Ab Initio Determination of the Geometric Structure and Internal

Apr 1, 1995 - Marcos A. De Oliveira, Hélio A. Duarte, Jean-Michel Pernaut, and ... Nicolas DiCésare, Michel Belletête, Claudio Marrano, Mario Lecle...
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J. Phys. Chem. 1995, 99, 4955-4963

4955

Ab Initio Determination of the Geometric Structure and Internal Rotation Potential of 2,2'-Bithiophene Enrique Orti,* Pedro M. Viruela, JosC Shnchez-Marin, and F. Tomhs Departament de Quimica Fisica, Universitat de Valtncia, Doctor Moliner 50, E-46100 Burjassot, Valtncia, Spain Received: November 2, 1994; In Final Form: January 17, 1995@

We report a detailed ab initio study of the molecular structure and conformational behavior of 2,2'-bithiophene. Fully optimized torsional potentials keeping planar the thiophene rings are calculated at the HF/3-2 1G*, HF/6-31G*, and MP2/6-31G* computational levels. The optimized geometries are analyzed in terms of conjugative effects and nonbonding interactions and are compared with gas-phase and solid-state experimental data. The reliability of a recent electron diffraction determination of the molecular structure of 2,2'-bithiophene is discussed in light of MP2 calculations, which provide a more delocalized structure than HF calculations. Very flat 4-fold potentials where minima correspond to s-cis- and s-trans-gauche structures are obtained at both the HF and MP2 levels. The flatness of the potentials justifies the variety of conformations experimentally observed for thiophene oligomers. A torsional angle of about 147' is predicted at the HF level for the most stable s-trans-gauche conformer in agreement with electron diffraction data. The inclusion of the electron correlation at the MP2 level comparatively destabilizes the planar s-trans conformer and reduces the torsional angle for the s-trans-gauche minimum to 142.2'. Additional MP2 calculations using the 6-31G** basis set affect the relative conformational energies by less than 0.2 kJ/mol. The torsional potentials are finally analyzed in terms of a Fourier decomposition truncated to the sixth term.

Introduction a-Conjugated oligo- and polythiophenes are attractive materials for a variety of applications in electronics and optoelectronics.' The electrical conductivity of polythiophenes can be enhanced by oxidative doping, varying from the insulator to the metallic regime, ca. 10-2-103 S/cm.2 In the neutral state, they exhibit remarkable third-order nonlinear optical re~ponses.~ Oligothiophenes are being largely investigated because, conversely to polythiophenes which are obtained as highly amorphous nonhomogeneous materials, they can be synthesized as well-defined and easily processable compound^.^ They provide thus interesting models for understanding the structural and electronic peculiarities which control the charge transport and optical processes in p~lythiophenes.~ Their properties can in fact reach or even surpass those of the polymers, and oligothiophenes with well-defined chemical structure are used in applications such as field effect transistors and lightemitting diodes (LED).7 The molecular origin of the electrical and optical properties presented by polythiophenes and other polyconjugated materials requires the intramolecular delocalization of the n electrons along the conjugated chain. This delocalization depends on the extent of the overlapping between the pz orbitals of the carbon atoms in positions a and a' of adjacent thiophene rings and is therefore govemed by the internal rotation around the interannular single bonds. The degree of planarity directly determines the effective conjugation length as well as the width of the JG bands, including the optical band gap. The backbone conformation is in fact responsible of the thermochromism that polyalkylthiophenes exhibit in solutions and can be used to control both electrical and optical properties. For instance, the eIectroluminescence characteristics of thiophene polymers are designed by modulating the backbone c~nformation.~

* E-mail: @

[email protected].

Abstract published in Advance ACS Absrrucrs, March 1, 1995.

0022-3654/95/2099-4955$09.0010

s-trans

(Q=180°) Figure 1. Rotational isomerism and atom numbering of 2.2'bithiophene. 0 denotes the torsional angle formed by the planes of the thiophene rings.

The low crystallinity of p o l y t h i o p h e n e ~ ~prevents .~~ the determination of the backbone conformation and molecular structure of the chains, and appropriate oligothiophenes with well-defined structures are needed to obtain reliable structural models for the polymers. The conformational behavior of the dimer (2,2'-bithiophene, see Figure 1) has been widely investigated both experimentally11-23and t h e o r e t i ~ a l l y ~and ~ - ~can be used as a model to gain information about the conformation of longer polythiophene chains. In an early gas-phase electron diffraction study," the molecule of 2,2'-bithiophene was concluded to be in a s-trans-like conformation with a twist angle of about 146O, but an essentially free rotation within torsional angles from 95" to 146" was not excluded. In the solid state at 133 K, 2,2'-bithiophene was assigned to be in a planar s-trans conformation.l* In solution, a s-trans-like conformation with a torsional angle of 140"150" was proposed on the basis of dipole moment13 and molar Kerr constant14 measurements. The preference for a s-translike conformer was also suggested by photoelectron datal5 and UV ~ p e c t r a . ' ~NMR . ~ ~ data in liquid crystalline solvent^^^.^^ discarded the presence of one single conformation and suggested that 2,2'-bithiophene exists as an equilibrium between s-trans and s-cis rotamers, the s-trans being the more stable conformation (70 f 5%).19 A rotational barrier of 20 f 8 kJ/mol was estimated for the s-trans s-cis interconversi~n.~~ Two recent NMR studies have reinvestigated the distribution of conforma-

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0 1995 American Chemical Society

Orti et al.

