J. Phys. Chem. B 2007, 111, 1271-1276
1271
Raman Dispersion and Intermolecular Interactions in Unsubstituted Thiophene Oligomers Alberto Milani,* Luigi Brambilla, Mirella Del Zoppo, and Giuseppe Zerbi Center for NanoEngineered MAterials and Surfaces (NEMAS), Dipartimento di Chimica, Materiali ed Ingegneria Chimica “G. Natta’’, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133 Milano, Italy ReceiVed: October 23, 2006; In Final Form: December 1, 2006
We present a critical analysis of the Raman spectra of unsubstituted oligothiophenes and rediscuss the wellknown Raman dispersion of conjugated systems explicitly considering intermolecular interactions. Temperaturedependent Raman spectra and DFT calculations for dimers of different chain lengths show that the effect of intermolecular interactions on the frequency and intensity of carbon-carbon (CC) stretching modes is nonnegligible. This effect has not been considered in previous works and might explain many spectral features of this class of compounds which are not completely interpreted by the usual models. Both intensities and frequencies are significantly affected by intermolecular interactions showing that molecular self-organization should be taken into account in future spectroscopic studies of conjugated molecules. In particular, the interactions among molecules cause an upward shift of the frequency of the R mode (amplitude mode) which can explain the lack of frequency dispersion with conjugation length of oligothiophenes, as experimentally observed for solid-state samples at room temperature.
I. Introduction
poyacetylene) can be written as
Since the first discovery of conducting polymers, oligothiophenes, polythiophenes and their derivatives have attracted much attention as materials for possible innovative electronic devices.1-4 Vibrational spectroscopy proved to be a powerful method to establish structure/property correlations for such materials and many features of polyconjugated molecules can be easily accounted for by analyzing their IR and Raman spectra.5-8 The Raman dispersion of the frequency of CC stretching modes in conjugated molecules of increasing length is a precise marker of the change of π-electron delocalization and it has been rationalized, among other models, with the Effective Conjugation Coordinate Model (ECC model).7-9 According to this approach, a particular vibrational coordinate, referred to as R, is introduced. This coordinate is strongly coupled to the π electrons. In polyenes it is related to the dimerization amplitude oscillation (i.e., it is defined as a collective in-phase shrinking of single and stretching of double CC bonds). In polyaromatic systems this coordinate can be generalized, and it describes an oscillation from a more aromatic to a more quinoid electronic configuration. In any case, the R coordinate describes an oscillation of the nuclei along the path which connects the molecular geometry of the ground state with the geometry of the relevant excited state. For this reason the electron-phonon coupling is maximum along the normal modes which can be described mainly in terms of the R coordinate. This observation explains why the frequencies and intensities of these modes are sensitive to the conjugation length. Usually only a few normal modes can be described mainly in terms of the R coordinate, and this explains the rather simple Raman spectra (only few lines). The experimental lowering of the frequency with increasing conjugation length has been rationalized within the ECC model, since the force constant FR, associated to the R coordinate, in the case of an ideal infinite polymer (e.g.,
FR ) K 0 - f 0 +
∑s f 0,s
(1)
where K0 ) (1/2)(K0R + k0r ) is the combination of diagonal CdC (K0R) and C-C (k0r ) stretching force constants of a reference unit (zeroth unit), f 0 is the interaction force constants between CC bonds within the zeroth unit, and the sum ∑sf 0,s is the sum of force constants between CC bonds of the zeroth unit and the CC bonds of the unit at a distance s from the zeroth one along the lattice. The distance s defines the “conjugation length’’ (which is usually shorter than the actual molecular chain length): the greater the extent of delocalization the larger is s. This implies that increasing delocalization causes the appearance of more terms in the sum of eq 1. It has been demonstrated10-12 that the valence interaction force constants between conjugated CC bonds must obey a precise sign rule: if f1, f2, ... are the valence interaction force constants between first, second, ..., neighboring CC bonds, then those with odd indices (f1, f3, f5, ...) are