J. Phys. Chem. B 2006, 110, 15839-15846
15839
Theoretical Study of Long Oligothiophene Dications: Bipolaron vs Polaron Pair vs Triplet State Sanjio S. Zade and Michael Bendikov* Department of Organic Chemistry, Weizmann Institute of Science, 76100 RehoVot, Israel ReceiVed: May 5, 2006; In Final Form: June 9, 2006
A series of oligothiophene dications (from the sexithiophene dication to the 50-mer oligothiophene dication, nT2+, n ) 6-50) were studied. Density functional theory (DFT) at the B3LYP/6-31G(d) level and, in some cases, also at BLYP/6-31G(d), was applied to study the singlet and triplet states of the whole series. We found that the singlet state is the ground state for all oligothiophene dications up to the 20-mer, and that the singlet and triplet states are degenerate for longer oligomers. Thus, the triplet state is never a pure ground state for these dications. We found that, for short oligothiophenes dication (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. Results from isodesmic reactions show that the stability of oligothiophene cation radicals over dications is inversely proportional to chain length. Small oligothiophene dications (n ) 6-12) were studied at the CASSCF(m,m)/6-31G(d) (m ) 4, 6, and 10) level. The major conclusions of this paper regarding the relative energy of the singlet state versus the triplet state and regarding the relative stability of the bipolaron versus the polaron pair were also supported by CASSCF calculations.
Introduction Polythiophenes are among the most promising and best studied conducting polymers,1 while oligothiophenes are important materials in organic electronics, for example in field effect transistors (FET),2 light emitting diodes (LED),3 and photovoltaic cells.4 The conduction mechanism in these useful polymers is a subject of intense investigation.5-7 Both interand intrachain interactions are important for desired conductivity and electronic properties. Bipolarons are dicationic species of π-conjugated systems where excess charges concentrate over a limited section of the chain. This leads to structural distortion only in that part of the chain being stabilized by electronphonon coupling. A polaron-pair represents charge separation over the different parts of the chain.5 Despite considerable efforts, one of the most basic questions still to be answered to understand conductivity and electronic properties in doped polythiophenes remains whether the charge carriers in doped polythiophenes are spinless bipolarons or spin-carrying polaron pairs, and it is crucial for the design and application of oligoand polythiophene-based organic semiconductor devices.5c,d,7,8 Initial experimental studies9 (using UV-Vis-NIR and ESR techniques) of highly doped polythiophene showed the bipolaron structure to be dominant. Later, this finding was supported by theoretical studies.10 However, the majority of the early theoretical studies used the model Hamiltonians of Su-SchriefferHeeger (SSH) and of Pariser-Parr-Pople (PPP), or low-level ab initio calculations such as HF/STO-3G, which may be considered questionable methods today for studying the existence of polaron pairs or bipolarons. Semiempirical calculations predicted that two polarons on the oligothiophene chain would * Corresponding author phone: +972-8-9346028; fax: +972-89344142; e-mail:
[email protected].
be more stable than a bipolaron for oligomers longer than the dodecamer,11 and many other reports of electronic structure calculations for oligothiophene dications also relied on semiempirical calculations,12 however, again the applicability of such methods to the task of distinguishing between bipolarons and polaron pairs is open to discussion. Most of the theoretical studies which deal with the question of whether polarons or bipolarons are the charge carriers in doped oligothiophenes appear outdated. G. Brocks predicted, using a pure DFT-LDA method, that the polaron pair is a stable charge carrier in oligothiophenes and that the bipolaron is intrinsically unstable with respect to separation into polarons.13 A majority of studies agree that bipolarons are the major charge carriers at high doping levels. Recent ESR studies14 suggested that, at very low doping concentrations (below 0.1%), only paramagnetic polarons carry electric charge, while at high doping concentrations (up to 1%) the diamagnetic bipolarons contribute to conductivity. Some recent experimental studies appeared to support the view that two polarons on a sufficiently long oligothiophene