Small Band-Gap Polymers Involving Tricyclic Nonclassical Thiophene

J. Phys. Chem. B 2002, 106, 3549-3556

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ARTICLES Small Band-Gap Polymers Involving Tricyclic Nonclassical Thiophene as a Building Block Masamitsu Tachibana,†,‡ Shoji Tanaka,§ Yoshiro Yamashita,| and Kazunari Yoshizawa*,† Institute for Fundamental Research of Organic Chemistry, Kyushu UniVersity, Fukuoka, 812-8581, Japan, Department of Molecular Engineering, Kyoto UniVersity, Kyoto 606-8501, Japan, Institute for Molecular Science, Okazaki 444-8585, Japan, and Department of Electronic Chemistry, Tokyo Institute of Technology, Nagatsuta, Yokohama 226-8502, Japan ReceiVed: April 26, 2001; In Final Form: January 10, 2002

The band electronic structures of one-dimensional polymers composed of thiophene, pyrrole, and tricyclic nonclassical thiophenes ([1,2,5]thiadiazolo[3,4-b]thieno[3,4-e]pyrazine and dithieno[3,4-b:3′,4′-e]pyrazine) are calculated and analyzed at the extended Hu¨ckel level of theory, with the development of highly conducting polymers in mind. The tricyclic nonclassical thiophenes that can impose quinoid-type characters to the resulting polymers are effective building blocks for the preparation of small band-gap polymers. Calculated band gaps are discussed in view of the frontier crystal orbitals and the bond length alternation of the polymers. The homopolymer of [1,2,5]thiadiazolo[3,4-b]thieno[3,4-e]pyrazine that is predicted to have a small band gap of 0.1 eV is a good candidate for an intrinsic conducting polymer without dopants.

I. Introduction

CHART 1

π-Conjugated polymers have attracted much interest since the discovery of metallic conductivity in doped polyacetylene.1 After this pioneering work a lot of π-conjugated polymers have been synthesized and characterized.2 π-Conjugated polymers can also have many interesting properties such as electroluminescence,3 which has stimulated research studies for technological application. In particular, the synthesis of π-conjugated systems with small band gaps has been the focus of attention because of their expected good nonlinear optical properties4 and intrinsic electric conductivity.5 A large number of studies have been performed both experimentally and theoretically in search of small band-gap polymers, with the introduction of fused ring systems,6 ladder-type polymers,7 substituents,8 donor-acceptor systems,9 and so on. However, band-gap values reported so far are not necessarily small enough to present metallic conduction without dopants. Linear π-conjugated systems such as polyacetylene are subject to Peierls distortion10 and are predicted to possess band gaps that depend on the degree of bond length alternation along the polymer backbone. Although band gap and bond alternation are not linearly correlated, it is important to reduce the bond length alternation for the band-gap reduction of one-dimensional systems. Because of the stability and structural versatility, thiophene-based systems have been extensively studied for the construction of small band-gap polymers. Some strategies for the band-gap reduction of thiophene-based systems have been proposed and applied. First, the fused-ring introduction of quinoid properties was suggested as a hopeful method.11 For * Corresponding author. E-mail: [email protected]. † Kyushu University. ‡ Kyoto University. § Institute for Molecular Science. | Tokyo Institute of Technology.

aromatic polymers such as polythiophene, two limiting structures, aromatic- and quinoid-type structures, can exist, as indicated in Chart 1. Actual polymers have geometries between the two limiting structures, depending on the extent of their contribution. The aromatic-type structure is dominant in the ground state of polythiophene. Bre´das et al. found a significant relationship between bond length alternation and band gap in the polythiophene chain and proposed that the introduction of adequate quinoid structures into the aromatic-type backbone can decrease the bond length alternation and may reduce the band gap accordingly.11 Bre´das predicted polyisonaphthothiophene to be a possible intrinsic conductor with a band gap of 0.01 eV.11b After that polyisonaphthothiophene was synthesized, but unfortunately it was shown to have a large band gap 1.5 eV.12 Kertesz et al. pointed out the difficulty of preparing small-gap polythiophene-based homopolymers13 and suggested that a copolymer of thiophene and isonaphthothiophene would realize a small band gap of 0.54 eV.14 This approach leads us to combine monomer units with different electronic properties and incorporate fused rings into conjugated systems. Along this strategy, a thiophene-based copolymer (shown in Chart 2) that has a band gap of 0.65 eV, much smaller than that of polythiophene (2.1 eV),15 was successfully synthesized.16 Recently a series of trimeric fused ring systems involving nonclassical thiophenes,17 indicated in Chart 3, have been synthesized and characterized by Tanaka and Yamashita.18 These mixed trimers have an electron-accepting fused ring with

