The Effect of Intermolecular Dipole− Dipole Interaction on Raman

J. Phys. Chem. B 2008, 112, 1619-1625

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The Effect of Intermolecular Dipole-Dipole Interaction on Raman Spectra of Polyconjugated Molecules: Density Functional Theory Simulations and Mathematical Models Alberto Milani,* Mirella Del Zoppo, Matteo Tommasini, and Giuseppe Zerbi Center for NanoEngineered Materials and Surfaces (NEMAS), Dipartimento di Chimica, Materiali e Ingegneria Chimica, G. Natta, Politecnico di Milano, Piazza Leonardo da Vinci 32, I-20133 Milan, Italy ReceiVed: July 23, 2007; In Final Form: October 23, 2007

In this work, we analyze the effect of intermolecular dipole-dipole interactions on Raman spectra of polyconjugated molecules. In particular, the behavior of push-pull polyenes has been studied. By means of density functional theory (DFT) calculations on isolated molecules and dimers, we have found that both the frequencies and intensities of the strongest Raman lines (R mode) are strongly influenced by intermolecular interactions. The results have been rationalized within the effective conjugation coordinate (ECC) theory developed in the past. The calculations for different configurations have also shown that the Raman spectra are sensible to different intermolecular geometries, thus implying a possible application of vibrational spectroscopy to the study of supramolecular properties of polyconjugated systems. The comparison with the available experimental spectra confirms the results obtained with the DFT computations. Finally, a very simple mathematical model is proposed for the prediction of the Raman frequencies of interacting systems. From the knowledge of just a few quantities for the isolated molecule and of some geometrical parameters, an estimate of the frequency of the dimers can be obtained. Despite its simplicity, this model gives results in very good agreement with DFT calculations carried out explicitly on dimers in several different arrangements.

I. Introduction Polyconjugated molecules and polymers are a class of materials of fundamental importance for molecular electronics.1 Their electronic, optical, and semiconductive properties have been the subject of intensive studies for more than 20 years and are presently the focus of innovative technology. With the help of spectroscopists and physicists who investigated the structural and physical properties of these materials, the efforts of organic chemists have been aimed at the synthesis of new molecules whose properties could be tuned and optimized in order to increase the performance of real devices.1 In recent years, the efforts made to study the properties of single molecules have been expanded by an analysis of molecular aggregates and solids. In other words, the interest of researchers has been focused on the “supramolecular properties” of polyconjugated materials.2-4 Indeed, the conductive, optical, and electronic properties are heavily affected by the interactions with the environment. Particularly relevant are solvent effects and intermolecular self-organization. However, the problem of dealing with these effects is challenging and difficult from the theoretical point of view, while experimentally it is often not easy to disentangle intramolecular and intermolecular effects. Vibrational spectroscopy is known to be a powerful method for the characterization of polyconjugated molecules. Thanks to the large electron-phonon coupling that characterizes this class of materials, much information on π-electron delocalization (and hence on electronic properties) can be deduced from a careful analysis of the Raman and infrared spectra.5-7 In particular, both the frequencies and intensities of the strongest Raman lines (traditionally referred to as “R mode” or amplitude * Corresponding author. E-mail: [email protected].

mode5,7,8) are strongly modulated by charge delocalization, and it can be stated as a general rule that the more conjugated the molecule, the lower the frequency of the R mode and the larger its intensity.5-7 Indeed, all the relevant electronic properties of π-conjugated molecules are strictly related to one structural parameter, namely, the average bond length alternation (BLA ) uj) (i.e., the average difference between the length of single and double adjacent CC bonds).9,10 The R mode describes the oscillations of the uj parameter about its equilibrium value, and it is the vibration with the strongest electron-phonon coupling. For this reason, each phenomenon that affects the degree of π-electron delocalization in a polyconjugated system (e.g., increasing chain length, conformational disorder, structural defects, etc.) can be, and has been, investigated by analyzing the Raman spectra. In principle, the “environment” could also play a significant role on the extent of π-electron delocalization, thus suggesting the use of Raman spectroscopy to study these effects. For instance, solvent effects on push-pull molecules used for nonlinear optics application11-13 have been studied with Raman spectroscopy.14,15 It has been shown that solvents of increasing polarity modulate the intramolecular charge transfer in such a way that uj decreases.9,13,16 In spite of these observations, the effect of intermolecular interactions on the vibrational spectra of polyconjugated molecules has been neglected in the past because it was believed to introduce just minor modifications. In a previous paper,17 we showed how intermolecular interactions (in particular, London dispersion forces) can play a relevant role in the interpretation of the Raman spectra of unsubstituted thiophene oligomers. In this paper, we investigate the effect of dipoledipole interactions on the Raman spectra of polyconjugated dipolar molecules. Our approach will use density functional