negative while those with even indices (f2, f4, f6, ...) are positive. The application of this general rule implies the sum ∑sf 0,s to be negative. Therefore an increase of conjugation causes FR to soften and the R mode to shift to lower frequencies. Within this approach, we expect that the R mode for oligomers of the same chemical species should gradually shift downward as molecules become longer and longer, reaching a value which corresponds to the largest conjugation. Most classes of polyconjugated molecules obey these rules and confirm the validity of this model. On the contrary,13 the R mode in thiophenes shows small or no frequency dispersion at all and this, within the ECC model, would mean no or small increase of delocalization with increasing chain length. However, a superlinear enhancement of the intensities of these Raman lines with increasing chain lengths (which is usually taken as a sign of delocalization) has
10.1021/jp066933k CCC: $37.00 © 2007 American Chemical Society Published on Web 01/24/2007
1272 J. Phys. Chem. B, Vol. 111, No. 6, 2007 been experimentally observed and theoretically predicted in previous works.13 Such an unusual behavior has been previously explained as a consequence of ring aromaticity opposed to charge delocalization along the chain and has been referred to as a “pinning’’ effect.13,14 Density-functional theory (DFT) calculations recently carried out in our group on oligothiophenes in vacuo showed that, contrary to previous Hartree-Fock calculations14 (for which the frequency of the prominent Raman mode does not change with chain length), the lengthening of the molecule causes a lowering of the Raman frequency. One possible explanation for this effect might be ascribed to the fact that DFT calculations tend to overestimate delocalization in one-dimensional systems.15,16 Even if this is probably true, both in this work and in previous ones9,17 we have shown that such calculations give physically correct results, at least for chain lengths moderately short as those considered herewith. In this work, we present a new study on Raman dispersion of oligothiophenes both from the theoretical and experimental point of view. We will show how temperature-dependent spectra and calculations on oligothiophenes dimers35 can give a consistent description of their vibrational spectra and suggest a possible explanation of the small dispersion observed. We will introduce the concept, generally neglected in spectroscopy, that intermolecular interactions play a fundamental role in this class of molecules and that they affect the vibrational behavior. II. Experimental In this work we have studied a series of thiophene oligomers, namely R-terthiophene, R-quaterthiophene, R-quinquethiophene, and R-sexithiophene, hereafter referred to as T3, T4, T5, and T6. T3 was purchased by Aldrich and has been used as received, T4 and T5 were kindly provided by Prof. M.C. Gallazzi and T6 by Prof. Papagni. The Raman spectra of T4, T5, and T6 have been obtained after sublimation in a glass vial sealed under vacuum. FT-Raman spectra were recorded on a Nicolet NXR 9635 FT-Raman spectrometer equipped with an InGaAs and a liquid nitrogen cooled Ge detector. The exciting laser line at 1064 nm of a diode pumped 2.0 W Nd:YVO4 laser has been used. The spectra (256 scans) were recorded with a resolution of 1 cm-1. Micro Raman spectra were recorded on a DILOR XY spectrometer with a liquid N2 cooled CCD detector and coupled with an Olympus microscope; excitations at 632.8 nm of a 50 mw He-Ne laser were used. The laser power on the sample ranged from 1 to 5 mW in order to prevent sample degradation. No spectral changes or sample degradation induced by the laser were observed during the acquisition of the spectra. Temperature-dependent Raman spectra were recorded with a Mettler FP82 hot stage (temperature range 28-250 °C and accuracy 0.1 °C) directly placed under the microscope objective (ULWD MSPLAN 50X Olympus). A. Raman Spectra. In the region 1420-1540 cm-1, the FTRaman (excitation at 1064 nm) and the Raman spectra of solid T3, T4, T5, and T6 recorded at room temperature (25 °C) and excited at 632.8 nm show no meaningful frequency dispersion of the R mode near 1460 cm-1 when the number of thiophene units increases (experimental Raman spectra are available as Supporting Information). It is worth noticing that, for every sample, excitations at 632.8 or 1064 nm give very similar Raman spectra, both in frequency and relative intensities, thus ruling out any possible preresonance effect. Indeed, the electronic spectrum of these compounds shows no absorption in this frequency range.