chain are more stable than the bipolaron.7,15 However, other recent studies suggested that a bipolaron is formed in doped polythiophenes. For example, studies of selfassembled polyelectrolyte multilayers consisting of polythiophene showed that polarons are primarily formed upon oxidation, and later disproportionate into neutral and dicationic segments,16 and another study concluded that the greater length of the oligothiophene subunit stabilizes bipolarons vs polaron pairs.8 It was also suggested recently that differences in the natures of the dopant used can change the polaron-bipolaron equilibrium.17 Attempts to theoretically study oligothiophene dications, including specific studies of dopants, have also been reported,
10.1021/jp062748v CCC: $33.50 © 2006 American Chemical Society Published on Web 07/27/2006
15840 J. Phys. Chem. B, Vol. 110, No. 32, 2006 and indicated that the bipolaron is significantly more stable than a polaron pair. However, in these calculations, the dopant was covalently bonded to the oligothiophene chain, and forming chemical species which do not allow polaron pair formation.18 Dimerization of two polarons on different chains to form an oligothiophene dimer was also considered as an alternative to formation of a bipolaron on a single chain,19 although calculations indicated that formation of polaron pairs in π-dimers of oligothiophenes20 is preferable over formation of a bipolaron. Furthermore, a recent paper does not support the existence of stable dimers for small (up to quaterthiophene) singly oxidized oligothiophenes.21 Recently, a DFT study by Gao et al.22 showed that the closedshell bipolaron structure is more stable for oligothiophene dications of pentathiophene and smaller (n e 5), while the openshell two-polaron structure is the ground state for sexithiophene dication (6T2+) and longer dications. This was rationalized as a polaron pair state already for the octathiophene dication. However, triplet states were not considered in this study.22 Furthermore, Geskin and Bre´das reported that the triplet state is more stable than the singlet state for chains equal to or longer than the heptathiophene dication and octathiophene dications at the BHandHLYP/3-21G* and ROHF/3-21G* levels, respectively.23 However, such methods artificially stabilized higher multiplets. Furthermore, the calculations were carried out only for closed-shell dications, since unrestricted Hartree-Fock (UHF) calculations resulted in huge spin contamination (S2 values were up to five). The triplet state was also found to be more stable in a CAS-AM1 calculation for the ocatathiophene dication and decathiophene dication compared to the singlet polaron pair; however, the stability of the singlet polaron pair increases with the size of the active space, compared to the triplet state.23 The question of whether the triplet is a ground state in oligothiophene dications is important not only for understanding the nature of charge carriers, but also because of the extensive applications of oligo- and polythiophenes in optoelectronic devices such as LEDs.3 Here we report on DFT and CASSCF studies of long oligothiophene dications (up to 50-mer) that we carried out to obtain more knowledge about the stability of a polaron pair vs bipolaron and of a singlet polaron pair vs a triplet polaron pair. We found that the triplet state is of lesser or equal stability compared to the singlet for every oligothiophene dication studied, and we provide more evidence for a preference for the polaron pair over the bipolaron electronic state for long oligothiophene dications. Theoretical Methods Oligothiophenes are denoted by nT, where n represents the number of heteroaromatic rings. All calculations were carried out using the Gaussian 03 program system.24 The geometries of nT, nT+, and nT2+ (n ) 6-10, 12, 14, 20, 30, and 50) were fully optimized using a hybrid density functional, Becke’s threeparameter exchange functional combined with the LYP correlation functional (B3LYP), and with the 6-31G(d) basis set.25 All molecules were constrained to C2h or C2V symmetry. Release of the symmetry constraint did not change the geometries, and molecules remain planar, as was tested in several cases for short, medium, and long oligothiophenes. Mulliken population analysis was used to calculate the charges (summarized for thiophene rings) of the oligothiophene dications at B3LYP/6-31G(d). In some cases, charges from natural population analysis (NPA charges)26 were also calculated at B3LYP/6-31G(d) and compared to the Mulliken charges. In addition, we calculated 10T2+,