10.1021/jp075763o CCC: $40.75 © 2008 American Chemical Society Published on Web 01/25/2008

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Figure 1. Structure of the DMADC3 molecule (H3C)2-N-(CH)5-C-(CN)2 investigated in this work and of the corresponding dimers. In this paper, the first one will be referred to as the “T-dimer”, the second as the “planar dimer” and the last as the “π-π dimer”. The geometries of the dimers have been completely optimized at the B3LYP and PBE1PBE levels of theory (6-311++G** basis set).

Figure 2. Structure of polyenals with four (left) and five (right) CdC bonds and their dimers. These molecules will be referred to respectively as PE4 and PE5 in this paper. The geometries of the dimers have been completely optimized (PBE1PBE/6-311++G**).

theory (DFT) calculations and will be supported by experimental data. In particular, we will consider a typical push-pull polyene13 and polyene aldehydes of different chain lengths (polyenals),18 and we will show that dipole-dipole interactions modify both the frequency and the intensity of the strongest Raman lines. Finally, a simple mathematical model for the calculation of the effect of these interactions on the vibrational frequencies will be presented: this model uses just the molecular parameters of the isolated molecule and the intermolecular distance. Numerical results are in good agreement with DFT calculations carried out on the interacting system (two interacting molecules) and prove the validity of the model as a method for predicting the effect of intermolecular interactions on the vibrational spectra. II. Computational and Experimental Section In order to investigate the effect of dipole-dipole interactions, we have chosen to focus on two kinds of push-pull molecules. These systems are characterized by a π-conjugated bridge connecting a donor (D) and an acceptor (A) terminal group, thus generating a dipolar molecule. The electronic properties of this class of molecules depend on the strength of the donor and acceptor groups and on the length of the π-conjugated bridge. The molecules considered in this work are the following:

(i) dimethylaminodicyanohexatriene13 (DMADC3) (see Figure 1), a molecule consisting of a polyenic bridge with three CdC bonds and rather strong acceptor (-CtN)2 and donor -N(CH3)2 groups, and (ii) polyene aldehydes (polyenals)18 of increasing chain lengths (ranging from two to nine CdC bonds). We take the terminal -CH3 group as an extremely weak donor group and the aldehyde (-CHO) as a rather weak acceptor group. In the present study we report DFT calculations carried out with the Gaussian 03 code.19 In order to study the effect of dipole-dipole interactions, the calculations have been carried out on a pair of molecules referred to as “dimers” in this paper. In particular, for DMADC3, three types of dimers have been investigated, namely (see Figure 1), (i) molecular dipoles arranged in a T configuration, which should be characterized by a zero net contribution of dipole-dipole interactions, and (ii and iii) antiparallel dipoles: in case (ii), the two molecules lie on the same plane, while in case (iii) they are arranged in a sandwich-like π-π stack. In these two geometries, the contribution by dipole-dipole forces has the same mathematical form, but the interacting molecules are characterized by significantly different intermolecular distances, which modulate the strength of interaction.

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Figure 3. Effect of dipole-dipole interactions: Raman spectra for DMADC3 and its possible dimers calculated with the PBE1PBE functional (left) and the B3LYP functional (right). The 6-311++G** basis set has been used for all the calculations. The intensities of the isolated molecules have been multiplied by two in order to normalize the spectra with respect to the number of molecules.