Milani et al. TABLE 1: Frequency Values for T3, T4, T5, and T6 in the Solid State (at 25 °C) and in Solution T3 T4 T5 T6
solid (cm-1)
solution (cm-1)
∆frequency
1458 1457 1456 1457
1463 1465 1467 1469
5 8 11 12
When the Raman spectra of samples in solution are considered, an appreciable and systematic upward shift of the R mode with respect to the frequencies measured in the solid state of each oligomer has been observed. In Table 1 we report for comparison the frequencies of the R modes for T3, T4, T5, and T6 in the solid state and in solution with chloroform. This upward shift can be easily rationalized in terms of the conformational disorder (well-known for this kind of molecules in solution) which reduces the conjugation length. Indeed, the conformational disorder induces a tilting of the pz-orbitals belonging to different thiophene rings which no longer exhibit the maximum overlap of the trans conformation. In other words, for the CC bonds between adjacent rings, the value of the Hueckel’s resonance integral β is expected to lower. From Table 1 it can be observed that the frequency of the R mode in solution increases with the oligomer length as if the longer the oligomers are, the larger the average conformational disorder is. The next question is whether conformational disorder can be introduced also by heating the solid samples even without reaching the melting point. To our knowledge only a very few works on the temperaturedependent Raman spectra of thiophenes have appeared;18,19 we thus decided to carry out such measurements and check for the occurrence of conformational disorder. In principle, by raising the temperature, some molecular rearrangement and conformational motion might be introduced within the crystalline structure, along with the expansion of the lattice. As discussed above in the case of solutions, if conformational disordering occurs in the solid it would cause an upward shift of the frequency of the R mode. Contrary to this expectation, an unquestionable (even if small) downward frequency shift of the R mode is observed (Figure 1 and Table 2). The frequency of each oligomer depends linearly on the temperature as shown in Figure 2, where it can also be seen that the longer the oligomer chain is, the steeper the frequency variation is. Actually, in order to confirm the linear trend, Raman spectra of longer unsubstituted thiophene oligomers should be measured; unfortunately these compounds cannot be synthesized. These experimental findings are in contrast with what is expected on the basis of the previous discussion on conformational disorder and require the introduction of some additional physics. Up to now we have considered that the extent of π-delocalization in polyconjugated molecules is modulated only by their molecular conformation (transplanar in the solid state and disordered in solution). Our experiments suggest that the origin of the frequency lowering might be ascribed to an intermolecular effect. In order to check this hypothesis, we have carried out quantum chemical calculations which are presented and discussed below. III. DFT Calculations DFT calculations at various levels have been carried out with Gaussian 03 code.20 First, we have assessed the reliability of the computational methods adopted by comparing the theoretical spectra of T3 in trans conformation, calculated with different
Unsubstituted Thiophene Oligomers
J. Phys. Chem. B, Vol. 111, No. 6, 2007 1273
Figure 1. Experimental Raman spectra of T4 (left) and T6 (right) with increasing temperature. In the case of T4, spectra have been recorded in steps ∆T ) 20 °C, starting from 30 to 210 °C. In the case of T6, ∆T ) 30 °C from 30 to 240 °C (see the Table 2 for numerical values of the frequencies). In the figures, the spectra at increasing temperatures are superimposed (and shifted vertically for sake of clarity).
TABLE 2: Frequencies (in cm-1) of the R Mode from the Raman Spectra of T3, T4, T5, and T6 at Increasing Temperatures T (°C) 30 32 50 60 70 85 90 110 120 130 150 170 180 190 210 240
T3
T4
1460.3 1460.0
1460.2 1459.7
1459.7 1459.5
1459.4 1459.2 1458.7 1458.4 1458.16 1457.8 1457.2 1457.1
T5
T6
1461.48
1460.2
1460.87
1459.5
1460.0
1458.8
1459.33
1458.4
1458.2
1457.9
1457.1
1457.2
1456.3
1456.3 1455.5
DFT exchange-correlation functionals, with the experimental ones. The experimental spectra used for this test have been recorded on solid-state samples. The most commonly used GGA Exc functionals (B3LYP, BLYP, B3PW91, BPW91) have been tested with the 6-311++G** basis set.21 All of them give a good description of the spectra, but hybrid functionals overestimate frequencies. The comparison is shown in Figure 3 where it can be seen that a satisfactory agreement is obtained both in frequency and relative intensities. No scaling factor has been applied to the frequency values. The best description of both spectroscopic observables (frequencies and intensities) is given by the BPW91 functional (where the B88 exchange functional of Becke22 is combined with the nonempirical correlation functional PW91 of Perdew and Wang23). Therefore the BPW91 functional has been used in all the calculations presented in this work. A. Isolated Molecules. In Figure 4 we show the Raman spectra for T3, T4, T5, T6, and T7 calculated as isolated molecules at the BPW91/6-311++G** level. An unquestionable frequency dispersion with the oligomer length is observed; this dispersion was never observed before either experimentally or theoretically.13,14 As we mentioned in the introduction, it has been shown that in some cases (e.g., linear conjugated chains) DFT calculations overestimate conjugation. We have thus carried out geometry optimization for T3 and T5 also at the MP2/6-311G** level
Figure 2. Linear fit for the frequency values (νR) of T3, T4, T5, and T6 as function of temperature. Errors for the slopes are indicated in paranthesis.
