1524
J. Phys. Chem. 1996, 100, 1524-1529
π Conjugation in 2,2′-Bithiophene and Its Dimethyl Derivatives: Model Compounds of Organic Conducting Polymers Based on Thiophene Rings Carlos Alema´ n*,† and Luis Julia‡ Departament d’Enginyeria Quı´mica, E.T.S.I.I.B., UniVersitat Polte` cnica de Catalunya, Diagonal 647, Barcelona 08028, Spain, and Departament de Materials Orga` nics Halogenats, Centre d’InVestigacio´ i DesenVolupament (CSIC), Jordi Girona 18-26, Barcelona 08034, Spain ReceiVed: June 9, 1995; In Final Form: August 28, 1995X
Conformational properties of 2,2′-bithiophene and its 3,3′-, 4,4′-, and 5,5′-dimethyl derivatives have been investigated by means of quantum mechanical methods. Computations were performed at the ab initio HF/ 3-21G, HF/6-31G*, HF-6-311G**, and MP2/6-31G levels. Results indicate that 4,4′- and 5,5′-dimethyl2,2′-bithienyl behave similarly to the unsubstituted compound. Thus, two minimum energy conformations were found for each compound which correspond to the anti-gauche and the syn-gauche, the latter being always less stable than the former. On the contrary, the preferences found for 3,3′-dimethyl-2,2′-bithienyl were drastically different, giving a unique energy minimum around the gauche-gauche conformation. This must be attributed to the strong repulsive interactions originated by the methyl substituents around the anti and syn conformations. Flexible geometry optimizations provided the torsional potentials for the four compounds. The barriers to internal rotation were analyzed in terms of the conjugative and nonbonded interactions between the rings.
Introduction Organic conducting polymers are the subject of a major research activity.1 Among these, polyheterocycles have attracted much attention because of a nondegenerate ground state and a possibility of nonlinear excitations such as polarons (radical cations) and bipolarons (dications).2-5 A characteristic usually associated with these compounds is the planarity, which favors a maximum overlap between the π atomic orbitals (π conjugation). The extent of conjugation in these polymers determines their utility, and the defects along the backbone diminish their charge carrier mobility. In particular, we are interested in polymers containing sulfur atoms, which play an important key role in partially connecting the π system of consecutive rings and allowing for delocalization of the electronic excitations.6,7 Thus, during the last years we have carried out a systematic effort aimed to investigate the electronic and geometrical properties of the poly(thiophene)s8-10 and poly(thiapentacene)s11 constituent oligomers. The influence of the existence of a torsion angle along the chains on the electronic and geometric structures of the conjugated polymers based on aromatic rings is very important. Thus, of the many possible types of defects present in conjugated polymers, the rotational defects are the most abundant ones for systems like poly(thiophene)s. The rotational defects produce “bends” and “kinks” along the polymer backbone which interrupt and weaken the extent of π conjugation in a given polymer chain. The incorporation of the rotational defects into the polymer is therefore determined, at least in part, by the rotational freedom exhibited by the constituent oligomers. On the other hand, the presence of substituents can cause a departure from planarity in polyheterocycles. Indeed, this feature has been recently demonstrated in the case of the pyrrole polymers by X-ray diffraction experiments on single crystals of the pyrrole oligomers.12 Furthermore, there is experimental evidence that * To whom all correspondence should be sent. † Universitat Polte ` cnica. ‡ Centre d’Investigacio ´ i Desenvolupament. X Abstract published in AdVance ACS Abstracts, December 15, 1995.
