Modeling the Structural and Electronic Properties of an Optically Active

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Modeling the Structural and Electronic Properties of an Optically Active Regioregular Polythiophene Oscar Bertran,† Juan Torras,*,‡ and Carlos Alema´n*,§,| Departament Fı´sica aplicada, EUETII, UniVersitat Polite`cnica de Catalunya, Pc¸a. Rei 15, 08700 Igualada, Spain, Departament d’Enginyeria Quı´mica, EUETII, UniVersitat Polite`cnica de Catalunya, Pc¸a. Rei 15, 08700 Igualada, Spain, Departament d’Enginyeria Quı´mica, E. T. S. d’Enginyeria Industrial de Barcelona, UniVersitat Polite`cnica de Catalunya, Diagonal 647, 08028 Barcelona, Spain, and Center for Research in Nano-Engineering, UniVersitat Polite`cnica de Catalunya, Campus Sud, Edifici C′, C/Pasqual i Vila s/n, Barcelona E-08028, Spain ReceiVed: March 11, 2010; ReVised Manuscript ReceiVed: May 22, 2010

A comprehensive theoretical study about the structural and electronic molecular properties of the optically active regioregular poly[(R)-3-(4-(4-ethyl-2-oxazolin-2-yl)phenyl)thiophene] and its model oligomers has been developed with use of quantum mechanical calculations. Results show two stable arrangements for the investigated oligomers. The first one consists of a plain structure with all the inter-ring dihedral angles arranged in a syn-gauche+ conformation rather than the anti-gauche+ typically found in substituted polythiophenes. This produces a reduction of the steric repulsions allowing the formation of a π-stacking alignment between phenyl groups of adjacent monomers. The second is a helical structure with six repeating units per turn that is constructed by alternating the syn-gauche+ and syn-gauche- conformations. The lowest π-π* transition energy predicted for an idealized polymer chain, which was derived from Density Functional Theory calculations, is in agreement with the reported experimental values obtained by UV-vis spectroscopy. SCHEME 1

Introduction π-Conjugated conducting polymers, such as polythiophene derivatives (PThs), have been the subject of intense research due to their interesting electronic and optical properties.1-3 Among them, chiral regioregular PThs4-7 bearing optically active substituents at the 3- or 3,4-positions of the thiophene ring have attracted particular interest due to their unusual chiroptical properties and potential applications, e.g., circular polarized electroluminescence devices8 and enantioselective sensors.9 In contrast to observations in conventional π-conjugated polymers, chiral PThs usually do not exhibit optical activity in the π-π* transition region in good solvents or at high temperatures but they show unique optical activity in poor solvents, at low temperature, or in films. This behavior has been attributed to the main chain chirality when they aggregate to form π-stacked supramolecular structures, which produces intense induced circular dichroism (CD) in the UV-visible region.7,10,11 Nevertheless, as far as we know, the origin of the optical activity in aggregated chiral PThs remains unclear yet.4,12 Studies on the relationships between the chiroptical properties of chiral regioregular PThs and the supramolecular structures formed by these materials upon aggregation have been mainly focused on poly[(R)-3-(4-(4-ethyl-2-oxazolin-2-yl)phenyl)thiophene] (hereafter PEOPT for the polymer and n-EOPT for oligomers with n repeating units; Scheme 1). The interest in * To whom correspondence should be addressed. E-mail: torras@ euetii.upc.edu or [email protected]. † Departament Fı´sica aplicada, EUETII, Universitat Polite`cnica de Catalunya. ‡ Departament d’Enginyeria Quı´mica, EUETII, Universitat Polite`cnica de Catalunya. § Departament d’Enginyeria Quı´mica, E. T. S. d’Enginyeria Industrial de Barcelona, Universitat Polite`cnica de Catalunya. | Center for Research in Nano-Engineering, Universitat Polite`cnica de Catalunya.