4956 J. Phys. Chem., Vol. 99, No. 14, 1995

tions and orientations of 2,2'-bithiophene dissolved in liquid crystalline solvents.20s21They conclude that the conformation of the molecules is strongly coupled with their orientation in the solvent and propose a mixture of a s-cis-gauche conformer (8 = 24.2") and a s-trans planar conformer with larger population (61%) to explain the NMR data. The molecular conformation of 2,2'-bithiophene has been recently reinvestigated by gas-phase electron diffraction22and fluorescence spectra registered for bithiophene seeded into a supersonic helium expansion.23 The electron diffraction results show that 2,2'-bithiophene exists in two nonplanar conformations in the gas phase, s-cis-gauche and s-trans-gauche, with torsional angles of 36 f 5" and 148 f 3" and relative abundances of 44 f 4% and 56 f 4%, respectively.22 The energy difference between the two conformations calculated from their relative abundance at -100 "C is estimated to be of 0.75 kJ/mol with the s-trans-gauche conformation as the most stable. The fluorescence excitation spectrum of bithiophene has two components which are assigned to the s-trans and s-cis conformers present in the vapor.z3 Chadwick and Kohler determine an energy difference between the two conformations of 4.85 f 0.54 kJ/mol by measurement of how the relative weights of the two spectra depend on the reservoir temperature. The large discrepancy between the cis-trans energy difference estimated by electron diffraction (0.75 kJ/mo1)22and fluorescence data (4.85 f 0.54 k . l / m ~ l )is~ ~due to the different assumptions made in their evaluation since both studies obtain similar cisltrans ratios. To the best of our knowledge, detailed crystallographic structures have been obtained for t e r t h i ~ p h e n e3',4'-dibutyl,~~ 2,2':5',2''-terthi0phene,~ 3,4',4''-"metl1yl-2,2':5',2''-terthiophene~~ and several alkyl-substituted'tetrathiophenes.27~28Less detailed crystallographic data have been also reported for pentathiophenes and he~athiophenes.~~ These studies show the great "plasticity" of oligothiophenes and, by extension, of polythiophenes. The ring coplanarity in the solid state is characteristic of bithiopheneI2 and its derivative^.^^.^^ This coplanarity is not necessarily retained in oligothiophenes with a polymerization degree equal to three or more.24-29 For instance, unsubstituted terthiophene has dihedral angles between adjacent thiophene rings of 6"9°.24 The most recent studies on tetrathiophenes28and longer oligothiophenesZ9show that, although the trans arrangement between adjacent rings is the most commonly found, the cis arrangement is also present. Semiempirical quantum-chemical calculations fail in describing the conformational behavior of 22-bithiophene since they generally predict the planar s-cis and s-trans forms as the most stable conformation^.^^-^^ Only the semiempirical AM1 method provides internal rotation potentials in agreement with experimental e v i d e n ~ e . ~It ~however .~~ yields an energy difference of only 1.92 kJ/mol between the most stable s-trans-gauche conformer and the absolute maximum of the potential located around the perpendicular c~nformation.~'Ab initio calculations lead to the planar rotamers when using STO-3G minimal basis set with partially38-39or fully40 optimized geometries even if polarization d functions are included on sulfur atoms.39 Rotational barriers of 17.1 and 28.8 kJ/mol are predicted for the s-trans s-cis interconversion at STO-3G and STO-3G* levels, respectively, the planar s-trans conformer being the most stable by about 4 k.l/mol in both cases.39 Split-valence 3-21G calculations also give the planar forms as the most stable conformers and reduce the barrier height to 11.3 k J / m ~ l . ~To I our knowledge, Kofranek et al.42 reported the first ab initio calculations predicting the existence of s-cis- and s-transgauche minima. Using a split-valence MIDI-4 basis set with

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polarization functions on sulfur atoms, they obtain a rigid rotor potential for 2,2'- bithiophene in which the s-trans-gauche minimum with a twist angle of 150" is separated by a barrier of -8 kJ/mol from a second local minimum with a twist angle of -40". During the final stage of the calculations presented in this paper, new ab initio calculations on the conformational properties of 2,2'-bithiophene have been r e p ~ r t e d . ~ Samdal ~ , ~ ~ . et ~ a1.22employ standard 3-21G* and 6-31G* basfi sets to optimize the s-cis- and s-trans-gauche minima for which twist angles of 44.29" (44.02') and 146.25' (147.76') are respectively predicted at the 3-21G* (6-31G*) level. These authors provide a representation of the torsional potential of 2,2'-bithiophene, but they give no detail of how this potential is calculated. Distefano et al.43optimize the geometry of the planar s-trans conformer at the 3-21G* level and use this geometry to generate a rigid rotor potential. This potential contrasts with that presented by Samdal et a1.22in the relative energy of the planar s-cis conformer. Quattrocchi et al.44obtain twist angles of 32" and 149.5" for the s-cis- and s-trans-gauche minima with a double-zeta polarized basis set. They use the geometries optimized for these minima and that computed for the planar s-trans conformer to calculate a partially rigid torsional potential for bithiophene. All these s t ~ d i e s ~show ~ , ~that ~ -double-zeta ~ basis sets including polarization functions on sulfur atoms are the minimum requirement to obtain a qualitatively correct description of the conformational behavior of 2,2'-bithiophene. In spite of the extensive number of experimental and theoretical works on the conformational properties of 2,2'bithiophene, the internal rotational potential of this molecule has not been fully described. Experimental data mainly concern the structure and stability of the conformational minima, and little information about the potential energy function describing the internal rotation (barrier heights, energy maxima, relative stabilities) is available. On the other hand, theoretical calculations are rather limited since they are based on the use of rigid or partially optimized rotor potentials and are restricted to the Hartree-Fock (HF) level. To the best 6f our knowledge, electron correlation effects are only considered in the work by Quattrocchi et aLU where the two HF minima are recalculated with second-order MBller-Plesset (MP2) perturbation theory. The aim of this work is to provide a complete characterization of the internal rotation potential of 2,2'-bithiophene. Fully optimized ab initio torsional potentials are calculated at the HF level and including electron correlation effects by MP2 perturbation theory. Standard split-valence double-zeta plus polarization functions basis sets are used throughout the work. The potential energy function for the internal rotation is finally obtained by fitting the energies calculated for different conformers to a truncated Fourier expansion.