10.1021/jp0115906 CCC: $22.00 © 2002 American Chemical Society Published on Web 03/19/2002

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CHART 2

CHART 3

CHART 4

small HOMO-LUMO separations, which can strongly impose quinoid characters on the resulting polymers. These trimeric units can also be viewed as an alternation of electron-deficient nonclassical thiophene and electron-donating thiophene or pyrrole, and such donor-acceptor systems should be favorable for the reduction of band gap.9 It was reported experimentally18a-d and theoretically18e that the three rings in the trimeric units are almost coplanar, which is preferable for the band gap reduction of π-conjugated systems. The co-trimers have small HOMOLUMO separations;18 for example, co-trimer 6 has an absorption maximum at λ ) 1345 nm (0.92 eV)18e and is indeed a good building block for an intrinsic conducting polymer.19 Actually, electrochemically determined band gaps of the homopolymers of 5 and 6 trimeric units were reported to be 0.30 and about 0 eV, respectively, which are among the smallest reported so far for π-conjugated systems.18e The reported zero band gap is not necessarily a reliable value for the neutral state of the polymer because of the difficulty in electrochemical dedoping, but the polymers with the nonclassical thiophene units are interesting systems that can lead to intrinsic conducting polymers. A polymer with a dimeric unit shown in Chart 4 was also synthesized by Roncali et al., its band gap being 0.36 eV.20 This polymer has enhanced solubility and stability under reductive redox cycling conditions and possible regular alternation of donor-acceptor units, which can lead to a stable polymer with an extremely small band gap. In this study, we calculated and analyzed the band electronic structures of the one-dimensional polymers based on thiophene, pyrrole, and tricyclic nonclassical thiophenes shown in Figure 1, with the development of intrinsic conducting polymers in mind. In this illustration, T means thiophene, P pyrrole, A

Figure 1. Polymers composed of thiophene, pyrrole, and tricyclic nonclassical thiophenes.

[1,2,5]thiadiazolo[3,4-b]thieno[3,4-e]pyrazine, and B dithieno[3,4-b:3′,4′-e]pyrazine. Various possible combinations of these were considered, in which polythiophene, (ATT)n, and (APP)n have been prepared by Tanaka and Yamashita.18 Aromatic-type bond alternation patterns are drawn for these polymers, but the reader will see that these pictures need improvement, due to the quinoid-type characters imposed by the tricyclic nonclassical thiophenes. We first performed geometry optimizations of oligomer models assuming coplanar structures with the MNDOPM3 (modified neglect of diatomic overlap, parametric method 3) method.21 Then the band electronic structures of the onedimensional polymers were calculated at the extended Hu¨ckel level of theory22 using optimized geometries of oligomer models. Calculated band gap values are discussed in view of frontier crystal orbitals and geometrical changes imposed by the tricyclic nonclassical thiophene units. We also estimated the band gaps of (A)n and (B)n by extrapolating the HOMO-LUMO gaps of the oligomer models (n ) 2-4) at the B3LYP23/6-31G*24 level of theory. II. Models and Computational Methods We investigated the band structures of the periodic linear π-conjugated systems that involve as units the tricyclic nonclassical thiophenes, [1,2,5]thiadiazolo[3,4-b]thieno[3,4-e]pyrazine (A), and dithieno[3,4-b:3′,4′-e]pyrazine (B) shown in Chart 5. No reasonable bond alternation can be drawn for these molecules with respect to their single and double bonds. Adjacent monomer units are arranged in a fashion that they point opposite directions.