PEOPT arises from an early study that showed the chirality induced upon complexation with metal ions in a good solvent such as chloroform, i.e., intense induced CD, even though the changes in UV-visible spectra were negligible.9 This feature was attributed to the intermolecular coordination of the oxazoline groups to the metal ions, which resulted in the formation of helical arrangements with a well-defined handedness. Thus, metal ions are coordinated on average with two nitrogen atoms belonging to the non-π-stacked polymer chains.13 Furthermore, changes in the CD spectra were detected varying the nature of the solvent. Specifically, the addition of poor solvents, such as methanol or acetonitrile, to the chloroform solution led to conformational changes that produced chiral aggregations with different handedness.8 However, solvent-induced Cotton effects were only detected for the regioregular 8-EOPT, no induced CD being found in smaller oligomers.14 Moreover, the chirality switching process of such supramolecular aggregates, in which the alternative addition of Cu2+ and a metal complexing agent led to a back and forth aggregate formation, respectively, was reported.15

10.1021/jp102223s  2010 American Chemical Society Published on Web 06/03/2010

Properties of an Optically Active Polythiophene This work presents a comprehensive theoretical study on n-EOPT oligomers with n ranging from 1 to 8, which has been motivated by the lack of structural and electronic information on PEOPT at the molecular level. More specifically, we propose an atomistic model for this polymer, which is based on the results provided by an exhaustive conformational study on oligomers. This model has been used to predict the ionization potential (IP) and the lowest πfπ* transition energy (εg) of PEOPT, which are the more characteristic electronic properties of conducting polymers. Furthermore, theoretical predictions have been compared with available UV-visible measures.14

J. Phys. Chem. C, Vol. 114, No. 25, 2010 11075 SCHEME 2

Methods Full geometry optimization of n-EOPT oligomers, with n ranging from 1 to 8, were performed with the Hartree-Fock (HF) method combined with the 6-31G(d,p) basis set,16 i.e., HF/ 6-31G(d,p) level. In spite of its simplicity, this method has been used extensively in previous studies providing a very satisfactory description of thiophene-containing oligomers in terms of both molecular geometries and relative energies.17,18 Calculations on 2-EOPT were carried out considering the three isomers constructed with the tail-to-tail (T-T), head-to-head (H-H), and headto-tail (H-T) polymer linkages, which have been denoted as 2-EOPT4,4′, 2-EOPT3,3′, and 2-EOPT3,4′, respectively. The potential of mean force (PMF) for the internal rotation of the 2-EOPT4,4′, 2-EOPT3,3′, and 2-EOPT3,4′ isomers was studied by scanning the inter-ring dihedral angle θ (defined by the S-C-C-S sequence) in steps of 15° between θ ) 0° (syn conformation) and 180° (anti conformation). A flexible rotor approximation was used, each point of the path being obtained from a geometry optimization of the molecule at the HF/631G(d,p) level considering a fixed value of θ. For each value of θ a number of molecular models, which were used as starting points for geometry optimization, were constructed considering all the possible arrangements of the benzyl, oxazoline, and ethyl moieties. IPs, which were estimated by using Koopmans’ theorem,19 reflect the capability to be ionized, at least partially, by an acceptor (p-type dopant). Specifically, IPs were taken as the negative of the highest occupied molecular orbital (HOMO) energy, i.e., IP ) -εHOMO. On the other hand, εg was approximated as the difference between the HOMO and the lowest unoccupied molecular orbital (LUMO) energies, i.e., εg ) εLUMO - εHOMO. Although HF calculations provide a satisfactory description of the electronic properties of polyheterocyclic molecules from a qualitative point of view, we are aware that this method tends to overestimate the values of IP and εg.20,21 Accordingly, the electronic properties presented in this work have been estimated by performing single point Density Functional Theory (DFT) calculations with the B3PW9122,23 method combined with the 6-31G(d,p) basis set,24 i.e., B3PW91/ 6-31G(d,p), on the molecular geometries optimized at the HF/ 6-31G(d,p) level. Electronic properties predicted by this theoretical procedure and experimental values are expected to be quantitatively comparable. Previous studies on π-polyconjugated systems indicated that the B3PW91 functional is able to reproduce very satisfactorily a wide number of electronic properties.18,25-28 It is worth noting that according to the Janak’s theorem,29 the approximation mentioned above for the calculation of the IP can be applied to DFT calculations, while Levy and Nagy evidenced that εg can be rightly approximated as the difference between εLUMO and εHOMO in DFT calculations.30 To obtain an estimation of the solvation effects on the relative stability of the minima obtained for 8-EOPT, molecular