0022-3654/96/20100-1524$12.00/0
the substitution pattern of the substituted poly(thiophene)s controls the degree of π-π conjugation between adjacent rings and hence the electrical and optical properties of the polymers.13,14 To understand the conformational preferences in poly(thiophene)s, a detailed structure examination of the constituent oligomers has been performed in some cases. For instance, the structure of the 2,2′-bithiophene, which may be envisaged as a simple model of poly(thiophene), is well-known in the vapor phase15 and in the crystal.16 In the vapor phase, the two rings of the 2,2′-bithiophene are nonplanar, with a torsional angle of 146°, whereas a planar arrangement is found in the crystal, with the two rings in the anti conformation. On the other hand, NMR spectroscopy experiments show that both the syn and anti conformations exist at room temperature.17 The energy difference between these two conformers was estimated to be around 0.2 kcal/mol. For larger oligomers, as well as for their alkylsubstituted derivatives, the crystal structure data show an allanti conformation,9,18-22 whereas in chloroform an anti-gauche conformation is found, which reduces the steric interactions.22,23 However, in spite of their interest, the characterization of the torsional barrier in poly(thiophene)s is far from satisfactory. Theoretical calculations can, in principle, provide a detailed description of the whole torsional potential. The only limitation to their systematic use is the definition of a reliable level of sophistication. For the 2,2′-bithiophene, the molecular structure and the torsional potentials have been studied by several authors using the minimal basis set STO-3G.24 Kofranek et al. calculated the torsional potential for this compound at the SCF level using the MIDI-4 basis set for carbon and a MIDI-4* for the sulfur atoms.25 The authors found a global anti-gauche minimum at a torsional angle close to 150°, which is in good agreement with the gas-phase electron diffraction results.15 As in other heteroatomic rings linked together by an essentially single bond,26 a second local minimum, syn-gauche, occurs around a torsional angle of about 40°. This second minimum was only 0.5 kcal/mol less stable than the global minimum. Furthermore, the authors characterized three stationary points © 1996 American Chemical Society
π Conjugation in 2,2′-Bithiophene
J. Phys. Chem., Vol. 100, No. 5, 1996 1525
by full geometry optimization and by evaluation of their vibrational frequencies. More recently, Quattrocchi et al.27 investigated the conformational behavior of the 2,2′-bithiophene using a DZP basis set. The authors carried out a geometry optimization of the minimum energy conformations. Nevertheless, the energies of the torsion around the inter-ring single bond were determined within the rigid-rotor approximation. In a very recent work, Ortiz et al.28 studied the internal rotation potential of 2,2′-bithiophene at the MP2/6-31G* level. The authors found an energy barrrier of 1.5 kcal/mol between the anti-gauche and syn-gauche conformations. In the remaining theoretical investigations on this topic, semiempirical29 and force-field30 methodologies were applied. The purpose of this work is to make a quantum mechanical study on the structure and torsional barriers of the 2,2′bithiophene (1) and its dimethyl derivatives. We initiated our work with a systematic study of the 2,2′-bithiophene using both semiempirical (AM1, ref 31; MNDO, ref 32) and ab initio (up to 6-311G**, ref 33) methods with inclusion of the MøllerPlesset electron correlation effects34 (with 6-31G, ref 35). The rotational barriers and the minima structures are compared with the experimental results. The results indicate that HartreeFock (HF) calculations with the 6-31G*36 basis set are accurate enough, but smaller basis sets or semiempirical calculations lead to poor results. Then, the barriers to internal rotation and the equilibrium structures for 3,3′- (2); 4,4′- (3), and 5,5′-dimethyl2,2′-bithienyl (4) were calculated using the 6-31G* basis set. Finally, the conformational behavior of the different compounds have been analyzed in terms of the conjugative and nonbonded interactions between the two rings.
Figure 1. Ab initio (HF/3-21G, HF/6-31G*, and HF/6-311G**) rotational barriers for 2,2′-bithiophene (1).
Ab initio and semiempirical calculations were performed using the Gaussian 9237 and MOPAC38 computer programs, respectively. The dependence of the results on the method used was investigated for 1. Thus, the geometry optimizations of the equilibrium structures and all the points along the curve describing the torsional potential were performed at the semiempirical AM131 and MNDO32 and the ab initio Hartree-Fock (HF) 3-21G39 and 6-31G*36 levels. In addition, single-point calculations were performed with the 6-311G**33 basis set using the HF/6-31G* geometries. The Moller-Plesset perturbation treatment34 was used to compute the electron correlation corrections to the energy from the structures optimized at the HF/6-31G* level. Since the MP2 computations at the 6-31G* level are computationally prohibitive for us, we evaluate the electron correlation effects using the 6-31G basis set. Indeed, previous comparisons between the MP2/6-31G* and MP2/631G relative energies using the HF/6-31G* geometries suggest that the latter reasonably represents the effect of the electron correlation contribution.40,41 The rotational profiles and the equilibrium structures for 2, 3, and 4 were computed at the HF/ 6-31G* level. All the computations were performed on the IBM/3090 and the CRAY-YMP at the Centre de Supercomputacio´ de Catalunya (CESCA). Results and Discussion
Methods The rotational profiles for 1, 2, 3, and 4 were computed spanning the torsional angle (θ) between the planes of the two rings in steps of 30°. A flexible rotor approximation was used for all the compounds investigated. Thus, the structure in each point of the path was obtained from geometry optimization at a fixed θ value. The equilibrium geometries of each compound were fully optimized using a gradient method. All the minimum energy structures were characterized as such by calculating and diagonalizing the Hessian matrix and ensuring that they do not have any negative eigenvalue.