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Computational Procedure The calculations were performed on an IBM 9021/500-2VF computer and on IBM RS/6000 workstations of the University of Valkncia using GAUSSIAN 8845 and GAUSSIAN 9246 programs. To study the internal rotation, the torsional angle I3 was scanned in steps of 30" between 8 = 0" (s-cis conformer) and I3 = 180" (s-trans conformer). The geometries of the resulting conformers and those of the s-cis- and s-trans-gauche minima were optimized at the HF level with the 3-21G* (d functions on S)47 and 6-31G* (d functions on S and C)48basis sets. Electron correlation effects were studied by reoptimizing these geometries using MP2 perturbation and the 6-31G* basis set. The optimized MP2 geometries were finally recalculated at the MP2 level with the 6-31G** (d functions

Geometric Structure of 2,2'-Bithiophene on S and C and p functions on H) basis set.54 This level of theory is denoted MP2/6-31G**//MP2/6-3 1G*. The Berny analytical gradient method55was used for the optimizations. In the geometry optimization, the thiophene rings in 2,2'bithiophene were assumed to be planar. CzV, C2, and C2h symmetry restrictions were imposed for planar s-cis, twisted, and planar s-trans conformations, respectively. The requested HF convergence on the density matrix was and the threshold values for the maximum force and the maximum displacement were 0.000 45 and 0.0018 au, respectively. The energy values computed for the different conformers were fitted to the following six-term truncated Fourier expansion:

c 6

V(4) =

1/2

vi(1 - cos qJ)

i= 1

where Vis the relative energy at the rotational angle 4. (4 has to be defined as 180" - 8 since the s-trans (8 = 180") conformer was selected as the energy origin.) This method of deriving the potential function for the internal rotation was first employed by PopleS6and V e i l k ~ dand , ~ ~it has been proved to provide an accurate and inexpensive way to get the situation and relative energies of the critical points in the torsional curve.58.59

Results and Discussion In this section we present and discuss the conformational behavior calculated for 2,2'-bithiophene at different computational levels. We focus first on the structural aspects and especially on how the inclusion of the electron correlation affects the geometric parameters and how these parameters correlate with recent gas-phase electron diffraction data. A detailed analysis is next performed of the torsional potentials inferred from the relative energies computed for different conformers. The conformational stabilities are compared with previous ab initio results and available experimental data. 1. Geometries. The molecular geometries of the 8 = 0", 30", 60", 90", 120°, 150", and 180" conformers of 2,2'bithiophene were optimized at the ab initio HF/3-21G*, HF/631G*, and MP2/6-31G* levels. Two additional geometry optimizations including the relaxation of the torsional angle 8 were performed in the vicinity of the s-cis and s-trans conformers in order to determine the location of gauche minima. All optimizations were carried out, keeping planar the thiophene rings. Table 1 summarizes the HF/6-31G* and MP2/6-31G* optimized geometries for the most significant s-cis planar, s-cisgauche, perpendicular, s-trans-gauche, and s-trans planar conformers. HF/3-21G* optimized parameters are very close to those obtained at the HF/6-3 lG* level and are not reported. Table 1 also includes the gas-phase electron diffraction and solid-state X-ray experimental geometries reported for 2,2'bithiopheneZ2and 5,5'-dibrom0-2,2'-bithiophene?~ respectively. The X-ray data obtained by Visser et a1.12 for 2,2'-bithiophene are not given because the molecule appeared to decompose during the X-ray exposure, preventing an accurate determination of bond distances and angles. For the sake of comparison, Table 2 collects the experimental microwave geometry reported for thiophenem together with those theoretically calculated at the HF/6-31G* and MP2/6-31G* levels. The interannular parameters are those which experiment the most significant changes with internal rotation (cf. Table 1). These changes originate in the evolution of the conjugative effects between the electronic clouds of both rings in going from planar to perpendicular conformations and in the different

J. Phys. Chem., Vol. 99, No. 14, 1995 4957

nonbonding interactions that take place in planar conformers. Thus, the central C2-C2' bond lengthens when passing from the s-cis and s-trans planar structures to the perpendicular conformation due to the loss of x-conjugation in the perpendicular form. Furthermore, the C2-C2' bond is predicted to be shorter for the s-trans than for the s-cis conformer, evidencing the more important nonbonding interactions that take place in the latter. For the s-cis rotamer, the nonbonding interaction between the C2-C3 and C2'-C3' double bonds, the short H3H3' contact, and the nonbonding interaction between the lone pairs of sulfur atoms are present. The S1-S1' distance (3.326 and 3.315 8, at the HF/6-31G* and MP2/6-31G* levels, respectively) is significantly shorter than the sum of the van der Waals radii (3.70 8,). The H3-H3' distance (2.402 8, at both theoretical levels) is equal to the van der Waals value (2.40 A). For the s-trans conformer, the distance Sl-H3' is 2.998 8, (HF/6-31G*) and 2.933 8, (MP2/6-31G*) to be compared with the van der Waals value of 3.05 8,. These nonbonding interactions also justify the fact that the interannular S 1-C2 and C2-C3 bonds are longer for the planar forms than for the perpendicular structure. In the same way, the bond angles S 1C2-C3 and C2-C3-H3 have respectively the smallest and the largest values for the planar conformers to alleviate the nonbonding interactions. Despite all these nonbonding interactions, the interannular C2-C2' single bond is calculated to have a length of only 1.450 8, (s-trans planar conformer) at the MP2/6-31G* level in agreement with X-ray (1.447 and electron diffraction (1.456 data. The electron diffraction value should be better correlated with those obtained for the s-cis-gauche (1.452 8,) and s-trans-gauche (1.45 1 A) conformers present in gas phase. The length predicted for the interannular bond length is significant shorter than in other biaryl systems like biphenyl (1.496 A, X-ray data)61 and reveals a great delocalization between the two conjugated rings. It is in fact comparable to that reported for the central bond of the closely related system 1,3,5,7-octatetraene (1451 8, from X-ray data62 and 1.452 8, from highly correlated calculation^^^), evidencing a polyeniclike behavior. The small value obtained for the C2-C2' length in the perpendicular conformation (1.461 A), when compared with the ethane single C-C bond length (1.537 A), should be attributed to hyperconjugative effects between the CJ electrons of one ring and the n electrons of the other ring.M MP2 calculations provide a more delocalized molecular structure than HF results. The inter-ring C2-C2' bond and the C3-C4 single bonds are calculated to be shorter at the MP2 level, and the C2-C3 and C4-C5 double bonds are obtained to be longer. This is also the case for the thiophene molecule, for which the MP2/6-3 lG* calculations predict a more accurate molecular geometry compared to microwave data (cf. Table 2).m For thiophene the average difference in absolute value between the experimental and theoretical values without considering the geometric parameters involving hydrogen atoms is calculated to be 0.0167 and 0.0024 A for the bond lengths and 0.44" and 0.11" for the bond angles at the HF/6-3 lG* and MP2/6-3 lG* levels, respectively. For 2,2'-bithiophene, HF/6-3lG* and MF2/ 6-3 lG* calculations provide optimized geometries in similar accord with gas-phase electron diffraction data. The average deviations between the geometry calculated for the s-transgauche conformer and the electron diffraction data are 0.013 and 0.012 A for the bond lengths and 0.87" and 0.93" for the bond angles at the HF/6-31G* and MP2/6-31G* levels, respectively. The MP2/6-31G* geometry obtained for 2,2'-bithiophene therefore seems to be considerably less accurate than that computed for thiophene.