For polyenals, only the sandwich-like π-π configuration has been studied for chain lengths ranging from two to five CdC bonds (Figure 2). In each case, all the geometrical parameters have been fully optimized, and the resulting intermolecular geometries are true minima of the intermolecular potential energy surface, free from any kind of geometrical constraints imposed in the calculations. Raman spectra have been calculated for all these geometries. In the computations, the hybrid DFT functional PBE1PBE20 has been used with the 6-311++G** basis set.21 It has been recently demonstrated that this functional gives a good description of dipole-dipole intermolecular interactions,22 in spite of being less computationally demanding than other theoretical methods such as coupled cluster, symmetry-adapted perturbation theory, and MPn theories. For comparison, all the calculations have also been carried out with the more widely used B3LYP hybrid functional23 with the same basis set. The results are similar both qualitatively and quantitatively. Experimental Raman spectra of DMADC3 are taken from ref 14. For polyenals, DFT calculations are compared with FTRaman spectra (λexc ) 1064 nm) recorded with a Nicolet 910 FT-Raman interferometer.18 III. Results and Discussion A. DMADC3. In Figure 3 we report the Raman spectra of the isolated DMADC3 molecule and its dimers calculated with PBE1PBE (left) and B3LYP (right) functionals. Before analyzing details of these spectra on the basis of intermolecular forces, it is important to check whether and how the PBE1PBE functional describes this system compared to the more widely used B3LYP functional. As Figure 3 shows, the two functionals give very similar spectral patterns for the dimers and the isolated molecules (see also the Supporting Information). The only difference is relative to the planar dimer, where a slightly different intensity ratio between the two strongest lines (1640 and 1588 cm-1 for PBE1PBE) is found for the two functionals. Since the results are qualitatively similar in all the calculations discussed in this paper, we adopt the PBE1PBE functional. Dipole-dipole interactions can be described by using multipole expansion. As a result,24 it is possible to represent the dipole interaction between two molecules A and B as

Uµµ ) -

µ Aµ B × f(θA,θB,φA,φB) 4π0R3

(1)

where µ is the magnitude of the dipole moment, R is the distance between the two molecules, and f is a function of the polar angles (θA,θB,φA,φB), which define the relative intermolecular position of the molecules.24 For the T-dimer, the dipole moments are orthogonal, f(θA,θB,φA,φB) ) 0, while, for the antiparallel dimers, f(θA,θB,φA,φB) ) 1.29 In this latter case, the interaction strength becomes uniquely modulated by the intermolecular distance R: for the DMADC3 planar dimer, the molecules are further apart (approximately 5.87 Å), while they are closer in the π-π dimer (approximately 3.85 Å). Hence, the strength of dipole-dipole interactions is zero for the T-dimer and is maximum for the π-π dimer. The analysis of the DFT calculated Raman spectra (Figure 3) shows that for the T-dimer we have just minor modifications of the frequency and intensity of the strongest Raman modes (R modes) with respect to the isolated molecules. In contrast, there are significant changes for the planar dimer, even larger in the case of the π-π dimer. In Figure 3, the intensities of the isolated molecules have been multiplied by two in order to normalize the spectra with respect to the number of molecules. Figure 3 shows that dipole-dipole interactions cause a downshift of the frequency of the R mode (1654 cm-1 in the isolated molecule). The stronger the interaction, the larger the shift. Accordingly, in the case of the planar dimer, where the intermolecular distance is larger and hence the dipole-dipole interaction is weaker, the frequency shift is calculated to be smaller than in the case of the π-π configuration. In the framework of the effective conjugation coordinate (ECC) model, a lowering of the R mode means larger π-electron delocalization and a more equalized bond alternation. As pointed out in the Introduction, a softening of the frequency of the R mode has been observed for solutions in solvents of increasing polarity: 13,14 in this frame, the solid state can be seen as a limiting case of a “solution” where solute and solvent are alike. This is indeed proved in Figure 4 where we report experimental Raman spectra of DMADC3 in the solid state and in a solution of CHCl3 and where a downshift of the R mode is

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Figure 4. Left: Experimental Raman spectra of DMADC3 for the solid state (above) and the solution of CHCl3 (below). For the spectrum in solution, the gray band is due to the solvent. The R line is labeled with 1, and the CtN stretching line is labeled with 2. The dashed lines are used to indicate the frequency shift of the R mode. Right: Calculated Raman spectra of DMADC3 isolated molecule and dimers in the range of 15002400 cm-1 (PBE1PBE/6-311++G**). The effect of intermolecular interactions on Raman intensities is consistent with the experimental spectra, as it can be seen from the comparison with the calculated CtN stretching lines between 2300 and 2400 cm-1.