geometries were reoptimized without any restriction in solution with use of a SCRF model. Specifically, the Polarizable Continuum Model (PCM) developed by Tomasi and coworkers31-34 was used to describe chloroform and acetonitrile as solvents. The PCM model represents the polarization of the liquid by a charge density appearing on the surface of the cavity created in the solvent. This cavity is built by using a molecular shape algorithm. Frequency analyses were carried out to verify the nature of the minimum state of all the stationary points obtained for 8-EOPT in the gas phase, in chloroform solution, and in acetonitrile solution, as well as to estimate the free energies of such minima. All quantum mechanical calculations presented in this work were performed with the Gaussian 03 computer program.35 Results and Discussion Conformational Analysis. To determine the conformation preferred by the 4-(4-ethyl-2-oxazolin-2-yl)phenyl substituent, quantum mechanical calculations on 1-EOPT were performed considering all the possible arrangements of the benzyl, oxazoline, and ethyl moieties, which are defined by dihedral angles χ, ξ, and ω, respectively (Scheme 2). Since two different minimum energy arrangements were expected for both χ and ξ, i.e., (∼45° and ∼135°) and (0° and 180°), respectively, while three possible dispositions were expected for ω (60°, 180°, and -60°), a total number of 2(χ) × 2(ξ) × 3(ω) ) 12 minima were anticipated for the potential energy hypersurface E ) E(χ,ξ,ω) of 1-EOPT. All these structures were constructed and subsequently used as starting points for full geometry optimizations at the HF/6-31G(d,p) level, which led to three different minimum energy conformations. These minima are shown in Figure 1, their dihedral angles and relative energies also being displayed. The energies of the three structures are very similar, as reflected by the small gap (0.9 kcal/mol) separating the most and the least stable minimum energy conformations. As can be seen, the repulsions between the hydrogen atoms contained in the thiophene and phenyl rings produce a folding in the corresponding dihedral angle, i.e., χ ) 39.0° and 141.1°, whereas such repulsions do not exist between the oxazoline and phenyl moieties that remain at the same plane, i.e., ξ ) 178.6° and 0.4°). The conformational preferences of 2-EOPT were determined considering the three possible isomers: 2-EOPT4,4′, 2-EOPT3,3′, and 2-EOPT3,4′, which are model systems of the T-T, H-H, and H-T polymer linkages, respectively. These simple model molecules will allow us to predict the preferred regiochemistry of polymer chains that, despite being set during the polymerization process, strongly depends on the repulsive and attractive interactions between consecutive monomeric units. As the energy difference among the three minima obtained for 1-EOPT is small and, additionally, significant steric repulsions are

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Figure 2. Relative energy (∆E), calculated with respect to the lowest energy conformation of the most stable isomer, against the dihedral angle θ for the minimum energy conformations of 2-EOPT3,3′ (gray circles), 2-EOPT3,4′ (black squares), and 2-EOPT4,4′ (empty triangles).

Figure 1. Minimum energy conformations of 1-EOPT derived from a systematic conformational search. Calculations were performed at the HF/6-31G(d,p) level. The dihedral angles of the side group and the relative energy (∆E) of each minimum are also displayed.

expected for some 2-EOPT isomers, the 12 arrangements mentioned above for the side chain of the monomer also have been considered for each thiophene ring of 2-EOPT. Accordingly, a total amount of (2 minima for the internal rotation of θ: anti-gauche and syn-gauche) × [122 - (12 2 )]possible arrangements of two side chains) ) 156 structures have been used as starting points for complete geometry optimizations in the conformational study of 2-EOPT4,4′ and 2-EOPT3,3′. For the 2-EOPT3,4′ isomer, the number of starting structures for complete geometry optimization increased to 2 × 122 ) 288 since in this case the substitutions at positions 3,4′ and 4,3′ are different. Calculations at the HF/6-31G(d,p) level led to 38, 22, and 36 minimum energy conformations for the 2-EOPT4,4′, 2-EOPT3,3′, and 2-EOPT3,4′ isomers, respectively, i.e., 96 minima from an initial set of 600 structures. The distribution of the interring dihedral angle θ against the relative energy is shown in Figure 2, which has been calculated with respect to the lowest energy minimum of the most stable isomer. As can be seen, there is a clear separation between the H-H, T-T, and H-T isomers, which must be attributed to the steric repulsions generated by the substituents. On the other hand, for each isomer the different minima are spread within a relatively narrow energy interval, i.e. ∼1.5 kcal/mol. Figure 3 displays the lowest energy minimum with θ arranged in syn-gauche and anti-gauche for the 2-EOPT4,4′, 2-EOPT3,3′, and 2-EOPT3,4′ isomers, whereas Table 1 lists the structural characteristics and some electronic properties of six such