4958 J. Phys. Chem., Vol. 99, No. 14, 1995

Orti et al.

TABLE 1: ODtimized Geometric Parameters for Selected Conformers of Z,Z'-Bithiophen@

-

s-cis planar

parameters".'

HF/6-31G*

MP2/6-31G*

perpendicular

s-cis-gauche

HF/6-31G*

MP2/6-31G*

@

0

0

44.08

43.30

90

90

C2-C2' s 1- c 2 C2-C3 c3-c4 c4-c5 C5-S1 C3-H3 C4-H4 &5-H5

1.4670 1.7401 1.3536 1.4315 1.3445 1.7233 1.0730 1.0735 1.0708

1.4522 1.7355 1.3872 1.4141 1.3768 1.7180 1.0855 1.0853 1.0828

1.4669 1.7394 1.3509 1.4336 1.3447 1.7243 1.0734 1.0734 1.0709

1.4525 1.7335 1.3848 1.4154 1.3777 1.7178 1.0857 1.0853 1.0828

1.4749 1.7389 1.3486 1.4347 1.3451 1.7232 1.0735 1.0734 1.0712

1.4606 1.7327 1.3836 1.4158 1.3782 1.7158 1.0857 1.0852 1.0830

C2'-C2-C3 s 1- c 2 - c 3 c2-c3-c4 c3-c4-c5 c4-c5-s1 c 5 -s 1- c 2 C2-C3-H3 C3 -C4-H4 C4-C5-H5

127.30 110.41 113.39 112.66 11 1.75 91.79 123.52 123.55 128.06

127.39 110.22 113.22 112.67 111.53 92.35 122.82 124.16 128.49

127.09 110.79 113.20 112.56 111.91 91.54 122.97 123.67 127.85

127.26 110.48 113.00 112.58 111.66 92.14 122.26 124.31 128.24

127.78 110.85 113.21 112.47 111.91 91.52 122.87 123.71 127.70

128.01 110.58 113.06 112.49 111.68 92.20 122.11 124.38 128.07

s-trans planar

s-trans-gauche

MP2/6-3 1G*

HF/6-31G*

HF/6-31G*

HF/6-31G*

MP2/6-3 1G*

exP

MP2/6-3 lG*

electron diffe

X-rag

147.73

142.24

180

180

36(5)- 148(3)

180

C2-C2' s 1- c 2 C2-C3 c3-c4 c4-c5 C5-S1 C3-H3 C4-H4 C5-H5

1.4648 1.7392 1.3515 1.4336 1.3444 1.7249 1.0736 1.0734 1.0709

1.4507 1.7333 1.3850 1.4154 1.3774 1.7183 1.0861 1.0852 1.0828

1.4635 1.7416 1.3520 1.4334 1.3435 1.7257 1.0737 1.0733 1.0708

1.4496 1.7362 1.3862 1.4150 1.3762 1.7191 1.0863 1.0852 1.0827

1.456(12) 1.733(1) 1.370(2) 1.452(2) 1.363(2) 1.719(1) 1.124(9) 1.123(9) 1.122(9)

1.447(1) 1.744(8) 1.363(11) J.413(11) 1.350(12) 1.713(9)

c2'-c2-c3 s 1- c 2 - c 3 c2-c3-c4 c3-c4-c5 c4-c5-s1 C5-Sl-C2 C2-C3-H3 C3-C4-H4 C4-C5-H5

128.31 110.75 113.20 112.63 111.85 91.58 123.27 123.61 122.87

128.50 110.62 113.00 112.59 111.66 92.13 122.47 124.28 128.22

128.33 110.53 113.37 112.63 111.83 91.64 123.52 123.55 128.00

128.65 110.32 113.23 112.57 11 1.67 92.21 122.83 124.20 128.39

126.3(6) 11 1.8(7) 1 11.9(12) 112.3(12) 112.3(7) 91.7(2)

130.7(7) 110.1(6) 114.1(7) 111.6(8) 113.2(6) 91.0(4)

" Optimized geometries at HF/6-31G* and MP2/6-31G* levels are also available for twisted conformations with 8 = 30°, 60°, 120", and 150".

" The number of atoms is given in Figure 1.

Bond L.engths are in angstroms and bond angles in degrees. Torsional angle defined by the planes of the two thiophene rings. e Gas-phase electron diffraction data from ref 22. Two nonplanar conformations with e = 36(5)" and 148(3)O and abundances of 44(4)% and 56(4)% were observed. The C-C-H bond angles are not quoted because they were fixed to average 6-31G* calculated values. f Solid state X-ray data for 5,5'-dibromo-2,2'-bithiophene from ref 30.