and we have verified that both MP2 and BPW91 give a very similar bond-length alternation for single and double CC bonds. MP2 is known to give a good description of charge delocalization and this means that DFT methods are able to describe accurately enough the conjugation of π-electron, at least for the molecules considered in this work. We have also carried out BPW91/6-311++G** calculations with the molecules distorted in various conformations. The geometry of the most stable conformers (for all the molecules studied in this work) corresponds to a slight deformation from planarity, as confirmed experimentally for T3 by X-ray diffraction.24 The calculated frequencies of the distorted conformations are consistent with the experimental upward shift observed for the R mode in solution which witness the decrease of π-electron conjugation along the chain backbone caused by the deviation from planarity.
1274 J. Phys. Chem. B, Vol. 111, No. 6, 2007
Milani et al.
Figure 5. T3 and T4 π-π stacked dimers.
Figure 3. Comparison of experimental and theroretical Raman specta of T3 with different DFT functionals.
Figure 4. Calculated Raman spectra for T3, T4, T5, T6, and T7 taken as isolated molecules (BPW91/6-311++G**). The spectra for T3 is shifted for sake of clarity. Intensities are reported on a common scale, no scaling factor has been applied.
TABLE 3: Calculated Frequencies of the R Mode for the Planar and Optimized Conformations of T3, T4, T5, and T6a T3 T4 T5 T6
planar (180°) (cm-1)
optimized (cm-1)
torsion angles
1456 1448 1441 1435
1456 1452 1445 1440
20° 15° 10° 12°
a Torsional angles refer to the rotation around the central interring CC bonds.
In Table 3 we report the frequency values of the R mode for T3, T4, T5, and T6 in the constrained planar and optimized (slightly distorted) conformations. Even if the optimized conformations are only slightly distorted from planarity, frequency upward shifts are clearly observable. A good agreement with the experimental values is obtained both quantitatively and qualitatively.36 Experiments show that in solution the conformational disorder is even larger, thus further decreasing the
conjugation length. Once again it can be concluded that conformational disordering cannot be responsible for the changes observed in the Raman spectra recorded at increasing temperatures. B. Intermolecular Interactions. In this study, we wish to show that it is possible to justify the lack or small frequency dispersion in solid oligothiophenes in terms of intermolecular forces. The simplest way to study the influence of intermolecular interactions on the vibrational spectra by means of high-level quantum chemical calculations is that of calculating the spectra of a dimer. We have calculated the spectra of the dimers of T3 and T4 constraining the molecules at different distances, and we have analyzed the changes in the spectra. In both cases the molecules have been assumed to be π-π stacked (Figure 5); the distances and orientation between their planes have been fixed and just the internal degrees of freedom of each molecule have been optimized. In the calculations on the dimers we kept using the BPW91 functional but we had to lower the basis set down to 3-21+G**.25 The approximations used in our calculation can be justified in the following way: (i) It is well-known that avaible DFT functionals do not accurately describe Van der Waals (VdW) interactions which results in the impossibility of finding a stable geometry configuration for VdW dimers.26-28 BPW91 seems to perform better in this respect,29,30 but other studies have shown the fortuitousness of this behavior and have tried to find solutions by an appropriate formal elaboration of EXC functionals.26,27 Only very recently these theoretical approaches have been applied to conjugated molecules, but they are not yet routinely available.31 In our calculations, the problem of the lack of a stable configuration has been overcome by carrying out the calculation on dimers fixing the intermolecular distance. (ii) Even if the 3-21+G** basis set is rather poor, the comparison with higher level calculations on the T3 dimer shows that it gives good qualitative results. (iii) Crystal structures of unsubstituted oligothiophenes show that they pack with a herringbone arrangement while alkylsubstituted oligothiophenes pack with π-π stacking.24 We have assumed a π-π stacking geometry for the sake of simplicity. To check whether the different packing could cause a meaningful difference on the results, we have calculated the spectra for T3 in the experimental herringbone packing with BPW91/6311++G** and BLYP/6-311++G**. The results are in qualitative agreement with those with the π-π geometry, thus justifying the validity of assuming π-π stacking. (iv) Our model is very naive and obviously does not take into account the effect of the whole crystalline structure. Still we believe it can give useful qualitative indications on the changes induced in the spectra by the intermolecular interactions. IV. Results The results of our calculations are reported in Figure 6. As expected, the formation of a dimer (i.e., the effect of taking into account intermolecular interactions) causes a frequency lowering in agreement with experiments. Even more evident is the decrease of intensities caused by the intermolecular interactions. In Figure 6 it can be seen that the intensity of the dimer
Unsubstituted Thiophene Oligomers
Figure 6. Comparison between theoretical Raman spectra of T3 (bottom) and T4 (top) isolated molecules and dimers. The intermolecular distances between the molecules of the dimer adopted in the calculation are given in brackets (in Å).