Rotational Barriers. The rotational profiles of 1 obtained from ab initio calculations are represented in Figure 1. The energies and torsional angles of the minima and saddle points obtained by the different basis sets are compiled in Table 1. Comparison between the 3-21G curve and those obtained with larger basis sets indicates that the first does not provide a good representation of the rotational barrier for this compound. Thus, the energy barrier seems to be largely overestimated and the global minimum appears in the anti conformation (θ ) 180°), in poor agreement with the experimental anti-gauche conformation (θ ) 146°). This defficiency was also detected by Quatrocchi et al.,28 who found the anti as the lowest energy conformation with the 3-21G basis set. However, better agreement with the experimental gas-phase data is obtained
TABLE 1: Energiesa (in kcal/mol) and Torsional Anglesb (θ) (in deg) of 2,2′-Bithiophene (1) Obtained by the Different Methods HF/3-21G//HF/321G HF/6-31G*//HF/6-31G* HF/6-311G**//HF/6-31G* HF/6-31G//HF/6-31G* MP2/6-31G//HF/6-31G* AM1//AM1
syn
syn-gauche
gauche-gauche
anti-gauche
anti
1.96 1.93 1.97 2.17 2.04 0.4
1.30 (θ ) 37.6) 0.68 (θ ) 42.2) 0.65 1.28 0.47 0.2 (θ ) 34.61)
2.57 1.69 1.36 2.53 1.33 0.4
0.0 (θ ) 147.9) 0.0 0.28 0.0 0.0 (θ ) 152.58)
0.00 0.37 0.48 0.0 0.58 0.1
Level of energy calculation // level of geometry optimization. b Torsional angle between the planes of the two rings. Syn, θ ) 0°; gauchegauche barrier, θ ) 90°; anti, θ ) 180°. a
1526 J. Phys. Chem., Vol. 100, No. 5, 1996
Figure 2. Comparison between ab initio HF/6-31G* and semiempirical (AM1 and MNDO) rotational barriers for 2,2′-bithiophene (1).
when polarization functions are included in heavy atoms. Thus, the global minimum is located around 148° at the HF/6-31G* level. This twisted conformation is found to be more stable than the anti conformation by 0.4 kcal/mol. Furthermore, the rotational barrier is 0.9 kcal/mol lower than that computed at the HF/3-21G level. The small difference found between the 6-31G*and the 6-311G** curves indicates that the first is sufficiently accurate in the case of 1. On the other hand, a second local minimum, syn-gauche, occurs around a torsional angle of about 40° at both the HF/3-21G and the HF/6-31G* levels. This second minimum lies about 1.3 and 0.7 kcal/mol above the anti-gauche conformation at the HF/3-21G and HF/ 6-31G* levels, respectively. The 6-311G** basis set provides the syn-gauche minimum at around 50°. This difference must be attributed to the fact that molecular geometries were not optimized using this basis set. Figure 1 shows that the twowell defined minima are separated by a barrier which corresponds to the gauche-gauche (θ ) 90°) conformation. This is unfavored with respect to the anti-gauche conformation by 1.7 and 1.4 kcal/mol at the HF/6-31G* and HF/6-311G** levels, respectively. This small energy barrier is fully consistent with the NMR data which indicate that both the anti and syn conformations can coexist at room temperature.17 The energies of the HF/6-31G* equilibrium structures were computed at both the HF/6-31G and MP2/6-31G levels. The results are also shown in Table 1. The first method gives results very similar to those obtained at the HF/3-21G level, whereas MP2 corrections provide reasonable barriers to rotation. Figure 2 shows the rotational profiles of 1 computed from semiempirical AM1 and MNDO methods. To compare profiles, we have also included the ab initio HF/6-31G* curve. As can be noted, the results provided by AM1 are in qualitative agreement with the HF/6-31G* data, although the calculated conformational energies are largely underestimated, as can be observed from Table 1. For instance, the AM1 barrier to rotation is only 0.4 kcal/mol. On the other hand, the use of the MNDO Hamiltonian leads to an erroneous rotational profile, indicating that the conformational behavior of 1 is not well reproduced by this semiempirical method. These results state that ab initio HF calculations using basis sets without polarization functions are not able to represent the conformational preferences of 1 and overestimate the barriers
Alema´n and Julia
Figure 3. Ab initio HF/6-31G* rotational barriers for 2,2′-bithiophene (1); and 3,3′- (2); 4,4′- (3); and 5,5′-dimethyl-2,2′-bithienyl (4).
