearly degenerate. To eliminate the contribution from the Hartree-Fock (HF) wave function, which is known to lead to high spin contamination for long conjugated systems,26 we optimized 30T4+ in singlet and quintet states and 30T6+ in singlet and septet states using the “pure” density functional BLYP/6-31G(d) method. In contrast to our findings using the B3LYP/6-31G(d) method (Table 1), the spin-restricted singlet wave function of 30T6+ does not show RHF-UHF instability at BLYP/6-31G(d). The 30T4+ singlet at RBLYP/6-31G(d) is 3.6 kcal/mol more stable


Zade and Bendikov

Figure 4. Bond length alternation for (a) 10T4+, (b) 20T4+, (c) 30T4+, and (d) 50T4+ (see the caption of Figure 2).

SCHEME 1. Structure of an Aromatic (left) and a Quinoid (right) Form of Oligothiophene

than the 30T4+ quintet at UBLYP/6-31G(d). The 30T6+ singlet at RBLYP/6-31G(d) is 14.6 kcal/mol more stable than the 30T6+ septet at UBLYP/6-31G(d). A pure density functional such as BLYP predicts degeneracy between all spin states at longer oligomer lengths than the B3LYP functional does. However, although the results at the B3LYP and BLYP levels are somewhat different quantitatively, the qualitative picture is the same at both levels. Tri- and Tetracations of Oligothiophenes. (a) RelatiVe Stability of the Oligothiophene Trication Vs a Dication plus Cation Radical and of the Tetracation Vs Two Dications. We have evaluated the stability of the oligothiophene trication vs a radical cation (polaron) and dication, as well as investigated the stability of the tetracation vs two dications. To do so, we used the isodesmic reaction as shown in eqs 1 and 2, respectively, utilizing UB3LYP/6-31G(d) open-shell singlet energies.28

nT3+ + nT f nT •+ + nT2+

(1)

nT4+ + nT f 2nT2+

(2)

First we note that the disproportionation energies for tri- and tetracations are very large (Figure 1). However, as expected,

the stability of the tri- and tetracations vs a cation radical and dication or two dications, as in eqs 1 and 2, increases with increasing chain length. Indeed, extrapolation to infinite oligomer lengths using the data from Figure 1 leads to practically zero disproportionation energy. We also note that the absolute energies of eq 2 are much higher than those of eq 1 (Figure 1). The disproportionation of 30T4+ releases 76.8 kcal/mol (Figure 1b); the disproportionation of 30T3+ releases 36.5 kcal/mol (Figure 1a), while the disproportionation12 of 30T2+ releases only 17.3 kcal/mol. Thus, the general trends seen in Figure 1 are also similar to the observed12 disproportionation of oligothiophene dications into two cation radicals, however, the absolute energies of eqs 1 and 2 are much higher than those observed for that disproportionation. (b) Bond Length Alternation and Charge Distribution in Oligothiophene Trications. The doublet and quartet states of trications 20T3+, 30T3+, and 50T3+ have very similar energies (doublet-quartet energy difference is 1.1, 0.1, and -0.3 kcal/ mol for 20T3+, 30T3+, and 50T3+, respectively, whereas the doublet of 10T3+ is significantly more stable (by 8.4 kcal/mol) than the corresponding quartet (Table 1). This stability trend is also reflected in the bond length alternation (BLA) and charge distribution data. A charged π-conjugated system tends to have a different geometry to that of the neutral system, and this is reflected in the carbon-carbon BLA trends (Scheme 1 and Figure 2).29 When the C1-C2 and C3-C4 bonds of a thiophene ring (Scheme 1) are shorter than the C2-C3 bond (so producing a Λ-shaped pattern in the sets of three linked data points shown in Figure 2), the ring is considered aromatic. By contrast, when the C1-C2 and C3-C4 bonds of a thiophene ring are longer than



Figure 5. Charge distribution for (a) 10T4+, (b) 20T4+, (c) 30T4+, and (d) 50T4+ (dash-dotted vertical lines separate a unit charge).