observed for the solid state with respect to solution, consistent with our calculations. Furthermore, DFT calculations suggest a decrease of the Raman intensity of the R mode as the intermolecular interactions increase. This is confirmed by the experimental spectra of the solution and the solid state. The large intensity decrease observed in going from the solution to the solid state can be estimated by looking at the intensity ratio between the R mode and the CtN stretching modes observed at 2200 cm-1. The effects of intermolecular interactions on these lines (labeled with 2 in Figure 4) is indeed much smaller, as we also find in our calculations (see Supporting Information). In this discussion, we have considered the spectrum of the solution as the experimental counterpart of DFT calculation on isolated molecules: obviously, this is not completely correct. However, it is reasonably true that, in solution, the interaction strength is smaller than in the solid. B. Polyenals. The same computational procedure adopted for DMADC3 has been applied to polyenals (PE-N), in particular PE3, PE4, and PE5. The theoretical importance of this class of molecules is due to the fact that they are dipolar derivatives of polyenes for which the ECC model has been initially introduced.5-7 For this reason, these are the ideal systems for investigating the effect of dipole-dipole interactions on the Raman spectra in the framework of ECC theory. In Figure 5 we report the calculated Raman spectra of isolated polyenals with a number of double bonds ranging from 3 to 9: a downshift of the frequency with increasing chain length is observed along with a superlinear increase of the intensity. This behavior is expected within the ECC theory.18,25 In the left panel of Figure 6, the DFT calculated Raman spectra for dimers of PE3, PE4, and PE5 are compared with the Raman spectra of the corresponding isolated molecules. The effect of dipole-dipole interactions is similar to what has been observed in the case of DMDC3: a downward frequency shift is observed for the interacting molecules together with a decrease

Figure 5. Calculated (PBE1PBE/6-311++G**) frequency and intensity dispersion of the R mode with the number N (N ) 3-9) of conjugated CdC bonds in polyenals as isolated molecules.

in the intensities. Furthermore, the extent of the frequency shift is slightly larger for increasing chain lengths (see Table 3), consistent with the increase of the molecular dipole with chain length. Finally, in the right panel of Figure 6, DFT results for PE4 and PE5 are compared with experimental FT-Raman spectra of the solid and of the solution in CHCl3: we again find good agreement between theory and experiment in the description of the effect of intermolecular interactions. For a better comparison, the DFT calculated frequencies have been scaled by a factor of 0.945, as normally accepted in DFT calculations of organic molecules.

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Figure 6. Left: DFT calculated (PBE1PBE/6-311++G**) Raman spectra of the isolated molecules and dimers of PE2, PE3, PE4, and PE5. Notice that the intensities of the isolated molecules have been multiplied by 2 in order to normalize with respect to the number of molecules. Right: Comparison between calculated and experimental spectra of PE4 and PE5 (solid and solution CHCl3). DFT values have been scaled by 0.945 in order to allow a better comparison with experimental spectra. The experimental spectra refer to samples that contain a mixture of PE4 and PE5. The corresponding bands are explicitly indicated.

In conclusion of this section, we can state that DFT calculations on DMADC3 and polyenals highlight the role of dipole-dipole interactions in modulating the frequencies and intensities of the strong Raman lines related to the amplitude mode. In particular, a downward frequency shift and a large decrease of the intensities are found for an increasing strength of the intermolecular forces. In the case of DMADC3, we have seen that the extent of these modifications suggests the possibility to also distinguish between dimers in different configurations, thus giving indications on the supramolecular arrangement in polyconjugated molecules by means of Raman spectroscopy. C. Mathematical Model. On the basis of the results of the previous section, we propose a very simple mathematical model for the interpretation of the effect of dipole-dipole interactions on the Raman spectra of polyconjugated molecules. This model is based on DFT calculated quantities and it does not require the explicit computation of the properties of the dimer but just some quantities computed for the isolated molecule. The only intermolecular parameter is the geometry of the dimer, which defines the f function and the intermolecular distance R. In this way, a general method for predicting the Raman spectra of interacting dipolar systems is proposed. In this paper, just the effect on vibrational frequencies will be modeled. Extensions of this model to account for Raman intensities are currently under study. In the past, other similar models have been proposed where the effect of intermolecular interactions on the vibrational properties has been described in terms of the interaction of two identical dipole moments.26 On this basis, we directly introduce the intermolecular dipole-dipole potential energy term in the expression of the potential energy of the interacting system. In the supermolecular approach, the energy of a dimer composed by identical molecules A can be written as (for antiparallel dimers, f(θA,θB,φA,φB) ) 1)