by 50-90% with respect to those obtained at higher levels of theory. The similarity between the results obtained at the HF/ 3-21G//HF/3-21G and HF/6-31G//HF/6-31G* levels suggests that the failures are independent of the method used in the geometry optimizations, and therefore they are inherent to the energy evaluations. Furthermore, our MP2/6-31G results are very similar to those obtained by Ortiz et al.28 at the MP2/631G* level, indicating that either the inclusion of electron correltion or the use of a basis set with polarization functions is required to represent correctly the gas-phase rotation around the planes of the two rings. On the other hand, the semiempirical data are in poor agreement with the present ab initio results, most probably because these methods are based on a minimal basis set. Comparison between the different methods indicates that the HF/6-31G* is the minimum level necessary to study the conformational preferences of bithiophenes. The evolution of the HF/6-31G* energy for the dimethyl derivatives 2, 3, and 4 as a function of the torsion angle between the aromatic rings is displayed in Figure 3. To have a better understanding of the effects introduced by the methyl substituents, we have included the curve of 1 computed at the same level of theory, which is taken as a reference point. The relative energies and torsional angles of the minima and saddle points for the three compounds are given in Table 2. The crystal structure of 4 was recently investigated,9 showing that the two thienyl rings are trans coplanar in the solid state, in good agreement with that reported for 1. Accordingly, a similar behavior would be also expected for both compounds in the gas phase. The most stable conformations for 3 and 4 correspond to the anti-gauche, which is located around θ ≈ 150° in both compounds. The perpendicular conformations for 3 and 4 are 1.8 and 1.9 kcal/mol higher than the global minimum, respectively. These values are fully consistent with that of 1 at the same level of theory (1.7 kcal/mol). A second minimum for 3 and 4 is calculated to arise when the torsional angle θ is 48° and 42°, respectively. The syn-gauche structure is only 0.7 kcal/mol less favored than the anti-gauche for 4, whereas an energy difference of 0.9 kcal/mol appears for 3, due to the proximity of the methyl groups. As can be seen in Table 1, the energy difference between the anti-gauche and syngauche conformations for 1 is 0.7 kcal/mol at the HF/6-31G*
TABLE 2: Energies (in kcal/mol) and Torsional Anglesa (θ) (in deg) of the 3,3′- (2); 4,4′- (3); and 5,5′-Dimethyl-2,2′-bithienyl (4) Computed at the HF/6-31G*//HF/6-31G*b compd
syn
syn-gauche
gauche-gauche
anti-gauche
anti
2 3 4
12.0 1.96 2.96
0.92 (θ ) 38.7) 0.72 (θ ) 42.1)
0.0 (θ ) 84.3) 1.89 1.76
0.0 (θ ) 149.5) 0.0 (θ ) 150.0)
6.00 0.32 1.32
Torsional angle between the planes of the two rings. Syn, θ ) 0°; gauche-gauche barrier, θ ) 90°; anti, θ ) 180°. b Level of energy calculation // level of geometry optimization. a
π Conjugation in 2,2′-Bithiophene
J. Phys. Chem., Vol. 100, No. 5, 1996 1527
TABLE 3: HF/6-31G* Optimized Geometriesa of 2,2′-Bithiophene (1) in the Equilibrium Structures parameter
syn
syn-gauche
anti-gauche
anti
C2-C3 C3-C4 C4-C5 C5-S C2-C2′ C3-H C4-H C5-H
1.353 1.432 1.344 1.723 1.467 1.073 1.073 1.071
1.351 1.433 1.345 1.724 1.466 1.073 1.073 1.071
1.351 1.434 1.344 1.725 1.465 1.073 1.073 1.071
1.352 1.433 1.343 1.726 1.464 1.073 1.073 1.071
∠C2-C3-C4 ∠C3-C4-C5 ∠C4-C5-S ∠C3-C2-C2′ ∠H-C3-C4 ∠H-C4-C5 ∠H-C5-S
113.4 112.7 111.7 127.3 123.1 123.8 120.2
113.2 112.6 111.9 127.0 123.8 123.7 120.2
113.2 112.6 111.8 128.3 123.5 123.8 120.3
113.4 112.6 111.8 128.3 123.1 123.8 120.1
θ
0.00
42.2
142.9
180.0
a
Distances in angstroms. Angles and q in degrees.