the C2-C3 bond (thus producing a V-shaped pattern in the sets of three linked data points shown the Figure 2), the ring is considered quinoid (Scheme 1). The BLA patterns for both the doublet and quartet states in 20T3+ and 30T3+ are similar to each other (parts b and c of Figure 2). They clearly show the presence of three distinct charge-carrying areas, each capable of bearing one polaron, in separated regions of the chain. This is seen most clearly in 20T3+, where the oligothiophene chain divides into three quinoid regions (one and a half of which are shown in Figure 2b) separated from each other by aromatic regions and where each quinoid region is capable of carrying one polaron (cation radical). Inspection of interring C-C bonds shows that these bonds become shorter in the middle of the unit charge region (bonds 8-12 in 20T3+), which is where the thiophene rings become quinoid. Then, in the charge-separating region (bonds 20-28 in 20T3+) the interring C-C bonds become longer and the thiophene rings become aromatic. Although, in 30T3+, the chain divides into two, rather than three, quinoid regions, nevertheless, three charge-bearing areas can be discerned. Thus, based on the BLA pattern, the electronic structures of both 20T3+ and 30T3+ correspond to the presence of three polarons and not to a bipolaron and a polaron. The charge distribution graphs (Figure 3) closely match the picture that emerges from the BLA pattern. For example, in 30T3+, the charge-separating region appears around ring number 9 (around C-C bond number 36) in both the BLA pattern and charge distribution graphs (Figures 2c and 3c). In 10T3+(Figure 2a), the doublet and quartet states have different BLA patterns; all rings are quinoid and thus neither pattern shows clear separation to three distinct charge-carrying areas, presumably because the oligothiophene backbone is too short in this instance.

Thus, 10T3+ does not adopt the three separated polarons configuration. In 30T3+, the middle charge is delocalized over a larger number of rings (about 12 rings); therefore, quinoid rings are not observed in the central region. This is even more pronounced in 50T3+ (Figure 2d) where quinoid rings are not observed throughout the whole molecule (all thiophene rings are aromatic), however, three charge-bearing regions (one and half of which are shown in Figure 2d) can be still seen in the figure. (c) Bond Length Alternation and Charge Distribution in Oligothiophene Tetracations. For 10T4+, the singlet is clearly the ground state, with the triplet and quintet spin states having significantly higher energies of 6.7 and 23.1 kcal/mol, respectively (Table 1).27 The S2 values of 10T4+ are as expected for the corresponding spin states. However, for the longer tetracations 30T4+ and 50T4+, all three spin states (U, UT, and QP) become degenerate (Table 1). Trends in the BLA patterns (Figure 4) and the charge distribution patterns (Figure 5) of the U, UT, and QP states of oligothiophene tetracations are similar to those of the trications discussed above (Figures 2 and 3) and to the open-shell singlet state of the oligothiophene dications discussed in our earlier work.12 On the other hand, trends in the BLA patterns (Figure 4) and the charge distribution patterns (Figure 5) of the R and T states of 30T4+ and 50T4+ are similar to the closed-shell singlet state of oligothiophene dications.12 The BLA patterns (Figure 4b) of three spin states for 20T4+, namely, the openshell singlet (calculated at UB3LYP/6-31G(d)), the triplet, and the quintet, are somewhat similar, showing clear separation into four charges, thus predicting a structure of two polaron pairs (four polarons). For the open-shell singlet (calculated at the UB3LYP/6-31G(d) level) and triplet states, all rings are quinoid


Zade and Bendikov

Figure 6. Energies vs the inverse of chain length for the disproportionation of the oligothiophene hexacation (a and b) and octacation (c and d) as per the equations shown on each graph: (a) eq 3, (b) eq 4, (c) eq 5, and (d) eq 6 (extrapolated using a quadratic fit).