Zade and Bendikov 20T2+, and 30T2+ with the “pure” density functional (BLYP) at the BLYP/6-31G(d) level to compare the energies and charge distributions calculated using pure DFT with those yielded by the hybrid DFT method. Dications were calculated in spinrestricted and spin-unrestricted singlet states, and in the triplet state. Spin-unrestricted singlets were calculated using unrestricted broken-symmetry UDFT methods. Guess)mix keyword was used in order to generate an appropriate guess for UDFT calculations. In some cases, the stability of the wave function was checked, and the wave function was reoptimized if necessary using the stable)opt keyword in Gaussian 03. The results for oligothiophene dications obtained at the RB3LYP level correspond to a bipolaron state, and the results obtained at the UB3LYP level correspond to a mixture of bipolaron and polaron pair state. An isodesmic reaction was used to evaluate the stability of the cation radical (polaron) versus the dication (bipolaron). Calculated results discussed in this paper are at the B3LYP/6-31G(d) level, unless stated otherwise. As was previously reported,22 the restricted wave function (at B3LYP/6-31G(d)) for the oligothiophene dication, starting from sexithiophene, shows RHF to UHF instability.27 We note that the unrestricted broken symmetry UB3LYP method considers the mixing of closed shell and open shell structures.28 Therefore, UB3LYP calculations always yield the solution which has a partially closed shell structure mixed with an open shell structure. Generally, the UB3LYP solution is always lower than, or of the same energy as, the RB3LYP solution. 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. We note that the singlet molecules calculated in this paper using unrestricted brokensymmetry UDFT methods are considered biradicals. 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 high-level ab initio calculations are impractical. Indeed, recently Davidson and Clark commented, “Until the reliability of a better model is established, broken spin DFT remains the most consistent choice for large molecules where complete active space SCF with perturbation corrections is not feasible.”29 For a more detailed discussion, see ref. 30. To support our DFT results, we also performed CASSCF calculations using a limited active space up to the CASSCF(10,10)/6-31G(d) level. CASSCF(m,m)/6-31G(d) (m ) 2, 4, 6, 10) single point calculations were performed using B3LYP/631G(d) optimized geometries for 6T2+, 8T2+, 10T2+, and 12T2+. First, single point calculations at the HF/6-31G(d) level were performed, and the resulting orbitals were examined using the GaussView for Windows program to ensure that only π-orbitals were included in the active space. The m/2 highest occupied molecular orbitals and the m/2 lowest unoccupied molecular orbitals were included in the active space. Complete geometry optimizations at the CASSCF(m,m)/6-31G(d) level were also performed in selected cases. Results and Discussion Conducting polymers usually do not have high molecular weights.31 In this paper, a broad range of oligothiophenes was studied, starting from relatively short oligomers (n ) 6) which can carry two positive charges and up to very long oligoth-
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TABLE 1: Relative Energies for the Optimized Oligothiophene Dication Structures in Spin-restricted Singlet (R), Spin-unrestricted Singlet (U), and Triplet (T) States at the B3LYP/6-31G(d) and BLYP/6-31G(d) Levels of Theory (all values are in kcal/mol), and S2 Values for the Spin-Unrestricted Singlet State S2 dication 6T2+ 7T2+ 8T2+ 9T2+ 10T2+ 12T2+ 14T2+ 20T2+ 30T2+ 50T2+ 10T2+ 20T2+ 30T2+
∆E(T-U)
∆E(R-U)
6.0 4.0 2.7 1.9 1.3 0.7 0.4 0.1 -0.1 -0.2
0.2 0.8 1.6 2.4 3.2 4.2 5.0 4.9 3.9 2.8
wave function is stable 0.6 0.2 0.2 0.4
∆E(T-R)
before annihilation
after annihilation
B3LYP/6-31G(d) 5.8 3.1 1.1 -0.6 -1.8 -3.5 -4.6 -4.8 -4.0 -2.7
0.32 0.60 0.77 0.86 0.92 0.98 1.00 1.01 1.00 0.99
0.03 0.14 0.25 0.32 0.37 0.40 0.39 0.31 0.17 0.08
BLYP/6-31G(d) 3.4 0.4 -0.2
0.56 0.72
0.01 0.01