Band-Gap Polymers Involving Tricyclic Nonclassical Thiophene

J. Phys. Chem. B, Vol. 106, No. 14, 2002 3551

CHART 5

It is important to precisely determine the torsion angles. Unfortunately, nonclassical thiophenes are unstable systems and their X-ray structural information is limited except a few examples.18a,d,25 However, we can reasonably assume coplanarity for the polymers and the oligomer models by the following reasons. According to previous AM126 calculations on the dimer models of [1,2,5]thiadiazolo[3,4-b]thieno[3,4-e]pyrazine with thiophene or pyrrole (AT or AP unit), s-trans coplanar structures are, in fact, most stable in energy.18e Similar systems involving thieno[3,4-b]pyrazinealsohavenearlycoplanarX-raystructures,18b,c due to the favorable inter-ring S-N or H-N interactions, where the nitrogen atoms in the pyrazine ring are important to retain the coplanarity.18c,e,27 Recent calculations at the AM1 and B3LYP/6-31G* levels of theory predicted coplanar stable structures for a series of thieno[3,4-b]pyrazine oligomers.28 X-ray structures of several nonclassical thiophene derivatives also show nearly coplanar geometries for the nonclassical thiophene moieties.18a,d,25 We therefore consider that the coplanar s-trans geometries are reasonable for the one-dimensional systems in Figure 1. We calculated the structures of dimer, 6-mer, and 10-mer models for the polymers composed of dimeric units (polythiophene (T)n, (AT)n, (AP)n, (BT)n, (BP)n, (A)n, and (B)n). For the polymers composed of trimeric units ((ATT)n, (APP)n, (BTT)n, and (BPP)n), trimer, 6-mer, and 12mer models were calculated. The geometries of these oligomers were optimized under C2h symmetry. In a simple aromaticquinoid competition, shorter oligomer models can be used to determine the structure of the ground state of a polymer, with respect to aromatic or quinoid type, by choosing proper terminal groups (-H for aromatic and dCH2 for quinoid forms).29 Here we used longer oligomer models terminated by -H throughout the present work because some of the oligomer models do not have clear aromatic or quinoid-type bond alternation, as described later. We show in Figure 2 some of the oligomer models calculated. Geometry optimizations of the oligomer models were performed using the PM3 method that has been successfully applied in predicting the molecular structures of organic compounds. The Gaussian 98 program package30 was used for the PM3 calculations. When we estimate the geometry of a polymer from oligomer calculations, we should be careful because oligomer models with insufficient length can lead to erroneous results in certain cases.31 Calculated structures of the 10-mer and 12-mer models are somewhat different from those of the dimer and trimer models, but are very similar to those of the 6-mer models, most of the differences between the corresponding bond lengths being within 0.003 Å. We therefore concluded that the 10- or 12-mer models are long enough to estimate the structures of the infinite onedimensional polymers. We then calculated the band structures of the one-dimensional polymers at the extended Hu¨ckel level using the geometries determined from the optimized structures of the central parts of the 10- or 12-mer models. We used the extended Hu¨ckel method22 implemented with YAeHMOP.32 Parameters we used in the extended Hu¨ckel calculations are C 2s (Hii ) -21.4 eV, ζ ) 1.625), C 2p (Hii ) -11.4 eV, ζ ) 1.625), N 2s (Hii ) -26.0 eV, ζ ) 1.950), N 2p (Hii ) -13.4

Figure 2. Oligomer models composed of AT and ATT units.