TABLE 2: Optimized Geometric Parameters of Thiophene parameters","

HF/6-3 1G*'

MP2/6-3 lG*C

expd

C2-C3 c3-c4 C2-H2 C3-H3

1.7258 1.3451 1.4369 1.0709 1.0735

1.7178 1.3762 1.4201 1.0823 1.0849

1.7140(14) 1.3696(17) 1.4232(23) 1.0776(15) 1.0805(14)

s1- c 2 - c 3 c2-c3 -c4 c 2 - s 1- c 5 Sl-C2-H2 C2-C3-H3

111.84 112.53 91.27 120.40 123.68

111.58 112.44 91.97 120.19 123.17

111.47 112.45 92.17 119.85 123.28

s 1- c 2

The atomic numbering is identical to that used in Figure 1 for 2.2'bithiophene. bBond lengths are in angstroms and bond angles in degrees. Geometry optimization was performed assuming C2), symmetry constraints. Microwave data from ref 60.

The apparent low accuracy of the MP2/6-31G* optimized geometry of 2.2'-bithiophene is due to the assumptions made in obtaining the experimental electron diffraction data by Samdal

et aLZ2 These authors assumed that, since the electron diffraction technique is not particularly sensitive to determine close distances, the differences between the three C-C bond lengths and the two C-S bond lengths within each thiophene ring were equal to the corresponding ab initio differences calculated at the HF/6-31G* level. This assumption is very drastic since it is well-known that Hartree-Fock calculations using splitvalence basis sets lead to too short double bonds and too long single bonds overestimating the bond length altemancy in conjugated systems. This shortcoming of HF calculations is clearly seen in Table 2 for thiophene. Unreliable estimates are therefore to be expected for the C-C bond distances of 2,2'bithiophene. For instance, the C3-C4 bond length is predicted to be 1.452 A, overestimating by -0.04 8, the X-ray data value of about 1.41 8, observed for this distance in different thiophene dimer^,^^.^' trimer^,*^-*^ and tetramer^.^^-^* The MP2/6-3 lG* calculations provide a value of 1.415 A, in good agreement with the X-ray data. The C3-C4 distance is in fact calculated to be slightly shorter than in thiophene (microwave value 1.423

Geometric Structure of 2.2'-Bithiophene

J. Phys. Chem., Vol. 99, No. 14, 1995 4959

TABLE 3: Relative Energies (Eo - Etrsas,in kl/mol) Calculated for 2,Z'-Bithiophene at Different Torsional Angles (8) conformation 0 (deg) HF/3-21G*" HF/6-31G*" MP2/6-31G*" MP2/6-3 1G**/lMP2/6-31G*b 0 (s-cis) 30

s-cis-gauchec 60 90 120

s-trans-gauche' 150 180 ( s - t r a n ~ ) ~

5.574 2.087 1.094 2.135 4.640 1.127 - 1.449 -1.397 0.0

6.518 2.675 1.622 2.777 5.530 1.689 - 1.407 - 1.386 0.0

4.090 -0.174 -1.189 0.174 2.986 -0.902 -3.323 -2.994

4.06 1 -1.231 3.118 -3.359

0.0

0.0

Geometries are optimized fixing 8 and keeping planar the thiophene rings. 0 is also optimized for the s-cis- and s-trans-gauche minima. Single-point calculations. The optimized values of 0 for the s-cis- and s-trans-gauche minima depend on the calculations level and are reported in Table 1. dThe total energies computed for the planar s-trans conformer at the HF/3-21G*, HF/6-31G*, MP2/6-31G*, and MP2/6-31G**//MP2/ 6-31G* levels are -1096.033 160, -1101.427 410, -1102.703 981, and -1102.750 648 hartrees, respectively. MPY6-31G* value 1.420 A) in accord with the x-conjugation exhibited by 2,2'-bithiophene along the octatetraene carbon skeleton. This argument also suggests that the distances inferred from electron diffraction measurements for the C2-C3 (1.370 A) and C4-C5 (1.363 A) double bonds are underestimated since they should be longer than in thiophene (1.3696 A).60 MP2 calculations obtain values of 1.385 and 1.377 8, for the C2C3 and C4-C5 bond distances, respectively, supporting that suggestion. The electron diffraction estimates for the S 1-C2 (1.733 A) and Sl-C5 (1.719 A) agree with the MP2/6-31G* predictions (1.733 and 1.718 A, respectively). It should be also mentioned that electron diffraction data largely overestimate the H-C bond distances (-1.12 A). All these features call for a reinterpretation of the electron diffraction data reported by Samdal et a1.,22which should be revisited at least in terms of the bond lengths. We finally focus in this section on the torsional angle 8. Both HF calculations at the 3-21G* and 6-31G* levels and MP2/631G* calculations predict the existence of gauche minima in the vicinity of the s-cis and s-trans planar forms in agreement with gas-phase electron diffraction data.22 The s-trans-gauche minimum is calculated for torsional angles of 146.22' and 147.73' at the HF/3-21G* and HF/6-3 lG* levels, respectively. These values perfectly match the experimental electron diffraction estimates of -146"" and 148 f 30Z2 and agree with previously reported theoretical value^.^^^^^ The torsional angles obtained by Kofranek et al$2 and Quattrocchi et aL4 using MIDI-4* and DZP basis sets are slightly larger (149.9' and 149.5', respectively). The optimization of the s-trans-gauche minimum at the MP2/6-31G* level reduces the value of 8 to 142.24'. This effect is due to the relative destabilization that the inclusion of correlation effects produces in the s-trans planar conformer that will be commented on below. Similar torsional angles are found for the s-cis-gauche minimum from HF/3-21G* (44.29'), HF/6-31G* (44.08'), and MP2/6-31G* (43.30') calculations. These angles agree with previously reported ab initio r e s ~ l t s and ~ ~ soverestimate ~~ the electron diffraction value of 35 f 5°.22 It should be noted that the s-cis-gauche minimum is less populated, and the experimental estimation is accompanied by a large error. Quattrocchi et a1.@ obtain a significantly smaller value of 32.2' for the torsional angle of the s-cis-gauche conformer using a DZP basis set. The main difference of this basis set with those used in this work is the inclusion of polarization functions on the hydrogen atoms. To test the influence of these functions, we have performed a full optimization of the s-cis-gauche minimum at the HF/6-31G** level. The torsional angle obtained from this calculation (43.73') is intermediate between those found from HF/6-31G* and MP2/6-31G* calculations and does not explain the small value reported by Quattrocchi et a1.@