Figure 3. Selected minimum energy conformations of 2-EOPT derived from a systematic conformational search for 2-EOPT. Calculations were performed at the HF/6-31G(d,p) level: (a) ag-4,4′; (b) sg-4,4′; (c) sg3,4′; (d) ag-3,4′; (e) sg-3,3′; and (f) ag-3,3′. Structural parameters are displayed in Table 1.

minima. As can be seen, the lowest energy structure, denoted ag-4,4′ (Figure 3a), corresponds to the anti-gauche conformation (θ ) 147.9°) of the 2-EOPT4,4′ isomer, in which the substituents adopt an arrangement relatively similar to that found for the most stable conformation of 1-EOPT. Thus, the only difference is located in the relative orientation of the oxazoline and phenyl rings, i.e., the dihedral angle ξ. The first local minimum, sg4,4′ (Figure 3b), is destabilized by only 0.7 kcal/mol and corresponds to a syn-gauche conformation (θ ) 45.2°) of the

Properties of an Optically Active Polythiophene

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TABLE 1: Structural and Electronic Properties of Selected Minimum Energy Conformations of 2-EOPT Calculated at the HF/6-31G(d,p) Levelb label

θ

χa

ξa

ωa

dphs

∆E

IP

εg

ag-4,4′

147.9

7.78

9.99

9.06

0.7

7.90

10.11

sg-3,4′

51.7

6.69

2.5

7.85

10.08

ag-3,4′

120.2

7.98

2.7

7.87

10.16

sg-3,3′

65.3

4.72

4.6

7.95

10.26

ag-3,3′

112.8

-178.8 -178.8 -178.8 -178.8 -178.8 -178.8 -178.8 -178.8 -178.8 -178.8 -178.8 -178.8

0.0

45.2

-1.3 -1.3 -1.2 -1.2 179.1 179.0 -1.0 -1.2 -2.0 -2.1 -1.1 -1.1

10.35

sg-4,4′

38.9 38.9 38.5 38.5 52.3 141.0 128.3 38.5 49.9 49.9 133.9 133.9

7.03

5.3

7.92

10.09

a For each minimum the top and bottom entry corresponds to the dihedral angle of the first and second repeating unit, respectively. Dihedral angles (θ, χ, ξ, and ω; see text) in degrees; distance between the phenyl centroids of adjacent repeating units (dphs) in Å; relative energy (∆E) in kcal/mol, ionization potential (IP) and π-π* lowest transition energy (εg) in eV. b