AA ) 0A + 0A -

µi µi CR

3

) 0A + 0A -

1 µi µi 1 µi µi ) 2 CR3 2 CR3 A + A (2)

where C ) 4π0, 0A is the energy of the isolated molecules, and A is the energy of the interacting molecule. The dipoledipole interaction -(µi µi/CR3)30 can be “distributed” over the two molecules, and on this basis the energy of the single interacting molecule A ≡  is

 ) 0 -

1 µi µi 2 CR3

(3)

In the harmonic approximation, the intramolecular force constants are described by the second derivatives of the intramolecular potential energy, evaluated at the equilibrium geometry:

fab )

( ) ∂2 ∂xa∂xb

(4)

0

Note that under the effect of intermolecular forces, the molecular geometries relax in a new minimum, in particular, a slightly more delocalized structure is obtained for both DMADC3 and polyenals. However, in the hypothesis of mechanical harmonicity and small relaxation displacements, we can still evaluate the energy derivatives at the equilibrium of the isolated molecule. By using eq 3 in eq 4 we obtain

fab ) f 0ab -

( )

(

1 ∂µi ∂µi 1 ∂µx ∂µx ∂µy ∂µy ) f 0ab + + 3 ∂x ∂x CR CR3 ∂xa ∂xb ∂xa ∂xb a b 0 ∂µz ∂µz (5) ∂xa ∂xb 0

)

f 0ab are the Cartesian force constants of the isolated molecule, and the last equation is obtained in the hypothesis of electrical harmonicity (i.e., (∂2µi/∂xa∂xb) ) 0). Calculations of the second derivatives of the dipole moments of PE4 have shown that their inclusion in eq 5 produces only negligible changes in the final numerical results for frequencies. Therefore, the burden of the computational procedure required for their numerical calculations is not justified in the spirit of the present approach.31 Cartesian first derivatives of the molecular dipole can be obtained by DFT calculation on the isolated molecule, and just

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TABLE 1: Comparison of Vibrational Frequencies (cm-1) of Relevant Calculated Raman Bands (PBE1PBE/6-311++G**) for Isolated DMADC3, the DMADC3 Planar Dimer, and Values Calculated with the Model Describing Dipole-Dipole Interactions (eq 5)a

a

isolated

dimer

model

1247 1599 1654 2339 2352

1248 1588 1640 2325 2343

1246 1589 1648 2339 2351

In this case, R ) 5.87 Å.

TABLE 2: Comparison of Vibrational Frequencies (cm-1) of Relevant Calculated Raman Bands (PBE1PBE/6-311++G**) for Isolated DMADC3, the DMADC3 π-π Dimer, and Values Calculated with the Model (eq 5)a

a

isolated

dimer

model

1247 1599 1654 2339 2352

1237 1582 1636 2317 2333

1244 1563 1639 2338 2349

In this case, R ) 3.85 Å.

TABLE 3: Comparison of Vibrational Frequencies (cm-1) of the Raman Line Relative to the R Mode (PBE1PBE/ 6-311++G**) for a Polyenal of an Increasing Number of Double Bonds (N) from 2 to 5a N

isolated

dimer

model

R (Å)

2 3 4 5

1716 1688 1666 1645

1711 1677 1654 1633

1711 1677 1650 1625

4.17 3.97 4.09 4.14

a The DFT calculated frequency values of the isolated molecules are compared with the DFT calculated values relative to the dimers and to the numerical values obtained by the application of the model (eq 5). In the last column, the intermolecular distance R used in the calculation is reported for each case.