except for the terminal rings. However, rings in the quintet state in the region of charge separation, where charges drop to their minimum values (around ring numbers 5, 10, and 15), are aromatic. In accordance with the charge distribution on closedshell singlet 20T4+ calculated at RB3LYP/6-31G(d) (Figure 5b), which predicts charge delocalization over the oligothiophene backbone, nearly all rings are quinoid (Figure 4b), except for two central rings and the two terminal rings, which are aromatic. This indicates that the tetracation of 20T has a double bipolaron character at RB3LYP/6-31G(d). The BLA picture for 30T4+ and 50T4+ (parts c and d of Figure 4) shows similar features to that of 20T4+ for all states except for the T state (Table 1). We have calculated two electronic states for triplet 30T4+ and 50T4+ (T and UT states, Table 1). The charge distribution picture for the triplet T state of 30T4+ and 50T4+ is significantly different from that of the quintet. The T state of 30T4+ and 50T4+ consist of one bipolaron and one polaron pair, while the UT state (Table 1) consists of four separated polarons (parts c and d of Figures 4 and 5). The electronic structure behaviors of oligothiophene tetracations are similar to those of oligothiophene dications. For 30T4+ and 50T4+, the singlet spin-unrestricted state charge distribution, along with that of the quintet, indicates the presence of four separated polarons instead of two bipolarons (parts c and d of Figure 4). For tetracations, the charge distribution graphs (Figure 5) closely match the picture arising from the BLA graphs (Figure 4). In 10T4+, there is charge delocalization over the oligothiophene backbone, excluding the terminal rings, in all spin states. In 30T4+ (Figure 5c), the charge distributions for the quintet state and singlet state calculated at UB3LYP/6-31G(d) are practically identical; however, taking into account the large S2

values for the singlet calculated at UB3LYP/6-31G(d), it appears that the singlet is heavily contaminated by the quintet. For both these states, a clear separation of charges is observed, with charge-separated regions centered at around ring numbers 7, 15, and 24, which are the same regions where charge separation based on the BLA data is observed in Figure 4c. The charge distribution picture for 20T4+ (Figure 5b) is intermediate between that of 10T4+ (Figure 5a) and 30T4+ (Figure 5c). On the basis of the BLA and charge distribution data, long oligothiophene tetracations consist of two polaron pairs (four separated polarons) without any significant contribution from bipolarons. Hexa- and Octacations of Oligothiophenes. (a) RelatiVe Stability of the Oligothiophene Hexa- and Octacations Vs the Dication, Trication, and Tetracation. We have evaluated the stability of the oligothiophene hexacation vs two trications and vs a dication and tetracation, as well as the stability of the octacation vs two tetracations and vs a hexacation and dication. The following equations are used, taking into consideration UB3LYP/6-31G(d) singlet energies28

nT6+ + nT f 2nT3+

(3)

nT6+ + nT f nT4+ + nT2+

(4)

nT8+ + nT f 2nT4+

(5)

nT8+ + nT f nT6+ + nT2+

(6)

The disproportionation energy for oligothiophene hexa- and octacations is very large (even for 50T6+ and 50T8+, the disproportionation energies are around 100 and 160 kcal/mol)



Figure 7. Bond length alternation for (a) 20T6+, (b) 30T6+, (c) 50T6+, (d) 20T8+, (e) 30T8+, and (f) 50T8+ (see the caption of Figure 2).

which means that, at least in the gas phase, even long polycations such as 50T are very unstable and repulsion between positive charges is still very large in 50T6+ and 50T8+. As in the case of oligothiophene tri- and tetracation disproportionation, hexa- and octacation stability increases with increasing chain length, according to eqs 3-6, and extrapolation to infinite oligomer lengths using the data from Figure 6 leads to a nearly zero disproportionation energy for infinitely long oligothiophene hexa- and octacations. This supports our conclusion that, for long oligothiophene polycations, similarly to long oligothiophene dications,12 the polaron pair state becomes dominant

and, in this state, two or more positive charges weakly interact with each other. (b) Bond Length Alternation and Charge Distribution in Oligothiophene Hexa- and Octacations. In addition, we have calculated open-shell singlet configuration for 20T6+, 30T6+, 50T6+, 20T8+, 30T8+, and 50T8+; a septet configuration for 20T6+, 30T6+, and 50T6+; and a nonetconfiguration for 20T8+, 30T8+, and 50T8+ at the UB3LYP/6-31G(d) level (Table 1). The septet state of 20T6+ is 21.7 kcal/mol higher in energy than the open-shell singlet state, while this difference decreases to 1.1 kcal/mol for 50T6+. The nonet state of 20T8+ is significantly