is significantly lower than the Raman intensity of the isolated molecule multiplied by two. The calculations have been repeated at different intermolecular distances (ranging from 3.5 to 5 Å). Increasing the distance implies a decrease of the intermolecular interactions. This can be experimentally obtained by increasing the temperature. The calculated trend in frequency and intensity is consistent with our previous discussion: lower intermolecular interactions (i.e., larger intermolecular distance) yield lower frequency and intensity of the R mode. V. Comparison between Theoretical and Experimental Results In this work we studied why, in the case of solid-state oligothiophenes, the strong Raman line strongly coupled to π-electrons does not show frequency shifts for different chain lenghts. This behavior could not be explained by the usual theories or invoking some conformational disordering, and we propose that it is the consequence of intermolecular effects. To justify and prove our hypothesis we have carried out some computations. Our calculations on oligothiophene dimers have shown that by changing the intermolecular distance, a frequency shift of the CC stretching mode is expected (Figure 6), consistent with the experimental finding (Figure 1), and this can be interpreted as a consequence of the variation of the intermolecular interactions. Since the frequency of the R mode is a probe of the extent of π conjugation, the increase of intermolecular interactions results in an “apparent’’ decrease in conjugation length. This means that whenever Raman dispersion of conjugated molecules is considered at least two effects must be taken into account: (i) π-electron delocalization and (ii) intermolecular interactions. Effects i and ii have an opposite effect on the frequency of the R mode: while an increase of delocalization causes a downward shift, an increase of intermolecular interaction causes an upward shift. Thus, when one looks at Raman dispersion in the condensed state, both effects must be taken into account. An apparent lack of dispersion (downward shift) with increasing conjugation length, as experimentally observed for thiophene oligomers, might be due to a balance between the two effects. Increasing the oligomer length
J. Phys. Chem. B, Vol. 111, No. 6, 2007 1275 certainly increases the conjugation length, but also the intermolecular interactions increase as a consequence of the superlinear increase of the molecular polarizability with chain lengths.32 Thus, when comparing oligomers with different chain lengths at a given temperature we are comparing systems which feel “different’’ intermolecular environments. In a first approximation, directional VdW interactions can be taken as vanishing as close as possible to the melting point. Thus, the “intramolecular’’ contribution to frequency dispersion should be measured as close as possible to the melting point where intermolecular interactions are negligible. Using the linear relationship shown in Figure 2 we have extrapolated the frequency values up to the melting point (in some cases the direct measure of the spectra at Tmelt was impossible because some kind of degradation occurred before melting). Table 2 shows that when we compare the frequencies of T3, T4, and T5 just below the melting point we recover the correct frequency dispersion T3 > T4 > T5 in qualitative agreement with the theoretical results. We note that the reversibility of the frequency shift has always been checked in our experiments by cooling again the system, thus assuring that no degradation has occurred. VI. Conclusion From the previous discussion it follows that the apparent lack of dispersion of thiophene oligomers at room temperature is the consequence of the balance between two opposite effects: (i) the increase of the chain length which increases the conjugation (downward frequency shift) and (ii) the increase of intermolecular interactions (upward shift). In the case of oligothiophenes the two competitive effects i and ii yield as a result small frequency variations. On the contrary, in the case of systems much more delocalized, such as polyene systems, effect i greatly overcomes effect ii. Notice that also in the case of polyacetylene, experimental evidence of an upward frequency shift with increasing pressure (from 0 to 125 Kbar) has been reported several years ago (but has never been accounted for).8,33 Moreover, more recent data on sexithiophene confirm a similar upward frequency shift with pressure.34 These effects are consistent with an increase of intermolecular interactions. The data presented in this work point to the fact, yet not much explored, that the conjugation length is modified by intermolecular interactions and decreases when the interactions are stronger. We think this work reveals the existence of an additional and competitive phenomenon which modulates the shifts of the R mode (or amplitude mode) in polyconjugated systems. The conclusions reached may form the basis for a more detailed and general understanding of the Raman spectra of polyconjugated materals in terms of π-delocalization and intermolecular forces. Acknowledgment. This work has been partly supported by MIUR (Ministero dell’Istruzione Universita Ricerca), Grants PRIN04 and FIRB03. Supporting Information Available: Experimental FTRaman (excitation at 1064 nm) and Raman spectra in the region 1420-1540 cm-1 of solid T3, T4, T5, and T6 recorded at room temperature (25 °C) and excited at 632.8 nm. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Roncali, J. Chem. ReV. 1992, 92, 711-738.