the knowledge of R is required. Using these new force constants given by eq 5, the vibrational frequencies perturbed by dipoledipole interactions can be calculated via standard techniques.27,28 In Tables 1 and 2 the vibrational frequencies of DMADC3 obtained using force constants derived from eq 5 are compared with those obtained by DFT calculations reported in the previous section for the isolated molecule, the planar dimer (Table 1), and the π-π dimer (Table 2). In these tables, not only are the CC stretching lines (R mode) reported, but also the other strong Raman lines of the molecule. The model reproduces qualitatively well the trends obtained by DFT calculations and correctly predicts a softening of the R mode under the effect of dipoledipole interactions. Quantitatively, our model overestimates the effect of intermolecular forces. This is probably due to both the approximations of the model and also the contribution of other important intermolecular interactions (e.g., dispersion forces) not fully handled by current DFT functionals. However, it is very encouraging to realize that such a simple model can give results in acceptably good agreement with computations. In Table 3 the results of the model for polyenals are presented relative to the frequency of the R mode. Again, a very good qualitative agreement is obtained; the different frequency shift that is observed for molecules of increasing length is also approximatively reproduced by the model. Furthermore, in this case, the numerical agreement with DFT calculations is strikingly good: the numerical values of the R frequency are identical for the shortest molecules with two and three CdC

bonds, while slight deviations are found for increasing molecular lengths. As indicated above, this behavior might be rationalized on the basis of the increase in conjugation with increasing chain length, which causes a larger contribution of other intermolecular forces not explicitly handled by the present approach. IV. Conclusion In this work, we have shown that intermolecular dipoledipole interactions have a large effect on the Raman spectra of polyconjugated dipolar molecules. By means of DFT calculations for the isolated molecules and for pairs of interacting molecules (dimers) in different geometries, we have shown that intermolecular interactions cause a softening of the frequency of at least the amplitude mode (i.e., R mode) associated with the strongest Raman lines and a large lowering of their intensities. The analysis of the experimental Raman spectra recorded for solutions (considered as consisting of noninteracting molecules of solute) and in the solid state (interacting systems) shows a very good agreement with computations and proves that Raman spectra can also be used to study intermolecular effects that take place in polyconjugated systems. Finally, a convenient mathematical model has been proposed to calculate the frequency shifts observed in the Raman spectra. This model just requires the knowledge of the spectroscopic properties of the single molecule and of a few geometrical parameters of the dimer. The agreement between the values obtained from the model and from DFT calculations on the dimers is very good and offers a reliable, though approximate, method for the prediction of the effect of intermolecular forces on the Raman spectra of interacting polyconjugated molecules. The results obtained in this work give a further contribution to the understanding of the intermolecular dependence of the vibrational frequencies for polyconjugated systems. Indeed, we are faced with the puzzling problem of oligothiophenes, which show a seemingly opposite behavior.17 Extended work is necessarily needed. Acknowledgment. The authors gratefully thank Dott. Luigi Brambilla and Dott. Andrea Bianco for providing the experimental FT-Raman data of polyenals. This work has been partly supported by Project FIRB 2003 “Molecular compounds and hybrid nanostructured materials with resonant and non resonant optical properties for photonic devices” (RBNE033KMA) and by Project CARIPLO 2006 “Self-assembled nanostructured materials for biological applications”. Supporting Information Available: (a) Comparison of the Raman spectra of DMADC3 computed with B3LYP and PBE1PBE functionals (6-311++G**). (b) Computed Raman spectra (PBE1PBE/6-311++G**) in the region ranging from 1500 to 2400 cm-1 for DMADC3 and its dimers: effect of intermolecular interactions on Raman intensities and comparison with CtN stretching lines. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Handbook of Conducting Polymers; Skotheim, T. A., Ed.; Dekker: New York, 1986; Vols. 1 and 2. Handbook of Conducting Polymers, 2nd ed.; Skotheim, T. A., Ed.; Dekker: New York, 1998; ISBN 0824773950. Handbook of Organic ConductiVe Molecules and Polymers; Nalwa, H. S., Ed.; Wiley: New York, 1997; ISBN 978-0-471-96275-5. (2) Dimitrakopoulos, C. D.; Malenfant, P. R. L. AdV. Mater. 2002, 14, 99. Horowitz, G. AdV. Mater. 1998, 10, 365. Katz, H. E.; Bao, Z. J. Phys. Chem. B 2000, 104, 671. Watson, M. D.; Fechtenko¨tter, A.; Mu¨llen, K. Chem. ReV. 2001, 101, 1267.

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