Zade and Bendikov

Figure 8. Charge distribution for (a) 20T6+, (b) 30T6+, (c) 50T6+, (d) 20T8+, (e) 30T8+, and (f) 50T8+ (dash-dotted vertical lines separate a unit charge).

higher in energy than the open-shell singlet state (by 52.6 kcal/ mol); however, this difference decreases to 5.5 kcal/mol for 50T8+ (Table 1). Thus, although in 50T8+ the spin states are not degenerate, it is clear that they will become degenerate for longer oligothiophene octacations. Trends in the BLA patterns (Figure 7) and the charge distribution patterns (Figure 8) of the oligothiophene hexa- and octacations are similar to those of the tri- and tetracations (Figures 2-5). The charge distribution graphs (Figure 8) closely match the picture which arises from the BLA graphs (Figure 7).

For the open-shell singlet state calculated at the UB3LYP/ 6-31G(d) level for 20T6+, all rings are quinoid except of the terminal rings (Figure 7a). Therefore, 20T is not long enough to accommodate six polarons in separate regions and the openshell singlet state of 20T6+ can be considered as three bipolarons. The septet state of 20T6+ shows some separation into polarons pairs, however, these are not clearly separated. In the case of the septet state of 30T6+, the BLA data (Figure 7b) somewhat suggest six polarons (12 rings are aromatic while all the remaining rings are quinoid), as does the charge distribution

Long Oligothiophene Polycations pattern (Figure 8b). However, in the open-shell singlet state of 30T6+, the BLA data do not show clearly separated areas (only eight rings are aromatic while all the remaining rings are quinoid). The BLA data and the charge distribution pattern in both the singlet and septet states for 50T6+ clearly indicate the presence of six separated polarons. The near degeneracy of the singlet and septet states of 50T6+ is reflected in the BLA and charge distribution data. Thus, with increasing chain length, the charges are more clearly separated into polarons and the higher spin states become degenerate. In 20T8+, there is charge delocalization over the oligothiophene backbone; all rings are quinoid at UB3LYP/6-31G(d) in the open-shell singlet and nonet states, thus 20T8+ clearly consists of four bipolarons. In 30T8+, there is a marked difference between the BLA patterns of the open-shell singlet and nonet configurations; all rings are quinoid in the singlet state, while eight rings are aromatic in the nonet state. Thus, the open-shell singlet state of 30T8+ consists of mostly bipolarons, while the nonet state shows some separation of charges based on the BLA pattern (Figure 7e). Polycations 20T and probably 30T are not long enough to accommodate the eight charges as separated polarons. For 50T8+, in both the openshell singlet and nonet states, the charge distribution pattern (Figure 8f) shows separated charge-carrying regions centered at around ring numbers 3, 8, 15, 22, 29, 36, 43, and 47, which are the same regions where charge separation based on the BLA data is observed (Figure 7f). Thus, in 50T8+, eight separated polarons are clearly present and we believe that this trend will continue for other oligothiophene polycations. Polaron Length in Doped Oligothiophenes. Estimating the effective length of a polaron in π-conjugated systems is of immense importance to understanding the conduction mechanism in conjugated polymers.6 According to the SSH model, the effective length of a soliton in a π-system (polyacetylene) is about 14 carbon atoms.6a Our calculations have shown that for 10T3+, 10T4+ (as well as for 14T4+), 20T6+, 20T8+, and 30T8+ there is no charge separation, while for the other cations in Table 1 (starting from 20T3+, 20T4+, 30T6+, and 50T8+) charge separation into regions that each bear a polaron is observed. Thus, the minimal conjugated length required for a polaron in polythiophene is about five thiophene rings according to B3LYP/6-31G(d) calculations. These results are in a nice agreement with experimental studies which indicate that the maximal doping for highest conductivity in polythiophene is about 20%, which corresponds to one positive charge per five thiophene rings.5,30 They also indirectly support the applicability of a hybrid density functional such as B3LYP to the study of charge distribution in positively charged oligo- and polythiophenes. Conclusions This is the first theoretical study of the different electronic states of oligothiophene polycations. In the case of oligothiophene polycations (similarly to what has been found for oligothiophene dications), the singlet state (in the case of tetra-, hexa-, and octacations) and the doublet state (in the case of trications) are most probably the ground states of the oligomers studied, while for longer oligomers, the different spin states of the polycations exhibit degeneracy. On the basis of the BLA, charge distribution, and relative energies data, we have shown that sufficiently long oligothiophene tri-, tetra-, hexa-, and octacations behave similarly to dications, with clear separation of charges into well-defined cation radical regions (a polaron pair configuration) along the oligothiophene chain. On the other