1276 J. Phys. Chem. B, Vol. 111, No. 6, 2007 (2) Garnier, F.; Yassar, A.; Hajlaoui, R.; Horowitz, G.; Deloffre, F.; Servet, B.; Ries, S.; Alnot, P. J. Am. Chem. Soc. 1993, 115, 8716-8721. Garnier, F. Philos. Trans. R. Soc. London, Ser. A 1997, 355, 815-827. (3) Fichou, D. J. Mater. Chem. 2000, 10, 571-588. (4) Horowitz, G. AdV. Mater. 1998, 10, 365. Katz, H. E.; Bao, Z. J. Phys. Chem. B 2000, 104, 671-678. Dimitrakopoulos, C. D.; Malenfant, P. R. L. AdV. Mater. 2002, 14, 99. (5) Kertesz, M.; Ho Choi, C.; Yang, S. Chem. ReV. 2005, 105, 34483481 and references therein. (6) Horowitz, B.; Vardeny, Z.; Ehrenfreund, E.; Brafman, O. Synth. Met. 1984, 9, 215. (7) Zerbi, G.; Gussoni, M.; Castiglioni, C. In Conjugated Polymers; Bredas, J. L., Silbey, R., Eds.; Kluwer Academic: Dordrecht, The Netherlands, 1991. Castiglioni, C.; Del Zoppo, M.; Zerbi, G. J. Raman Spectrosc. 1993, 24, 485. (8) Gussoni, M.; Castiglioni, C.; Zerbi, G. In Spectroscopy of AdVanced Materials; Clark, J. H., Hester, R. E., Eds.; Wiley and Sons: New York, 1991. (9) Castiglioni, C.; Tommasini, M.; Zerbi, G. Philos. Trans. R. Soc. London, Ser. A 2004, 362, 2425-2459. (10) Crawford, B. L.; Califano, S. Spectrochim. Acta 1960, 16, 889. (11) Scherer, J. R.; Overend, J. Spectrochim. Acta 1961, 17, 719. (12) Kakitani, T. Prog. Theor. Phys. 1983, 49, 1; 1983, 50, 18; 1984, 51, 656. (13) Agosti, E.; Rivola, M.; Hernandez, V.; Del Zoppo, M.; Zerbi, G. Synth. Met. 1999, 100, 101. (14) Hernandez, V.; Castiglioni, C.; Del Zoppo, M.; Zerbi, G. Phys. ReV. B 1994, 50, 9815-9823. (15) Bylaska, E. J.; Weare, J. H.; Kawai, R. Phys. ReV. B 1998, 58, R7488 and references therein. (16) Bulat, F. A.; Toro-Labbe´, A.; Champagne, B.; Kirtman, B.; Yang, W. J. Chem. Phys. 2005, 123, 14319 and references therein. (17) Bianco, A.; Del Zoppo, M.; Zerbi, G. J. Chem. Phys. 2004, 120, 1450-1457. (18) Ramirez, F. J.; Aranda, M. A. G.; Hernandez, V.; Casado, J.; Hotta, S.; Lopez Navarrete, J. T. J. Chem. Phys. 1998, 109, 1920. (19) Danno, T.; Kurti, J.; Kuzmany, H. Phys. ReV. B 1991, 43, 4809. (20) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Montgomery, J. A., Jr.; Vreven, T.; Kudin, K. N.; Burant, J. C.; Millam, J. M.; Iyengar, S. S.; Tomasi, J.; Barone, V.; Mennucci, B.; Cossi, M.; Scalmani, G.; Rega, N.; Petersson, G. A.; Nakatsuji, H.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Klene, M.; Li, X.; Knox, J. E.; Hratchian, H. P.; Cross, J. B.; Bakken, V.; Adamo, C.; Jaramillo, J.; Gomperts, R.; Stratmann, R. E.; Yazyev, O.; Austin, A. J.; Cammi, R.; Pomelli, C.; Ochterski, J. W.; Ayala, P. Y.; Morokuma, K.;