iophenes (up to 50-mer) that were never studied previously using DFT or ab initio methods. The molecular weight of 50T is 4102 g/mol. Thus, 50T can be considered a realistic model for polythiophene.32 For oligothiophene dications, our calculation corresponds to a doping level ranging from 4% (in the case of 50T2+) to 33% (in the case of 6T2+). In the case of high and medium doping levels, our results are applicable to experimentally studied doped polythiophenes, while in the case of a low doping level, our results are applicable to the initial doping of polythiophene and, more importantly, we model the situation observed in FETs2 where the density of charge carriers is relatively low. Relative Stability of the Singlet State vs the Triplet State and of the Polaron Pair vs the Bipolaron. For very short oligomers up to 5T2+, the spin-restricted wave functions are stable at B3LYP/6-31G(d). However, for 6T2+ and longer oligomers, the restricted wave function shows RHF-UHF instability and the energy of the unrestricted (U) wave function (UB3LYP/6-31G(d)) becomes lower than the energy of the restricted (R) wave function (RB3LYP/6-31G(d)).22 This means that the dications of very short oligomers exist in a bipolaron state; however, for dications of longer oligomers, the polaronpair configuration (two separated cation radicals) contributes significantly to the ground-state structure. The energy difference (∆E(R-U) ) E(RB3LYP) - E(UB3LYP)), which relates to bipolaron instability, increases with increasing oligomer length (Table 1 and Figure 1) through to 14T2+. Thus, for 6T2+, the value of ∆E(R-U) is 0.2 kcal/mol, for 10T2+ it increases to 3.2 kcal/mol, for 14T2+ it is 5.0 kcal/mol, and stays similar for 20T2+. For 30T2+ and 50T2+, ∆E(R-U) even decreases to values of 3.9 and 2.8 kcal/mol, respectively. The contribution of the polaron pair configuration to the structure of the ground-state becomes more important as oligomer length increases. The S2 values in Table 1 increase with increasing oligomer lengths up to 14T2+. To eliminate the contribution from the Hartree-Fock wave function, which is known to lead to high spin contamination for long conjugated systems, we optimized 10T2+, 20T2+, and 30T2+ using the “pure” density functional BLYP/6-31G(d) method (Table 1). In contrast to the findings at B3LYP/6-31G(d) method, the wave function of 10T2+, being one of the longer short oligothiophene dications, does not show RHF-UHF instability at BLYP/6-31G(d). The wave function of 20T2+ becomes unstable at RBLYP/6-31G(d), however, the energy difference ∆E(R-U) ) E(RBLYP) - E(UBLYP) is only 0.2 kcal/mol. This difference is still small even for 30T2+ (0.4 kcal/mol); however, the energy of the spin-unrestricted singlet state is
always below that of the spin-restricted singlet state for sufficiently large oligothiophene dications. The BLYP and B3LYP wave functions have been found to behave similarly to each other also in studies of oligoacenes.27 For short oligothiophenes (e.g., 6T2+), the triplet state of the dication is significantly higher in energy than the corresponding singlet state, however, the energy difference decreases rapidly with increasing chain length (Figure 1). The energy difference ∆E(T-U) for 6T2+ is 6.0 kcal/mol, for 10T2+and 14T2+, it decreases to 1.3 and 0.4 kcal/mol, respectively, while for 20T2+, 30T2+, and 50T2+, it is practically zero (the singlet is more stable than the triplet for 20T2+ by only 0.1 kcal/mol, and for 30T2+ and 50T2+, the triplet state is slightly more stable than the singlet by only 0.1 and 0.2 kcal/mol, respectively). These findings indicate that, at UB3LYP/6-31G(d), singlet state dications are more stable than triplet state dications for oligomers shorter than 20T2+, whereas, for 20T2+ and longer oligomers, the singlet and triplet states become practically degenerate, and the triplet state is never a pure ground state for these dications (which is in contrast to the predictions from the restricted DFT calculations23).33 Indeed, the S2 value before annihilation (Table 1) is relatively small (0.32) for 6T2+, increasing up to 1.00 for 14T2+. The S2 value stays at 1.0 for longer oligothiophene dications, which indicates that 14T2+ and longer oligothiophene dications might be considered as 50:50 mixtures of the singlet (S2 ) 0) and triplet (S2 ) 2) states. BLYP/6-31G(d) calculations lead to
Figure 1. Relative energies of the optimized triplet (T) states minus those of the corresponding optimized singlet (S) state (i.e., E(T-S)) for both the spin-restricted (R; i.e., ∆E(T-R)) and spin-unrestricted (U; i.e., ∆E(T-U)) structures in oligothiophene dications as a function of chain length at the B3LYP/6-31G(d) and BLYP/6-31G(d) levels of theory. The graph is based on the data in Table 1. (Squares, ∆E(T-U)(B3LYP); circles, ∆E(T-R)(B3LYP); up-triangles, ∆E(T-U)(BLYP); down-triangles, ∆E(T-R)(BLYP)).