same isomer. In both minima, ag-4,4′ and sg-4,4′, the values of θ are similar to those typically found for 2,2′-bithiophene bearing small size substituents and even the unsubstituted dimer.17,18,25,26,28 On the other hand, the distribution of the θ values for the minima of the three 2-EOPT isomers (Figure 2) shows that the conformational characteristics of the 2-EOPT3,4′ are intermediate between those of the 2-EOPT3,3′ and 2-EOPT4,4′. For the 2-EOPT3,4′ isomer θ ranges from 50.3° to 55.3° and from 120.2° to 120.5° for the syn-gauche and anti-gauche arrangements, respectively. These narrow intervals are accompanied by small variations in the relative energy, i.e., smaller than 1.3 kcal/mol. The lowest energy minimum of the 2-EOPT3,4′ isomer, sg-3,4′ (Figure 3c), corresponds to a syn-gauche conformation (θ ) 51.7°), being destabilized by 2.5 kcal/mol with respect to the ag-4,4′. However, the corresponding anti-gauche conformation (θ ) 120.2°), ag-3,4′ (Figure 3d), is only 0.2 kcal/mol less stable than the sg-3,4′. The arrangements of the substituents in both the sg-3,4′ and the ag-3,4′ minima are significantly different from that found for the minima of the 2-EOPT4,4′ isomer. A remarkable characteristic of the 2-EOPT3,4′ isomer is that the arrangements of the two substituents are different for each minimum, such difference being localized in the dihedral angle formed by the thiophene and phenyl rings (χ). Finally, the most stable minimum of the 2-EOPT3,3′ isomer corresponds to a syn-gauche conformation (θ ) 65.3°), sg-3,3′ (Figure 3e). This structure is unfavored by 4.6 kcal/mol with respect to the global minimum ag-4,4′, which should be attributed to the steric interactions induced by the substituents at the 3,3′ positions. The first local minimum with a gauche-gauche arrangement (θ ) 112.8°), ag-3,3′ (Figure 3f), is destabilized by 0.7 kcal/mol with respect to the sg-3,3′ conformation. Accordingly, the repulsion between the substituents increases with θ, even though these unfavorable interactions are partially alleviated by inducing small distortions in the dihedral angle χ. Thus, χ adopts values of 49.9° and 133.9° for the sg-3,3′ and ag-3,3′ minima (Table 1), respectively, the arrangement adopted by the two substituents being identical for each minimum. This represents a distortion of +10° and -7° with respect to the values obtained in the absence of such repulsions for the minima of 1-EOPT. Table 1 lists the distances between the centroids of the two phenyl rings (dphs), showing that the interaction between such aromatic groups is more pronounced in the sg-3,3′ minimum. Specifically, inspection of the phenyl moieties in the sg-3,4′ and sg-3,3′ structures shows a T-shaped arrangement (dphs )

Figure 4. Potential of mean force for the rotation of the inter-ring dihedral angle θ calculated at the HF/6-31G(d,p) level for 2-EOPT4,4′ (gray triangles), 2-EOPT3,4′ (black squares), and 2-EOPT3,3′ (gray diamonds). Energies are relative to the global minimum.

6.69 Å) and an off-centered parallel displaced π-stacking (dphs ) 4.72 Å) alignment, respectively. These two dispositions are the most commonly cited relative orientations between aromatic moieties, the parallel-displaced structure being more stable than the T-shaped arrangement by 0.5-0.7 kcal/mol.36,37 This feature is fully consistent with the enhancement of the relative stabilization between the syn-gauche and anti-gauche arrangements found for the 2-EOPT3,3′ and 2-EOPT3,4′ isomers. Thus, the sg3,4′ structure (T-shaped phenyl rings) is 0.2 kcal/mol more stable than the ag-3,4′ one, whereas the sg-3,3′ minimum (paralleldisplaced π-stacking) is favored by 0.7 kcal/mol with respect to the ag-3,3′ one. Potential of Mean Force. Figure 4 displays the PMFs obtained in the gas phase for the 2-EOPT4,4′, 2-EOPT3,3′, and 2-EOPT3,4′ isomers, which were calculated by scanning the dihedral angle θ at the HF/6-31G(d,p) level. The flexible rotor approximation was applied, geometry optimizations being performed considering the more stable conformations of the substituents for each value of θ. Thus, for each point of the path, which was scanned using ∆θ ) 15°, a number (N) of initial structures was constructed varying the values of χ, ξ, and ω (Scheme 2) according to the results obtained in the conformational study of the previous section. The value of N was 78 for 2-EOPT4,4′ and 2-EOPT3,3′ (a total amount of 936 initial structures for the whole PMF of each isomer), and 144 for 2-EOPT3,4′ (1728 initial structures for the whole PMF). Beside the minimum energy conformation discussed in the previous section (Table 1), the PMFs allowed the barriers for

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Figure 5. Molecular structures obtained for 8-EOPT after full geometry optimization of the sg+-sg- [lateral (a) and axial (b) views] and all-sg+ models [lateral (c) and axial (d) views].