level. These calculations establish that the presence of the methyl groups at positions 5,5′ does not have any relevant effect on the conformational properties of bithiophene. On the other hand, substitution at 4,4′ provides slight repulsive steric interactions between the methyl groups on the syn region of the potential energy surface, which gives a higher relative energy for the syn-gauche conformation as the unique difference with respect to 1. This is clearly shown in Figure 3, where the three compounds display very similar energy profiles. The case of 2 appears very different. The most stable conformation is the gauche-gauche one, which corresponds to a torsional angle θ of 84.3°. The syn and anti conformations are 12.0 and 6.0 kcal/mol less stable than the gauche-gauche, respectively. The main reason for these conformational preferences has to be found in the repulsive interactions originated by the methyl groups. Thus, in the syn conformation strong contacts appear between the two methyl groups, whereas in the anti conformation electrostatic interactions exist between the lone pairs of the sulfur atom in one ring and the methyl group attached to the other ring. These interactions are removed when the θ angle increases to 84.3°. It is difficult to predict the conformation of 2 in the solid state. Crystal packing effects usually result in an increase of the torsion angle up to 180°. However, in the case of 2, the strong repulsions between the methyl groups and the sulfur atoms make it difficult to reach the anti conformation. Equilibrium Structures. Table 3 shows the computed geometries for the HF/6-31G* equilibrium structures of 1: syn, syn-gauche, anti-gauche, and anti. The most streaking feature is that geometric parameters are very similar for these four stationary points. For instance, the bond lengths for the syngauche and anti-gauche minima differ by only 0.001 Å. A comparison with the crystallographic bond lengths and bond angles of alkyl-substituted bithiophenes, determined by X-ray diffraction, indicates a good agreement for the anti-planar conformation. Similar results were also obtained for 2, 3, and 4. Table 4 shows the HF/6-31G* optimized geometry of the lowest energy minimum for the three dimethyl derivatives. The dependence of the bond length between the rings and the torsion angle for 1 is shown in Figure 4. As can be noted, the most stable conformational zone (θ ≈ 150°-180°) leads to the shortest inter-ring bond. A similar finding was reported earlier by Bredas and co-workers24d at the HF/STO-3G level. The X-ray diffraction data indicate a value of 1.48 Å,15 which is about 1.15% larger than our theoretical one (1.463 Å). It is
TABLE 4: HF/6-31G* Optimized Geometriesa of 3,3′- (2); 4,4′- (3); and 5,5′-Dimethyl-2,2′-bithienyl in the Lowest Energy Conformers parameter
3,3′-
4,4′-
5,5′-
C2-C3 C3-C4 C4-C5 C5-S C2-C2′ C3-H C3-C(methyl) C4-H C4-C(methyl) C5-H C5-C(methyl)
1.343 1.442 1.352 1.722 1.476
1.345 1.442 1.350 1.728 1.465 1.075
1.345 1.435 1.350 1.738 1.463 1.074
∠C2-C3-C4 ∠C3-C4-C5 ∠C4-C5-S ∠C3-C2-C2′ ∠H-C3-C4 ∠C(methyl)-C3-C4 ∠H-C4-C5 ∠C(methyl)-C4-C5 ∠H-C5-S ∠C(methyl)-C5-S
112.0 113.3 111.8 128.4
120.6
125.3 120.0
θ
84.3
149.5
a
1.505 1.074 1.071
1.074 1.504 1.071 1.500 113.9 112.6 111.5 128.2 123.0
122.3 123.6
113.3 113.6 110.6 128.6 123.4 123.1 121.1 150.8
Distances in angstroms. Angles and θ in degrees.