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Figure 2. (a) Energies for the reaction shown in the boxed inset (equation 1) versus oligothiophene chain length. (b) Energies of eq 1 versus the inverse of oligothiophene chain length. Upper inset shows graph for highest five n values (n g 12).
SCHEME 1: Structure of a Neutral Fragment of Oligothiophene (left) and Two Resonance Structures for Dication Fragments of Oligothiophene (right).
the same conclusion, with the open shell singlet state being more stable than the triplet state for short oligomers, while for 20T2+ and longer oligothiophenes, the two states are degenerate. Our findings are similar to those for oligoacenes, where both DFT and CASSCF results predicted the singlet state to always be the ground state, with the triplet state lying several kcal/mol above the singlet.27 Relative Stability of Oligothiophene Dications vs Oligothiophene Cation Radicals. We have evaluated the stability of the oligothiophene dication versus two cation radicals using an isodesmic reaction, as shown in eq 1,34 in which UB3LYP/631G(d) singlet energies were used.
nT+nT2+ f 2nT•+
(1)
Figure 2a shows the change in disproportionation energy vs the number of thiophene units as the oligothiophene chain increases. For short oligothiophenes, such as 6T, the dication is less stable than two cation radicals by as much as 63.5 kcal/mol.35 However, the stability of a dication vs two cation radicals increases with chain length. Correlating the energy of eq 1 with the inverse of the number of thiophene units in the oligothiophene chain gives a linear plot with R2 ) 0.99 for all values of n, and with R2 ) 0.999 for medium to large n (n g 12, Figure 2b). So, for short oligothiophenes, a double charge residing on one molecule is significantly less stable than a single charge residing on each of two molecules. For longer oligothiophenes (such as 30T2+ or 50T2+), a double charge can be spread over a longer conjugated chain and the energy of the oligothiophene dication begins to become comparable to the energies of two separated charges (i.e., of two oligothiophene cation radicals). Indeed, for long oligothiophene dications, the polaron-pair state becomes dominant and, in this state, two positive charges weakly interact with each other. For very long oligothiophenes i.e., 50T, the dication is less stable than two cation radicals by 12 kcal/ mol.35 Indeed, this difference approaches zero as the length of the chain increases, with a predicted value of -4.1 kcal/mol for eq 1 for an infinite value of n (see insert of Figure 2b).36 Bond Length Alternation and Charge Distribution in Oligothiophene Dications. 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 bond length alternation (BLA) trends (Scheme 1 and Figure 3).37 When the C1C2 and C3-C4 bonds on 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 3), the ring is considered aromatic. By contrast, when the C1-C2 and C3-C4 bonds on a thiophene ring are longer than the C2-C3 bond, (thus, producing a V-shaped pattern in the sets of three linked data points shown in Figure 3) the ring is considered quinoid. From the BLA pattern, four points are worthy of note (Figure 3). First, for short oligothiophene dications, e.g., for 6T2+, while the triplet state optimized geometry differs from the other two geometries investigated, the BLA patterns for the spin-restricted and spin-unrestricted optimized geometries are similar to each other. This indicates (in contrast to a previous suggestion that the open shell polaron pair geometry is the ground state for 6T2+)22 that the contribution of a polaron pair to the electronic structure of the short oligothiophene dication is small, with the major contribution to electronic structure coming from the bipolaron state (Figure 3a). The second point is that, for medium- to long-length oligothiophene chains (Figure 3b and 3c), the optimized geometries of the spin-restricted and spinunrestricted states differ from each other, with the triplet state adopting a geometry similar to that of the spin-unrestricted singlet state. Thus, for example, in 14T2+ there are marked differences in the BLA patterns of the RB3LYP/6-31G(d) (spinrestricted) and UB3LYP/6-31G(d) (spin-unrestricted) optimized geometries (Figure 3b). This suggests that the contribution from the polaron pair state begins to become significant in medium length oligothiophene dications such as 14T2+. For 14T2+ at UB3LYP/6-31G(d), the four center rings (of which two appear in the half-chain shown in the figure) are aromatic, with the four rings on each side of them being quinoid (producing two separated quinoid regions, each capable of carrying charge, see Scheme 1), while the two terminal rings on each side are, again, aromatic. By contrast, for RB3LYP/6-31G(d), the middle 10 rings (of which five are shown in the figure) are quinoid, and the two terminal rings on each side of them are aromatic. As mentioned, the BLA pattern of the optimized triplet state is quite similar to that of the singlet geometry calculated at UB3LYP/ 6-31G(d), while, by 20T2+, the spin-unrestricted singlet and
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Figure 3. Bond length alternation for (a) 6T2+, (b) 14T2+, (c) 20T2+, and (d) 30T2+. 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 intra-ring bonds (the second of these bonds is the middle ring bond), while every fourth point on the x-axis corresponds to an inter-ring C-C bond. The points are linked solely as a visual aid. (Squares, spin-unrestricted singlet; circles, spin-restricted singlet; and up-triangles, triplet states, all at the B3LYP/6-31G(d) level of theory.)