the internal rotation of each 2-EOPT isomer to be characterized. As expected, the barriers are located near the syn (θ ) 0°), gauche-gauche (θ ) 90°), and anti (θ ) 180°) arrangements. As can be seen, the gauche-gauche barrier separating the antigauche and syn-gauche minima is relatively low in all cases (1.7, 2.0, and 1.5 kcal/mol for 2-EOPT4,4′, 2-EOPT3,4′, and 2-EOPT3,3′, respectively). Interestingly, the gauche-gauche barrier of the 2-EOPT3,4′ isomer is displaced toward θ ) 105°, this feature being attributed to the partial compensation of the repulsive interactions originated by the side chains when θ ) 90°. On the other hand, the profile obtained for the 2-EOPT4,4′ isomer shows a distinctive feature with respect to the other two. Specifically, the energy region connecting the anti barrier and the ag-4,4′ minimum is very flat. Indeed, the anti barrier is more stable than the sg-4,4′ minimum evidencing that the interaction between the side chains of the two repeating units is negligible in this case. Polymer Structure. CD measurements on n-EOPT oligomers showed the formation of π-stacking aggregates,14 even though Cotton effects were found to depend on n. Thus, 8-EOPT tends to form chiral aggregates independently of the solvent whereas no solvent induced CD was exhibited by smaller oligomers, e.g. n ) 2 and 4.14 On the other hand, PEOPT showed a transition from the disordered coil-like arrangement detected in chloroform to a rod-like π-stacked structure in the presence of poor solvents, originating chiral supramolecular aggregates.8 This section is devoted to study the conformation of the 8-EOPT oligomer, which due to its critical length is especially important for the formation of supramolecular helical aggregates. A system constituted by H-T linkages was used to build three different models for 8-EOPT, which were optimized without any restriction at the HF/6-31G(d,p) level. Such models, which differ in the conformation of the inter-ring dihedral angles θ, were the following: (i) all the repeating units were arranged in anti-gauche+ (all-ag+ model); (ii) all the repeating units were arranged in syn-gauche+ (all-sg+ model); and (iii) the syngauche+ and syn-gauche- were alternated along the oligomer chain (sg+-sg- model). The substituents were initially arranged by using the dihedral angles χ, ξ, and ω previously found for the sg-3,4′ and sg-3,4′ minimum energy conformations (Table 1).

TABLE 2: Electronic Properties (εg and IP; in eV) Predicted for n-EOPT and PEOPT at the B3PW91/ 6-31G(d,p)//HF/6-31G(d,p) Level along with Available Experimental Values
gn-EOPT model

4

6

8

∞

IPPEOPT

all-syn all-anti all-sg+ sg+-sg-

3.42 3.47 4.19 3.95

3.05 3.11 4.06 3.73

2.88 2.96 4.01 3.63

2.42 2.48 3.80 3.32

4.63 4.70 5.58 5.19

exptla

3.60

2.67

2.38

2.28

a

From ref 14.

Results indicated that the all-ag+ model was much less stable than those involving the syn-gauche conformations. This was reflected by the mixture of anti-gauche and syn-gauche arrangements found for the different repeating units of the allag+ model after geometry optimization. Accordingly, this model has been rejected for PEOPT. Figure 5 shows the optimized structures obtained for the sg+-sg- and all-sg+ models. As can be seen, the polymer chain adopts a ring and a helical conformation in the former and the latter model, respectively. More specifically, the sg+-sg- model corresponds to a plain structure that could induce a helical conformation by steric repulsion between closing ring edges. Such a hypothetical helix is predicted to present a large diameter and a small pitch due to the approximately ∼15 repeating units required to close the ring. In contrast, the helix derived from the all-sg+ model, which involves around 6 repeating units per turn, shows an internal diameter of 1.3 Å and a pitch of 20.8 Å per turn. However, as the dispersion contribution is not included in the HF method, additional calculations have been performed using the Density Functional Theory approach, which includes noncovalent interactions, i.e., M05-2X,38 M062X,39 and ωB97X-D.40 Table 3 lists the average values of the interpitch distance (Rp), the internal diameter of a helical turn (Φ), and the inter-ring dihedral angle θ. Interestingly, the inclusion of dispersion interactions leads to a change in the helical symmetry. Thus, HF calculations predict a helical turn with 6 repeating units, whereas it increases to 7 repeating units per turn when dispersion interactions are