I

- 4 " ' " ' ' " " ' ' '

0

30

60

90

I

120

w)

"

'

150

180

Figure 2. Plots of the optimized HF/3-21G* HF/6-31G* (- - -), and MP2/6-31G* (-) torsional potentials V of 2.2'-bithiophene as a function of the dihedral angle 8. The potential energy functions V are obtained as explained in the text. (.a*),

2. Torsional Potential. Table 3 collects the relative energies obtained for different conformations of 2.2'-bithiophene from HF/3-21G*, HF/6-31G*, and MP2/6-31G* calculations including geometry optimization and from MP2/6-3 lG**//MPY63 lG* single-point calculations. The s-trans planar conformer is always taken as the energy origin. Figure 2 plots the potential energy curves for the intemal rotation of 2,2'-bithiophene as a function of the dihedral angle 8. These curves were obtained by fitting the relative energy values calculated for conformations with 8 = e", 30', 60', 90', 120°, 150', and 180' to a six-term Fourier expansion as explained above. The values calculated for the coefficients V, of these expansions are given in Table 4. Both HF and MP2 calculations predict a 4-fold potential for the intemal rotation of 2,2'-bithiophene. The most stable conformation always corresponds to a s-trans-gauche minimum with a torsional angle of about 145' (see Table 1). A second local minimum, s-cis-gauche, occurs for a torsional angle of about 44'. These results are in perfect agreement with electron diffraction data which predict the coexistence of the two gauche conformers, the s-trans-gauche being the more abundant (56 f 4%).22 The torsional potential is calculated to be very flat in all cases. The maximum energy difference between two conformations is only 7.925 kl/mol at the HF/6-31G* level and 7.420 kJ/mol at the MP2/6-31G* level. This result suggests a great flexibility for 2,2'-bithiophene and justifies the variety of conformations experimentally observed for thiophene

oligomer^.^^-^^

4960 J. Phys. Chem., Vol. 99, No. 14, 1995

Orti et al.

TABLE 4: Fourier-Fitted Torsional Potentials of 2,2’-Bithio~hene parameteFb HF/3-21G* HF/6-3 1G* MP2/6-3 1G* VI v2

VZ V4

v5 v6 OCG

AEcc en AETS eTG

AETG

4.205 2.093 1.186 -3.634 0.183 -0.240

4.880 2.573 1.447 -3.941 0.191 -0.302

3.355 1.435 0.640 -4.633 0.091 -0.496

44.33 1.080 88.46 4.651 146.42 -1.443

44.15 1.595 88.63 5.539 147.80 - 1.405

43.22 - 1.234 88.26 3 .OO 1 142.02 -3.349

V, (kJ/mol) are the coefficients of the six-term Fourier expansion. O and AE refer respectively to the torsional angle (in degrees) and the relative energy (EO - E,,, in kJ/mol) calculated from the fitted potential for the s-cis-gauche (CG) and s-trans-gauche (TG) minima and for the perpendicular transition state (TS).

The s-trans-gauche minimum is computed to be 1.407 kJ/ mol more stable than the planar s-trans conformer and is separated by a barrier of 6.089 kJ/mol from the s-cis-gauche minimum at the HF/6-31G* level. Almost identical results (1.449 and 6.089 kJ/mol, respectively) are found at the HF/321G* level. The introduction of the electron correlation at the MP2/6-31G* level increases the barrier through the s-trans conformer to 3.323 kJ/mol and has a small effect on the barrier through the perpendicular conformer (6.309 kJ/mol). The greater stability of the s-trans-gauche conformer compared with the fully planar s-trans structure should be attributed to the steric interaction between sulfur and hydrogen atoms that destabilizes the planar form. The energy difference between the two conformers is small enough to justify the presence of the fully planar structure in the solid ~ t a t e ~due ~ to , ~the~packing , ~ ~ forces. The values calculated for the barrier height through the perpendicular conformation (6.1-6.3 kJ/mol) suggest an easy interconversion between the two gauche minima explaining the coexistence of s-cis and s-trans conformers in gas phasezz and in s o l ~ t i o n . ~The ~ - ~experimental ~ barrier of about 20 & 8 kJ/ mol reported by Bucci et al.19 is considerably larger than the theoretical estimates because perpendicular conformations are more impeded in liquid crystalline solvents. The s-cis-gauche minimum is computed to be 4.896 (4.480) kJ/mol more stable than the planar s-cis conformer and is separated by a barrier of 3.908 (3.546) kJ/mol from the s-transgauche minimum at the HF/6-31G* (HF/3-21G*) level. The inclusion of correlation effects slightly increases both barriers to 5.279 and 4.175 kJ/mol, respectively. This local energy minimum is calculated to be 2.543 and 3.027 kJ/mol higher in energy than the s-trans-gauche absolute energy minimum from HF/3-21G* and HF/6-3 lG* calculations. The energy difference between both minima is reduced to 2.134 kJ/mol at the MP2/ 6-31G* level. This small energy difference agrees with that obtained by Quattrocchi et al.44of about 1.7 kJ/mol using singlepoint MP2 calculations and supports the fact that similar populations are experimentally obtained for s-cis- and s-transgauche Conformers. Samdal et a1.22predict relative abundances of 44 f 4% and 56 f 4%, respectively, from gas-phase electron diffraction data at 97-98 “C. This implies a s-cis-gauchehtrans-gauche ratio of about 0.79, in perfect concordance with the ratio of 0.77 reported by Chadwick and KohlerZ3at 100 “C by measuring the relative intensity of the two components observed in the fluorescence excitation spectrum of 2,2’bithiophene seeded into a supersonic helium expansion. Samdal et a1.22assume the entropies of the two conformations to be