triplet states have become practically degenerate (Table 1) and, consequently, a high degree of similarity is expected between their geometrical structures. These observations again suggest that the polaron pair state makes a significant contribution to the electronic structure of singlet medium- to long-length oligothiophene dications. Third, it should be noted that the BLA patterns for all three states are nearly same for 30T2+ (Figure 3d). Finally, for spin-unrestricted singlet and triplet states, the number of aromatic rings in the middle of the chain increases with increasing oligomer chain length up to 14T2+, whereas for spin restricted states, all the rings are quinoid except the terminal rings. However, for 30T2+, all rings are aromatic in the optimized geometries of all three states. Thus, overall, the difference between the RB3LYP and UB3LYP optimized geometries, in terms of the BLA patterns, becomes significant for middle size oligothiophene (14T2+), while the difference is small for shorter (n < 10, see Supporting Information) and for longer (n g 20) oligothiophenes. This correlates nicely with the data in Figure 1, where the energy difference between the RB3LYP and UB3LYP solutions increases as the size of the oligomer increases for oligomers having n < 14. It then stays constant, and even decreases, for larger values of n, which means that the energy difference per repeat unit actually decreases as n increases for n > 14. The calculated Mulliken charges (summarized for thiophene rings) on the oligothiophene dications are given in Figure 4. For medium to long oligothiophene dications, i.e., 14T2+, 20T2+, and 30T2+, the charges calculated for the RB3LYP/6-31G(d) singlet optimized geometry are nearly equally delocalized over the oligothiophene backbone, with the two outer rings carrying larger charges. A similar trend has been observed by Gao et al.,22 for short oligothiophene dications. When UB3LYP/6-31G-
(d) singlet optimized geometries were used, the charge on the central rings of the backbone was significantly smaller than on the other rings, with the charge increasing from the middle to the end of the chain.38 For example, in 14T2+ (Figure 4b), the four middle rings carry the smallest charge of all the rings. Indeed, according to Figure 3b, these four rings are aromatic, while the other rings (except for the terminal rings) are quinoid. This phenomenon of increasing charge from the middle to the ends of the chain is especially pronounced for longer oligothiophene dications (20T2+ and 30T2+; Figure 4c, d). This pattern represents the presence of two separated polarons at the two sides of the chain, with the separation region lying in the middle of the chain. For 6T2+, the charge distributions in both the RB3LYP/6-31G(d) and UB3LYP/6-31G(d) optimized singlet geometries are similar, in agreement with the assumption that the polaron-pair state makes little contribution to the electronic structure of 6T2+ (Figure 4a). The charge distribution for a singlet state optimized at UB3LYP/6-31G(d) slowly approaches the values of the corresponding triplet state as chain length increases. For 14T2+, 20T2+, and 30T2+, the charge distributions for spin-unrestricted singlet and triplet states are very similar to each other, suggesting (similarly to the conclusion based on the BLA data) that, for medium to long oligothiophene dications, the contribution of the polaron-pair state is significant.39 Since, Mulliken population analysis is strongly basis set dependent, we have compared the calculated Mulliken charges (Figure 4) with the charges obtained from natural population analysis (NPA, Figure 5). For 30T2+ (both triplet and spinunrestricted singlet), the NPA charges show significant charge localization toward the two chain ends, while the charge in the middle of the backbone is lower. For the spin-restricted state of 30T2+, charge delocalization is observed (Figure 5). Thus,
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Figure 4. Mulliken charge distribution in (a) 6T2+, (b) 14T2+, (c) 20T2+, and (d) 30T2+. (Circles, spin-restricted singlet state; squares, spinunrestricted singlet state; triangles, triplet state. All calculations performed at the B3LYP/6-31G(d) level of theory).