Milani et al. Voth, G. A.; Salvador, P.; Dannenberg, J. J.; Zakrzewski, V. G.; Dapprich, S.; Daniels, A. D.; Strain, M. C.; Farkas, O.; Malick, D. K.; Rabuck, A. D.; Raghavachari, K.; Foresman, J. B.; Ortiz, J. V.; Cui, Q.; Baboul, A. G.; Clifford, S.; Cioslowski, J.; Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz, P.; Komaromi, I.; Martin, R. L.; Fox, D. J.; Keith, T.; Al-Laham, M. A.; Peng, C. Y.; Nanayakkara, A.; Challacombe, M.; Gill, P. M. W.; Johnson, B.; Chen, W.; Wong, M. W.; Gonzalez, C.; Pople, J. A. Gaussian 03, revision C.02; Gaussian, Inc.: Wallingford, CT, 2004. (21) Krishnan, R.; Binkley, J. S.; Seeger, R.; Pople, J. A. J. Chem. Phys. 1980, 72, 650. (22) Becke, A. D. Phys. ReV. A 1988, 38, 3098. (23) Burke, K.; Perdew, J. P.; Wang, Y. In Electronic Density Functional Theory: Recent Progress and New Directions; Dobson, J. F., Vignale, G., Das, M. P., Eds.; Plenum: New York, 1998. Perdew, J. P.; Burke, K.; Wang, Y. Phys. ReV. B 1996, 54, 16533. (24) Fichou D. Handbook of oligo- and polythiophenes; Wiley-VCH: New York, 1999 and references therein. (25) Binkley, J. S.; Pople, J. A.; Hehre, W. J. J. Am. Chem. Soc. 1980, 102, 939. (26) Dobson, J. F.; Wang, J.; Dinte, B. P.; Mclennan, K. He, H. M. Int. J. Quant. Chem. 2005, 101, 579-598. Dobson, J. F.; Wang, J. Phys. ReV. Lett. 1999, 82, 2123. (27) Langreth, D. C.; Dion, M.; Rydberg, H.; Schroeder, E.; Hyldgaard, P.; Lundqvist, B. I. Int. J. Quant. Chem. 2005, 101, 599-610. Andersson, Y.; Langreth, D. C.; Lundqvist, B. I. Phys. ReV. Lett. 1996, 76, 102. Lundqvist, B. I. Int. J. Quant. Chem. 1995, 56, 247-255. (28) Millet, A.; Korona, T.; Moszynski, R.; Kochanski, E. J. Chem. Phys. 1999, 111, 7727. (29) Tsuzuki, S.; Luthi, H. P. J. Chem. Phys. 2001, 114, 3949. (30) Langlet, J.; Berges, J.; Reinhardt, P. Chem. Phys. Lett. 2004, 396, 10-15. (31) Chakarova, S. D.; Schroeder, E. J. Chem. Phys. 2005, 122, 054102. (32) Gussoni, M.; Rui, M.; Zerbi, G. J. Mol. Struct. 1998, 447, 163215. (33) Brillante, A.; Syassen, K.; Haufland, M.; Heeger, J. Mol. Cryst. Liq. Cryst. 1985, 117, 331. (34) Loi, M. A.; Cai, Q.; Chandrasekhar, H. R.; Chandrasekhar, M.; Graupner, W.; Bongiovanni, G.; Mura, A.; Botta, C.; Garnier, F. Synth. Met. 2001, 116, 321. (35) In this work, the word “dimer” means a pair of interacting molecules, regardless of the number of thiophene rings which forms each molecule. (36) In the case of T3, we find no frequency shift for the optimized case. However, calculations with the central ring rotated by 45° yield for the frequency of the R mode a value of 1459 cm-1.