identical and predict an energy difference of only 0.750 kJ/mol by equalizing the s-cis-gauche/s-trans-gauche ratio to exp(-AE/RT). Chadwick and KohlerZ3obtain an energy difference of 4.85 f 0.64 kJ/mol by fitting the ratios inferred at different temperatures to RO exp(-hE/RT). The evaluation procedure therefore leads to significantly different estimates for the energy difference between the s-cis-gauche and s-trans-gauche conformations. Our theoretical estimates are intermediate between the experimental values. The energetic position of the fully-planar s-cis conformer relative to the perpendicular structure has been widely discussed. The s-cis conformer is expected to be destabilized due to the interannular nonbonding interactions between the lone pairs of the sulfur atoms and between the C2-C3 and C2’-C3’ double bonds. At the STO-3G level,40it is calculated to be the second minimum 12.8 kJ/mol more stable than the perpendicular conformer. The use of a split-valence 3-21G basis set destabilizes the planar forms and reduces this difference to only 2.64 kJ/m0L41 The inclusion of polarization d functions on sulfur atoms at the 3-21G* level increases the flexibility of the basis set to treat the nonbonding interactions between the sulfur atoms and finally places the s-cis form over the perpendicular c o n f o r m a t i ~ n . ~However, ~.~~ the relative energy of these two conformations strongly depends on the procedure employed to calculate the torsional potential. Distefano et al.43predict the s-cis conformer to be more energetic by only 0.3 1 kJ/mol using a rigid rotor potential based on the geometry optimized for the s-trans conformer. Samdal et a1.22obtain a larger difference of about 5 kJ/mol, but they do not explain how the potential was calculated. Kofranek et al.42finds the s-cis conformer to be more stable using a MIDI-4* basis set and a rigid rotor approach. Our fully optimized torsional potentials clearly establish that the planar s-cis conformer corresponds to the absolute maximum of the potential being destabilized by about 1 kJ/mol with respect to the perpendicular disposition. The energy difference calculated at the HF/3-21G* level (0.934 kJ/ mol) is only slightly modified at the MP2/6-31G* level (1.104 kJ/mol). The planar s-cis conformer is predicted 5.574 kJ/mol higher in energy than the planar s-trans conformer at the HF/3-21G* level. The inclusion of polarization d functions on carbon atoms at the HF/6-31G* level increases this difference to 6.518 kJ/ mol due to the better description of the interactions between the C2-C3 double bonds that take place in the s-cis conformer. Furthermore, the dipole moment calculated for the thiophene ring at the HF/6-31G* level (0.90 D) is slightly larger than that obtained at the HF/3-21G* level (0.76 D). In the s-cis conformer, the dipole moments of the thiophene rings have a nearly parallel alignment which contributes to its energetic destabilization. Calculations at the MP2/6-3lG* level reduce the energy difference between the s-cis and s-trans conformers to 4.090 kJ/mol. The inclusion of electron correlation effects stabilizes in fact all conformations with respect to the s-trans planar conformer compared with HF results (see Figure 2). For instance, the energy difference between the s-cis planar conformer and s-trans-gauche minimum varies by only 0.512 kJ/ mol in passing from HF/6-31G* to MP2/6-3 lG* calculations. These results suggest that differential correlation effects are larger for twisted and s-cis planar conformers than for the s-trans planar structure. We have also investigated the influence of including polarization p functions on hydrogen atoms by performing single-point MP2/6-3 1G**/IMP2/6-3lG* calculations for the five stationary conformations of the torsional potential. As can be seen from Table 3, the relative energies of the different conformers remain

Geometric Structure of 2,2'-Bithiophene

-8

-

I

S I

1

1

1

I

S

$

8

I

A

J. Phys. Chem., Vol. 99, No. 14, 1995 4961

1

1

f

I\

t

1

~

1

1

'

"

'

I ( \

,

'

'

'

and accounts for the main part of the cis-trans energy difference. The V2 term reflects the tendency of the molecule to adopt a planar conformation in order to maximize its conjugative stability. It usually shows the highest contributions to the torsional potential for conjugated systems. This is not the case for 2,2'-bithiophene because the planar forms are highly destabilized by the nonbonding interactions. The tendency to adopt a twisted conformation is mainly carried by the V4 term. The V3 term contributes to the appearance of the s-cis-gauche minimum by destabilizing the planar s-cis structure. The V5 and v6 terms have minor contributions to the torsional potential although at the MP2/6-3 1G* level the value of v6 is comparable to that of V3. Compared to 2,2'-bif~ran,~~ the values obtained for the Vi coefficients of 2,2'-bithiophene are considerably smaller due to the flatness of the torsional potential. The VI and V;! terms mainly determine the 2-fold torsional potential of 2,2-bifuran and are calculated to be 8.28 and 20.84 kVmol, respectively, at the 4-31G level. For 2,2'-bithiophene, the V1 and V4 terms have the largest values (3.36 and -4.63 kJ/mol, respectively, at the MP2/6-3 lG* level), and they mostly account for the two main characteristics of the torsional potential, i.e., the unstability of the s-cis conformer and the appearance of the gauche minima. The V2 term has a value of only 1.44 kJ/mol for 2,2'-bithiophene and accounts for the small barrier through the perpendicular conformation. In order to check the reliability of the Fourier-fitted torsional potentials of Table 4, we have used these potentials to calculate the characteristics (torsional angle and relative energy) of the gauche minima and the perpendicular transition state. It should be recalled that these potentials are generated making use of the energies calculated for 8 = 0", 30", 60", 90", 120°, 150", and 180°, and no data concerning the critical points are introduced in the fitting. The values obtained are also collected in Table 4. Torsional angles for the gauche minima are calculated within an accuracy of 0.2" with respect to those obtained from geometry optimization (cf. Tables 1 and 4).The relative energies computed for these minima agree with those reported in Table 3 within an accuracy of 0.04 kJ/mol. These results support the validity of the Fourier-fitted torsional potentials obtained for 2,2'-bithiophene. These potentials can find application to predict the conformational preferences and the configurational statistics of longer oligothiophenes and polythiophenes in a noncrystalline phase. As discussed in the Introduction, the conformational properties of polythiophene chains play a crucial role in determining the highly interesting electrical and optical properties these materials show for technological applications.