TABLE 2: CASSCF(m,m)/6-31G(d)//B3LYP/6-31G(d) Calculated Energy Differences (in kcal/mol) for the Triplet State versus the Singlet State Using UB3LYP/6-31G(d) Geometries of Oligothiophene Dicationsa ∆E ) ET - ESb (4,4)a 6T2+
[24.9]c
33.2 9.0 1.1 [12]c,d 11.1
8T2+ 10T2+ 12T2+
Figure 5. NPA charge distribution in 30T2+ at the B3LYP/6-31G(d) level of theory. (Circles, spin-restricted singlet state; squares, spinunrestricted singlet state; triangles, triplet state.)
the calculated NPA charges closely resemble the calculated Mulliken charges (Figure 4d), and we can conclude that the charge localization observed for the spin-unrestricted singlet state is not dependent on the charge partitioning scheme used. “Pure” DFT methods are known to predict significant charge delocalization.40 Indeed, Mulliken charges calculated at BLYP/ 6-31G(d) (see Supporting Information) show complete delocalization of charge for 20T2+ and 30T2+ in all three state, except over the end rings, with practically no difference in the charge distribution in all three states. Insights on Oligothiophene Dications from CASSCF Calculations. To further investigate the stability of the singlet state over the triplet state (Table 2), and of the singlet polaron pair over the singlet bipolaron (Table 3), we optimized the geometries of short oligothiophenes 6T2+ and 10T2+ at the CASSCF/6-31G(d) level. We also performed CASSCF/6-31G-
(6,6)a
(10,10)a
21.9 15.7 6.8 4.8
10.3 [15.4]c 14.6 9.7d,e 1.9
a The active space size, (m,m) is given in round parenthesis. b Ttriplet state. S-singlet state using a spin-unrestricted optimized geometry. c The values in square parenthesis are for molecules optimized at CASSCF/6-31G(d). d Optimization did not completely converge according to default Gaussian 03 criteria, however, the energy values were oscillating around the numbers given in the Table. e The RB3LYP/ 6-31G(d) optimized geometry has been used for singlet calculations.
TABLE 3: Calculated Number of Electrons Located outside Closed-shell Bonding Orbitals from CASSCF(m,m)/ 6-31G(d)//B3LYP/6-31G(d) Calculationsa,b (4,4)a 6T2+ 8T2+ 10T2+ 12T2+
(6,6)a
(10,10)a
S
T
S
T
S
T
0.09 0.29 0.97 1.03
1.03 1.00 1.05 1.00
0.19 0.32 1.06 1.11
1.06 1.08 1.10 1.10
0.30 0.35 0.52c 1.20
1.25 1.15 1.25 1.23
a The active space size, (m,m) is given in round parenthesis. b Ttriplet state. S-singlet state CASSCF/6-31G(d) calculations started from the UB3LYP/6-31G(d) optimized geometry. c The RB3LYP/6-31G(d) optimized geometry has been used for singlet calculations.