J. Phys. Chem. C, Vol. 111, No. 28, 2007 10671 hand, the electronic structures of short oligothiophene polycations such as 10T3+, 10T4+, 20T6+, 20T8+, and 30T8+ have a largely bipolaron nature. So, bipolarons are only formed when there is insufficient space on the chain to separate the polarons. We have addressed the question of the effective length of a polaron in π-conjugated systems, and we have found that about five thiophene rings are required to accommodate a polaron, which is in nice agreement with a typical doping level for polythiophene. Acknowledgment. We thank the MINERVA Foundation for financial support. M.B. is the incumbent of the Recanati career development chair and a member ad personam of the Lise Meitner-Minerva Center for Computational Quantum Chemistry. Supporting Information Available: Tables of absolute energies and the Cartesian coordinates of the optimized geometries of all calculated oligothiophene polycations at B3LYP/ 6-31G(d) are given. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) (a) Electronic Materials: The Oligomer Approach; Mu¨llen, K., Wegner, G., Eds.; Wiley-VCH: Weinheim, Germany, 1998. (b) Handbook of Oligo- and Polythiophenes; Fichou, D., Ed.; Wiley-VCH: Weinheim, Germany, 1999. (c) Handbook of Conducting Polymers, 2nd ed.; Skotheim, T. A., Elsenbaumer, R. L., Reynolds, J. R., Eds.; Marcel Dekker: New York, 1998. (d) Conjugated Polymers: The NoVel Science and Technology of Highly Conducting and Nonlinear Optically ActiVe Materials; Bre´das, J. L., Silbey, R., Eds.; Kluwer Academic Publishing: Dordrecht, The Netherlands, 1991. (e) Handbook of Organic ConductiVe Molecules and Polymers; Nalwa, H. S., Ed.; John Wiley & Sons: New York, 1997; Vols. 1-4. (f) Tour, J. M. Chem. ReV. 1996, 96, 537. (g) Roncali, J. Chem. ReV. 1997, 97, 173. (h) Groenendaal, L. B.; Jonas, F.; Freitag, D.; Pielartzik, H.; Reynolds, J. R. AdV. Mater. 2000, 12, 481. (i) Perepichka, I. F.; Perepichka, D. F.; Meng, H.; Wudl, F. AdV. Mater. 2005, 17, 2281. (2) (a) Horowitz, G.; Peng, X.; Fichou, D.; Garnier, F. J. Appl. Phys. 1990, 67, 528. (b) Paloheimo, J.; Kuivalainen, P.; Stubb, H.; Vuorimaa, E.; Yli-Lahti, P. Appl. Phys. Lett. 1990, 56, 1157. (c) Garnier, F.; Hajlaoui, R.; Yassar, A.; Srivastava, P. Science 1994, 265, 1684. (d) Dodabalapur, A.; Katz, H. E.; Torsi, L.; Haddon, R. C. Science 1995, 269, 1560. (e) Dimitrakopoulos, C. D.; Malenfant, P. R. L. AdV. Mater. 