Summary and Conclusions A detailed ab initio study of the internal rotational potential of 2,2'-bithiophene has been performed in order to gain some insight into the conformational properties of longer oligothiophenes and polythiophenes. Fully optimized torsional potentials have been calculated at the HF/3-21G*, HF/6-31G*, and MP2/6-31G* levels. Bond lengths and bond angles obtained at both the HF and the MP2 levels well reproduce the experimental data in gas phase and in the solid state. MP2 calculations provide a more delocalized structure and suggest that some of the assumptions made in a recent electron diffraction determination of the molecular structure of 2,2'bithiophene should be revisited. A very flat 4-fold potential is obtained for the internal rotation of 2,2'-bithiophene at both the HF and MP2 levels. The most stable conformation is always calculated to correspond to a

4962 J. Phys. Chem., Vol. 99, No. 14, 1995 s-trans-gauche structure located around 147" at the HF level and at 142.2" at the MP2 level. A second local minimum is found for a s-cis-gauche structure with a torsional angle of about 44". The small energy difference (2.13 kJ/mol at the MP2/6-3 lG* level) between these minima explains the experimental evidence that they have similar relative abundances. They are separated by barrier heights lower than 6.2 kJ/mol, and the s-cis planar conformer is predicted as the absolute maximum. The flatness of the torsional potential results from the large destabilization of the planar conformers mainly due to the nonbonding interactions involving the voluminous sulfur atoms. This flatness justifies the variety of conformations experimentally observed depending on the state of aggregation. It has been recently shown that it plays a crucial role for the understanding of the optical absorption spectra of 2,2'bithiophene.' The inclusion of polarization d functions on C atoms in passing from the 3-21G* to the 6-31G* basis set slightly destabilizes the s-cis and perpendicular forms with respect to the s-trans conformer. The inclusion of electron correlation at the MP2 level stabilizes all conformations with respect to the s-trans conformer compared with the HF results; i.e., differential correlation effects are calculated to be larger for twisted structures and particularly for the s-cis planar conformer. Additional calculations at the MP2 level including polarization p functions on hydrogen atoms vary the relative energies by less than 0.2 kJ/mol. Truncated Fourier expansions of the torsional potential provide a valuable tool for the analysis of the potential in comparison with related systems in terms of conjugative, steric, and other nonbonding interactions. The V I and V4 terms mainly determines the 4-fold potential of 2,2'-bithiophene with important contributions from the V2 and V3 terms and smaller contributions from the Vs and v6 terms. The Fourier-fitted torsional potential accurately reproduces the characteristics of the stationary points and can be used to predict the conformational properties of longer oligothiophenes.

Acknowledgment. This research was supported by the DGICYT Projects PB91-0935 and PB90-1016. We thank the Servei D'Informhtica de la Universitat de Valkncia for the use of their computing facilities. Technical assistance by W. Diaz is also gratefully acknowledged. References and Notes (1) (a) Roncali, J. Chem. Rev. 1992, 92, 711. (b) Wessling, B. Adv. Mater. 1991, 3, 507. (c) Gamier, F. Angew. Chem., Int. Ed. Engl. 1989, 28, 513. (d) Patil, A. 0.;Heeger, A. J.; Wudl, F. Chem. Rev. 1988, 88, 183. (2) Roncali, J.; Yassar, A.; Gamier, F. Synrh. Met. 1989, 28, C275. (3) Conjugated Polymers, Novel Science and Technology of Conducting and Nonlinear Active Materials; Bredas, J. L., Silbey, R., Eds.; Kluwer: New York, 1991. (4) Hotta, S.; Waragai, K. Adv. Muter. 1993, 5, 896. ( 5 ) (a) Bauerle, P.; Segelbacher, U.; Gaudl, K.-U.; Huttenlocher, D.; Mehring, M. Angew. Chem., Int. Ed. Engl. 1993, 32, 76. (b) Horowitz, G.; Yassar, A.; von Bardeleben, H. J. Synth. Mer. 1994, 62, 245. (c) Ehrendorfer, Ch.; Kaqfen, A. J. Phys. Chem. 1994, 98, 7492. (6) Gamier, F.; Horowitz, G.; Peng, X . ; Fichou, D. Adv. Mater. 1990, 2, 592. (7) Gill, R. E.; Malliaras, G. G.; Wildeman, J.; Hadziioannou, G. Adv. Mater. 1994, 6, 132. (8) (a) InganSis, 0.;Salaneck, W. R.; Osterholm, J.-E.; Laakso, J. Synrh. Met. 1988,22,395. ,(b) Salaneck, W. R.; Inganas, 0.;Themans, B.; Nilsson, J. 0.;Sjogren, B.; Osterholm, J.-E.; Bredas, J. L.; Svensson, S. J. Chem. Phys. 1988, 89, 4613. (9) Mo, Z.; Lee, K.-B.; Moon, V. B.; Kobayashi, M.: Heeger, A. J.; Wudl, F. Macromolecules 1985, 18, 1972. (10) (a) Briickner, S.; Porzio, W. Makromol. Chem. 1988, 189. 961. (b) Yamamoto, T.; Morita, A.; Miyazaki, Y.; Maruyama, T.; Wakayama,

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