(d) single point calculations on the B3LYP/6-31G(d) optimized geometries for longer oligothiophenes up to 12T2+. We used an active space of up to 10 electrons in 10 orbitals, although
Study of Long Oligothiophene Dications we note that even the short oligothiophene 6T2+ has 22 π-electrons and 12 nonbonded electron-pairs on sulfur atoms. Calculations using a larger active space are unfeasible using currently available computational capabilities. These calculations (Table 2) clearly support our conclusion from DFT calculations that the triplet is never a pure ground state for oligothiophene dications, since the singlet state is more stable than the triplet in all cases.41 CASSCF calculations also clearly support the conclusion that the polaron pair becomes the dominant electronic configuration for long oligothiophenes (Table 3). Indeed, these calculations show that for a medium sized oligothiophene dication, such as 12T2+, a significant amount of the electron (approximately a whole electron) is located outside of closed shell bonding orbitals, strongly suggesting a significant contribution from the polaron pair state, as is also evident from the DFT calculations. For example, CASSCF/6-31G(d) single point calculations show that 6T2+ has only 0.09, 0.19, and 0.30 electrons outside closed-shell bonding orbitals for the (4,4), (6,6), and (10,10) active spaces, respectively (for comparison, benzene has 0.13 electron outside closed-shell bonding orbitals at CASSCF(6,6)/6-31G(d)), while the corresponding figures for 12T2+ are 1.03, 1.11, and 1.20 electrons outside closed-shell bonding orbitals. Thus, even for a medium sized oligothiophene, such as 12T2+, there is approximately a whole electron located outside of closed-shell bonding orbitals, which means that the polaron pair state can be assigned to 12T2+. For 6T2+ and 8T2+, CASSCF calculations yielded electron distributions in which there is a significant contribution from the singlet bipolaron state with a smaller contribution from the singlet polaron-pair state, in excellent agreement with the energies, BLA and charge distribution data obtained from the B3LYP/6-31G(d) calculations. We have mentioned above that B3LYP calculations predict a significant contribution from the polaron pair state only for longer oligothiophenes such as 20T2+. Conclusions Dications of long oligothiophenes (of up to 50 thiophene rings) have been studied using DFT and, in some cases, also using the CASSCF method. We find that the triplet is never the pure ground state for these molecules. Based on various criteria, such as the relative energies of the restricted and unrestricted calculations, BLA and charge distribution data, we conclude that, in relatively short oligothiophene dications, such as 6T2+, the polaron pair state only slightly contributes to the electronic structure of the dication, with the major contribution coming from the bipolaron state. In medium size oligothiophene dications, such as 14T2+, the contribution from the polaron pair state begins to become significant; while 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. Indeed, we show that the stability of a single oligothiophene dication versus two cation radical oligothiophene molecules increases with increasing chain length, and that there is an excellent correlation between relative disproportionation energy and the inverse of chain length. Although our results clearly show that the polaron pair state becomes the dominant electronic state for long oligothiophene dications, it is important to note that our calculations were performed in the gas phase and without counteranions. Also, we considered only one oligomer chain, thus eliminating possible π-stacking. However, we believe that our results show important trends in the electronic structure of oligothiophene dications with increasing chain length, which is equivalent to
J. Phys. Chem. B, Vol. 110, No. 32, 2006 15845 reducing the amount of doping. We also note that the CASSCF method predicts that oligothiophene dications will exist mostly in the polaron pair state, starting from even shorter oligothiophene chain lengths than predicted using the B3LYP method. Thus, CASSCF predicts even more charge separation than the hybrid DFT B3LYP method, while “pure” DFT method such as BLYP predict less charge separation than the hybrid DFT method B3LYP. Acknowledgment. This paper dedicated to Prof. Fred Wudl, the pioneer of polythiophene chemistry and great teacher, on the occasion of his 65th birthday. We thank Prof. J. M. L. Martin (Weizmann Institute of Science) and Prof. D. F. Perepichka (McGill University) for helpful discussions. This research is supported by Research Grant Award No. IS-3712-05 from the BARD Research and Development Fund, the MINERVA Foundation and the Lord Sieff of Brimpton Memorial Fund. 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; the Cartesian coordinates of the optimized geometries of the dications at different theoretical levels; graphs of charge distribution and bond length alternation for 8T2+and 10T2+ (as well as 30T2+ at BLYP/6-31G(d)); bond distances of 30T2+ at B3LYP/6-31G(d) (as in Figure 3d) in spin-restricted singlet, spin-unrestricted singlet and triplet states. 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, 1998. (b) Handbook of Oligoand Polythiophenes; Fichou, D., Ed.; Wiley-VCH: Weinheim, 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: Netherlands, 1991. (e) Handbook of Organic ConductiVe Molecules and Polymers; Nalwa, H. S., Ed.; John Wiley & Sons: New York, 1997; Vol. 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. (j) Katz, H. E. J. Mater. Chem. 1997, 7, 369. (g) 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.; Ba¨uerle, P.; Umbach, E. AdV. Mater. 1993, 5, 922. (c) Mitschke, U.; Ba¨uerle, P. J. Mater. Chem. 2000, 10, 1471. (d) 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. (e) 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) Lafolet, F.; Genoud, F.; Divisia-Blohorn, B.; Aronica, C.; Guillerez, S. J. Phys. Chem. B 2005, 109, 12755.
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