Properties of an Optically Active Polythiophene considered. Furthermore, moderate variations (∼10%) are observed for both the pitch and inter-ring dihedral angle θ, with larger increments being detected for the internal diameter Φ. The sg+-sg- ring is favored with respect to the all-sg+ helix by 1.5 kcal/mol in the gas phase, and subsequent reoptimizations in solution at the PCM-HF/6-31G(d,p) level increase this free energy gap to 2.4 and 2.5 kcal/mol in chloroform and acetonitrile, respectively. Similarly, previous quantum mechanical calculations at the semiempirical level on the helical conformations of polythiophene and their derivatives indicated that the stability of the coil structure increases with the size of side groups.41 Induced CD was experimentally detected for 8-EOPT in mixtures of chloroform and poor solvents,14 the induced CD intensities increasing with time. It is worth noting that the sg+sg- model, which is the most stable in the absence of external forces (gas-phase) and in solution, is a good candidate to form intermolecular π-stacking aggregates because of the planarity with a semicircle shape. In contrast, the stability of the all-sg+ model, which already corresponds to a helical structure, decreases with the polarity of the solvent. Furthermore, the later model, which is more suitable for the PEOPT, does not fit the experimental results obtained for the octamer, i.e., the chirality increases with the concentration of poor solvents. Electronic Properties. The electronic properties of n-EOPT oligomers with n ) 2, 3, 4, 5, 6, and 8 were calculated considering four different models, which were constructed by using H-T linkages. These were the following: (i) a structure with all the inter-ring dihedral angles θ fixed at 180° (all-anti model); (ii) a structure with all the inter-ring dihedral angles θ fixed at 0° (all-syn model); (iii) the all-sg+ model; and (iv) the sg+-sg- model. The geometries of these structures were optimized partially (all-anti and all-syn models) or completely (all-sg+ and sg+-sg-) at the HF/6-31G(d,p) level. To obtain accurate estimations of the εg and IP, single point calculations at the B3PW91/6-31G(d,p) level were performed on the optimized geometries of the four models. Thus, recent studies indicated that the approach based on the use of different quantum mechanical methods for geometry optimization and for properties calculation produces reliable results.21,25-27,42 Figure 6 shows the linear behavior (correlation coefficients r > 0.99) for the variation of the calculated εg and IP with the inverse chain length (1/n) for the four models considered. Linear regression analyses, which are also displayed in Figure 6, allowed extrapolate εg and IP values for an infinite chain of PEOPT. Table 2 compares the predicted and experimental εg and IP values for n-EOPT (n ) 4, 6, and 8) and PEOPT (n ) ∞). The experimental optical band gap values εg have been estimated from the reported UV-vis spectra in chloroform solution,14 by analyzing the absorption edge and assuming a direct transition. As can be seen, the calculated electronic properties depend significantly on the backbone conformation. Thus, the loss of the planarity produces a significant increase in both the εg and IP, the maximum increments being of ∼1.4 and ∼1 eV, respectively. Both the large size of the substituents and the π-stacking interactions between the aromatic side groups of adjacent repeating units favor the syn-gauche arrangements, increasing the lowest transition energy in detriment of the optical and electrical properties. A similar behavior was recently reported for a polythiophene derivative bearing bulky side groups,28 in which the syn-gauche arrangement originated by the steric interactions between the substituents increased significantly the εg and IP values with respect to the all-anti and all-syn conformations.

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Figure 6. Variation of the (a) εg (in eV) and the (b) IP (in eV) against 1/n, where n is the number of repeating units for the all-anti (gray diamonds), all-syn (empty triangles), all-sg+ (black squares), and sg+sg- (empty squares) models. Lines correspond to the linear regressions, which allowed the results to be extrapolated to infinite polymer chains (see Table 1).

TABLE 3: Average Values of the Interpitch Distance (Rp, in Å), Internal Diameter of the Helical Turn Projected over the Perpendicular Plane to the Helical Axis (Φ, in Å), and the Inter-Ring Dihedral Angle (θ, in deg) Calculated for the 8-EOPT Oligomer with HF and Several DFT Methods Combined with the 6-31G(d,p) Basis Set HF ωB97X-D M06-2X M05-2X