Figure 4. Evolution as a function of the torsional angle between the rings (θ) of the HF/6-31G* inter-ring bond length for 2,2′-bithiophene (1); and 3,3′- (2); 4,4′- (3); and 5,5′-dimethyl-2,2′-bithienyl (4).
well-known that correlation effects are necessary to give bond lengths and angles closest to the experimental values.42,43 On the contrary, monodeterminantal wave functions tend to decrease the equilibrium bond lengths when the size of the basis set increases. For instance, Bredas and co-workers24d found a bond length between the rings of 1.481 Å at the HF/STO-3G level, which is closer to the experimental data than our HF/6-31G* value. Figure 4 also displays the dependence of the bond length between the rings and the torsional angle for 2, 3, and 4. The results for 3 and 4 are similar to those provided for 1, the shortest distance being obtained in the anti conformation. Thus, the π contributions to the inter-ring bond order do not alter significantly by the effect of the 4,4′- and 5,5′-dimethyl substitution relative to the 1 case. On the other hand, the inter-ring bond elongates by only 0.012 Å in the three compounds when the torsional angle goes toward the gauche-gauche conformation. This short variation suggests that the inter-ring bond has a small double-bond character. Indeed, Bredas and co-workers24d estimated that the π contribution represent only about 6.4% of the total inter-ring bond order in the case of 1. The present results reveal that the π contributions remain small also for 3 and 4.
1528 J. Phys. Chem., Vol. 100, No. 5, 1996
Alema´n and Julia
TABLE 5: Torsional Potentials (in kcal/mol) of 2,2’-Bithiophene (1) Obtained by Different Basis sets V1 V2 V3 V6
HF/3-21G
HF/6-31G*
HF/6-311G**
1.8 -0.8 1.0 0.4
1.3 -0.2 0.4 0.3
1.1 -0.0 0.4 0.2
V1 V2 V3 V6
Regarding 2, the situation appears to be different, since the shortest distance was found near the gauche-gauche conformation, which is close to its energy minimum. As can be noted, the inter-ring bond length for 2 is larger in all the rotational paths than for 1, 3, and 4, suggesting that the π contributions are lower than in such cases. Note that the decrease of π contributions to the inter-ring bond order is in fair agreement with the perpendicular position between the rings predicted for the energy minimum, which precludes the loss of π interactions. Energy Contributions. Barriers in compounds of this type are frequently examined by their decomposition into a truncated Fourier expansion:
Vφ ) ∑Vn/2[1 + cos(nφ - γn)]
TABLE 6: Torsional Potentials (in kcal/mol) of 3,3′- (2); 4,4′- (3); and 5,5′-Dimethyl-2,2′-bithienyl (4) Obtained by HF/6-31G* Calculations
(1)
where Vn is the torsional energy barrier of the n-Fourier term for the rotation around the bond, γn is the phase angle of the n-Fourier term, which determines the torsion angle of the maximum energy, and φ is the torsion angle. To simplify the analysis, it is usual to consider all the phase angles (γn) equal to 0 and perform the fitting between the quantum mechanical and torsional energies. The sign of each Vn parameter indicates the phase angle of the n-Fourier term.44 If Vn is positive, the phase angle is 0°, and if it is negative, the phase angle is 180°. Several studies have shown that three terms are sufficient for a reliable fit: 1-fold, 2-fold, and 3-fold.45,46 We have included also a 6-fold term in order to give the same importance to the even and odd terms. It may be expected that the conformational behavior of bithiophene-like systems is governed by two factors: (i) the π interaction between the two rings, which tends to keep the molecule planar; and (ii) the nonbonded interactions between the groups attached to the different rings. It is well-known that the conjugative interactions only contribute to the 2-fold term in the Fourier expansion, whereas the nonbonded interactions contribute to all terms. This observation permits the comparison of the conformational characteristics obtained for the different compounds investigated in terms of the energy contributions. The four-term Fourier expansions of 1 are collected in Table 5. As can be seen from the comparison of the 2-fold term for the different computational methods, the HF/3-21G basis set overestimates the conjugative