2002, 14, 99. (f) Horowitz, G. AdV. Mater. 1998, 10, 365. (g) Katz, H. E. J. Mater. Chem. 1997, 7, 369. (h) Halik, M.; Klauk, H.; Zschieschang, U.; Schmid, G.; Ponomarenko, S.; Kirchmeyer, S.; Weber, W. AdV. Mater. 2003, 15, 917. (3) (a) Geiger, F.; Stoldt, M.; Schweizer, H.; Baüerle, P.; Umbach, E. AdV. Mater. 1993, 5, 922. (b) Mitschke, U.; Baüerle, P. J. Mater. Chem. 2000, 10, 1471. (c) Barbarella, G.; Favaretto, L.; Sotgiu, G.; Zambianchi, P.; Bongini, A.; Arbizzani, C.; Mastragostino, M.; Anni, M.; Gigli, G.; Cingolani, R. J. Am. Chem. Soc. 2000, 122, 11971. (d) Barbarella, G.; Favaretto, L.; Sotgiu, G.; Antolini, L.; Gigli, G.; Cingolani, R.; Bongini, A. Chem. Mater. 2001, 13, 4112. (4) (a) Brabec, C. J.; Sariciftci, N. S.; Hummelen, J. C. AdV. Funct. Mater. 2001, 11, 15. (b) Hoppe, H.; Sariciftci, N. S. J. Mater. Res. 2004, 19, 1924. (5) Patil, A. O.; Heeger, A. J.; Wudl, F. Chem. ReV. 1988, 88, 183. (6) (a) Heeger, A. J.; Kivelson, S.; Schrieffer, J. R.; Su, W. P. ReV. Mod. Phys. 1988, 60, 781. (b) Bre´das, J. L.; Street, G. B. Acc. Chem. Res. 1985, 18, 309. (c) Miller, L. L.; Mann, K. R. Acc. Chem. Res. 1996, 29, 417. (d) Salaneck, W. R.; Friend, R. H.; Bre´das, J. L. Phys. Rep. 1999, 319, 231. (7) Furukawa, Y. J. Phys. Chem. 1996, 100, 15644. (8) Bredas, J. L.; Beljonne, D.; Coropceanu, V.; Cornil, J. Chem. ReV. 2004, 104, 4971. (9) Lafolet, F.; Genoud, F.; Divisia-Blohorn, B.; Aronica, C.; Guillerez, S. J. Phys. Chem. B 2005, 109, 12755. (10) (a) Kaneto, K.; Hayashi, S.; Ura, S.; Yoshino, K. J. Phys. Soc. Jpn. 1985, 54, 1146. (b) Chen, J.; Heeger, A. J.; Wudl, F. Solid State Commun. 1986, 58, 251. (c) Colaneri, N.; Nowak, M.; Spiegel, D.; Hotta, S.; Heeger, A. J. Phys. ReV. B 1987, 36, 7964. (d) Fichou, D.; Horowitz, G.; Xu, B.; Gamier, F. Synth. Met. 1990, 39, 243. (11) (a) Bre´das, J. L.; The´mans, B.; Fripiat, J. G.; Andre´, J. M.; Chance, R. R. Phys. ReV. B 1984, 29, 6761. (b) Bre´das, J. L.; Wudl, F.; Heeger, A. J. Solid State Commun. 1987, 63, 577. (c) Bertho, D.; Jouanin, C. Phys. ReV. B 1987, 35, 626. (d) Silva, G. M. E. Phys. ReV. B 2000, 61, 10777. (12) Zade, S. S.; Bendikov, M. J. Phys. Chem. B 2006, 110, 15839.

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Theoretical Study of Long Oligothiophene Polycations as a Model for

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