Rp

Φ

θ

20.8 23.6 22.9 22.4

1.3 2.0 2.4 2.8

54.6 48.9 46.3 44.6

Comparison of the εg values displayed in Table 2 for n-EOPT oligomers and PEOPT indicates that, in general, the best agreement between the experimental and theoretical estimations corresponds to the planar models, which are expected to form aggregates easily when the polarity of the solvent increases. Results displayed in Table 2 allow a clear relationship between the conformation and εg to be derived. Specifically, in the modeled structures εg grows with the deviation from planarity: + + εgall-syn < εgall-anti < εgsg -sg < εgall-sg . Although this is an expected behavior, the enlargement of εg is larger for the systems reported in this work than those reported for polythiophenes with conventional substitutents.25,26 For an infinite chain (PEOPT) the difference between the experimental and the theoretical εg values is significantly smaller for the all-syn and all-anti models (0.14 and 0.20 eV, respectively) than for the all-sg+ one (1.52 eV). Regarding the sg+-sg- model, the εg is overestimated by 1.04 eV with respect to the experimental value determined in solution. This is a reasonable difference taking into account that DFT calculations were performed neglecting both the influence of the environment and excited states. Moreover, different conformational states (for both the backbone and the side groups) are expected to be involved in a realistic polymer chain, especially in solution.

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Conclusions The conformational properties of n-EOPT with n ranging from 1 to 8 have been examined by using ab initio quantum mechanical calculations. Specifically, systematic conformational analyses have been performed for 1-EOPT and 2-EOPT, whereas several idealized structural models have been considered for larger oligomers. Results indicate that the 2-EOPT4,4′ isomer is 2.5 and 4.7 kcal/mol more stable than the 2-EOPT3,3′ and 2-EOPT3,4′ ones, respectively. Interestingly, the two latter isomers tend to adopt a syn-gauche conformation, the phenyl rings of the adjacent monomers adopting a T-shaped and an off-centered parallel displaced stacking alignment, respectively. These interaction patterns become one of the most important stabilizing factors of the structural models proposed for the larger oligomers and the polymer. On the other hand, a PMF has been computed as a function of the inter-ring dihedral angle θ for each of the three 2-EOPT isomers. Calculations show how the bulky side groups adapt their arrangement to the θ values. Two possible models have been proposed for 8-EOPT: the sg+-sg- and the all-sg+, which correspond to a planar ring structure and a helix with six repeating units per turn, respectively. The former model is 1.5 kcal/mol more stable than the latter one in the gas phase, the energy difference increasing to 2.4 and 2.5 kcal/mol in chloroform and acetonitrile solution, respectively. The sg+-sg- model is a good candidate for the formation of aggregates stabilized by intermolecular π-stacking interactions, which is in agreement with the experimental observations reported for 8-EOPT. However, this planar model is not possible for the polymer because of the ring shape adopted by the backbone, a helical arrangement being the most appropriated in this case. Calculation of the electronic properties on idealized oligomers formed by H-T linkages revealed a strong dependence of both the εg and the IP on the backbone conformation. In spite of the approximations introduced to model PEOPT, the electronic properties predicted for the polymer are in good agreement with the experimental estimation. Acknowledgment. This work has been supported by MICINN and FEDER (Grant MAT2009-09138), and by the Generalitat de Catalunya (research group 2009 SGR 925 and XRQTC). The authors are indebted with the “Centre de Supercomputacio´ de Catalunya” (CESCA) for the computational resources provided. Support for the research of C.A. was received through the prize “ICREA Academia” for excellence in research funded by the Generalitat de Catalunya. References and Notes (1) Roncali, J. Chem. ReV. 1997, 97, 173–206. (2) Skotheim, T. A.; Elsenbaumer, R. L.; Reynolds, J. R. Handbook of conducting polymers; Marcel Dekker: New York, 1998. (3) Kline, R. J.; McGehee, M. D. Polym. ReV. 2006, 46, 27–45. (4) Langeveld-Voss, B. M. W.; Janssen, R. A. J.; Meijer, E. W. J. Mol. Struct. 2000, 521, 285–301. (5) Bao, Z.; Lovinger, A. J. Chem. Mater. 1999, 11, 2607–2612. (6) Pu, L. Acta Polym. 1997, 48, 116–141. (7) Bouman, M. M.; Havinga, E. E.; Janssen, R. A. J.; Meijer, E. W. Mol. Cryst. Liq. Cryst. 1994, 256, 439–448. (8) Goto, H.; Yashima, E.; Okamoto, Y. Chirality 2000, 12, 396–399. (9) Yashima, E.; Goto, H.; Okamoto, Y. Macromolecules 1999, 32, 7942–7945.

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