interactions. Furthermore, the nonbonded interactions were also overestimated by the smallest split valence basis set, although less than the conjugative interactions; that is, the HF/3-21G torsional energy barriers are overestimated around 46% (V1), 223% (V2), 108% (V3), and 40% (V6) with respect to the HF/6-31G* results. As a consequence, the HF/3-21G torsional potential of 1 is biased in favor of the planar conformation. This fact makes clear that the HF/3-21G global minimum is located at the anti conformation, whereas the HF/6-31G* is found around the anti-gauche conformation. On the other hand, the HF/6-311G** results are similar to the HF/6-31G* ones, with the exception of the 2-fold term, which is underestimated. However, this must be attributed to the fact that the molecular geometries were not optimized within this computational method. The four-term Fourier expansions of 2, 3, and 4 computed at the HF/6-31G* level are given in Table 6. In general, the more
2
3
4
0.7 6.1 0.6 0.2
1.4 -0.4 0.6 0.3
1.4 -0.3 0.7 0.3
striking difference between 1 and its methyl derivatives is the enhancement of the Vn terms for the latter. The V2 terms suggest that the stability of the planar conformation is similar in 1, 3, and 4. Thus, the three compounds display similar conjugative interactions, whereas the steric and nonbonded interactions are greater in 3 and 4 than in 1. On the other hand, 2 presents very different torsional energy terms. As can be noted, V2 is positive, indicating that the phase angle is 0°. Consequently, the energy minima must be found in the perpendicular conformations (θ ≈ 90° and -90°) rather than in the planar conformations (θ ≈ 0° and 180°). Of course, the high value of V2 is not due to the π interaction between the two rings, which will tend to keep the molecule planar rather than perpendicular. This value must be attributed to the steric and electrostatic interactions that in the present case have a greater contribution to the V2 term than to the V1, V3, and V6. Synopsis Summarizing, the barriers to internal rotation about the bond between the planes of the two rings have been calculated for 1 and its dimethyl derivatives 2, 3, and 4 using ab initio quantum mechanical calculations. With 1 the calculated barrier is strongly dependent on the basis set, indicating that the HF/631G* is the minimum level necessary to study the conformational preferences of the bithiophenes. Thus, both the semiempirical and ab initio calculations using basis sets without polarization functions were not able to represent correctly the conformational preferences of 1. The conformational preferences of 3 and 4 were similar to that of 1. Two minima were found for each compound, the anti-gauche and syn-gauche conformations, the latter being less favored than the former. Furthermore, the energy barriers calculated at the HF/6-31G* level appear also to be similar to that of 1. The analysis of the components of the barriers reveals that they have the same origin as that of 1. On the contrary, the HF/6-31G* calculations on 2 indicate a preference for the gauche-gauche conformation, the nonbonded interactions being responsible of this anomalous behavior. Acknowledgment. The authors are grateful to the Centre de Supercomputacio´ de Catalunya (CESCA) for financial support for supercomputer time. References and Notes (1) (a) Handbook of Conducting Polymers, Skotheim, T. J., Ed.; Marcel Dekker: New York, 1986; Vols. 1 and 2. (b) Proceedings of the International Conference on Science and Technology of Synthetic Metals (ICSM ’94), Seoul, Korea, 1994; published in Synth. Met. 1995, 69. (2) Frommer, J. E.; Chance, R. R. In Electrical and Electronic Properties of Polymers; A State-of-the-Art Compendium, Kroschwitz, J. I., Ed.; John Wiley: New York, 1988; p 56. (3) Fesser, K.; Bishop, A. R.; Campbel, D. K. Phys. ReV. B. 1983, 27, 4804. (4) Scott, J. C.; Bre´das, J. L.; Yakushi, K.; Pfluger, P.; Street, G. B. Synth. Met. 1984, 9, 165. (5) Bertho, D.; Jovanin, C.; Lussert, J. M. Phys. ReV. B 1988, 37, 4039. (6) Bre´das, J. L.; Chance, R. R.; Sibey, R.; Nicolas, G.; Durand, Ph. J. Chem. Phys. 1982, 77, 371. (7) Duke, C. B.; Paton, A.; Salaneck, W. R. Mol. Cryst. Liq. Cryst. 1982, 83, 177.
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