eV, ζ ) 1.950), S 3s (Hii ) -20.0 eV, ζ ) 2.122), S 3p (Hii ) -11.0 eV, ζ ) 1.827), and H 1s (Hii ) -13.6 eV, ζ ) 1.300), where Hii and ζ represent the orbital energy and the Slater exponent, respectively. Although Hartree-Fock calculations generally overestimate the band gaps of polymers,33 this oneelectron approximation method is reliable in band-gap calculations34 and has been widely used. We can also estimate the band gaps of polymers using excitation energies or HOMO-LUMO separations of oligomers with different numbers of monomer units.28,35 Kwon and McKee showed that high-level calculations on oligomer models up to tetramers are satisfactory for the estimation of the band gaps of polythiophene-based polymers.28 Unfortunately, we cannot apply this strategy for all of the polymers because high-level calculations of our big oligomer models based on the mixed dimer and trimer units are impossible. We used this method for (A)n and (B)n to look at the applicability of the extended Hu¨ckel method. The band gaps of (A)n and (B)n were estimated from the HOMO-LUMO separations of the oligomers at the B3LYP/ 6-31G* level. Here we imposed C2h and C2V coplanar structures on the dimer and tetramer models, and the trimer models, respectively. The band gaps converged on nearly 0 eV, but slightly negative. Since errors within 0.5 eV are involved in this method, we can reasonably conclude that (A)n and (B)n have very small band gaps of 0-0.5 eV. This result is in good agreement with the extended Hu¨ckel calculations described below. III. Results and Discussion A. Optimized Structures of Oligomer Models. We present in Figure 3 optimized structures of the 10- and 12-mers concerning their central moieties. Unfortunately, there is no experimental information about our nonclassical thiophene systems, but we can give a good explanation for the geometries. The structure of (T)10 shows a clear aromatic-type character

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Figure 3. Optimized structures of the 10-mer or 12-mer models. Bond lengths are in Å.

with strong bond length alternation (C1-C2 ) 1.426 Å, C2-C3 ) 1.376 Å, and C3-C4 ) 1.440 Å), the result being consistent with the previous calculation by Kertesz and collaborators.13 Co-oligomers (ATT)4 and (BTT)4, in which the ratio of thiophene and nonclassical thiophene is 2:1, have C-C bond lengths somewhat different from those of (T)10. In (ATT)4, C1C2 is 0.044 Å longer, C2-C3 is 0.052 Å longer, and C3-C4 is 0.006 Å shorter than the corresponding C-C bonds in (T)10. For the thiophene units and the inter-ring bonds between them, the C5-C6 and C7-C8 bonds are shortened and the C4-C5 and C6-C7 bonds are lengthened, by 0.003-0.005 Å compared to those of (T)10. Although the geometrical change from (T)10 is very small, the bond length alternation along the carbon main chain is reduced in (ATT)4 and (BTT)4. The thiophene and interring parts are very similar in (ATT)4 and (BTT)4; the only difference in these is the N and C-H parts, but they are distant form the carbon main chains and have no significant electronic effect. Thus, the carbon backbones of co-oligomers (ATT)4 and (BTT)4 are less aromatic than that of (T)10. Optimized geometries of (AT)5 and (BT)5 are similar to those of (ATT)4 and (BTT)4 in their nonclassical thiophene moieties, the difference between the corresponding bond lengths being within 0.001 Å except the C3-S bonds. The C3-C4 and C5C6 bonds are shorter and the C4-C5 bond is longer than those of (ATT)4 and (BTT)4, by 0.002-0.005 Å. Thus, the bond length alternation in (AT)5 and (BT)5 is decreased compared to that in (ATT)4 and (BTT)4 and the aromatic-type character of (AT)5

and (BT)5 is further decreased, as expected from the larger ratio of nonclassical thiophene involved (thiophene: nonclassical thiophene ) 1:1). Therefore the tricyclic nonclassical thiophenes successfully impose quinoid-type characters to the carbon main chain. The pyrrole-containing and the thiophene-containing oligomers are similar in geometry. (APP)4 and (BPP)4 have less aromatic-type structures; (AP)5 and (BP)5 exhibit weaker aromatic-type structures than (APP)4 and (BPP)4. There is almost no bond-length alternation in the pyrrole moieties of (APP)4 and (BPP)4, the difference between the C4-C5 and C5-C6 bonds being within 0.004 Å, and we can see slight quinoid-type bond alternation in (AP)5 and (BP)5, C4-C5 being about 0.015 Å longer than C5-C6. Thus, the pyrrole moieties have more quinoid characters than the thiophene moieties when mixed with [1,2,5]thiadiazolo[3,4-b]pyrazine or dithieno[3,4-b]pyrazine. No significant structural change is seen when thiophene is replaced by pyrrole, but the pyrrole-containing co-oligomers have slightly decreased bond alternation along the carbon backbones compared to the thiophene-based counterparts. In contrast, (A)10 and (B)10 show strong quinoid-type structures. The short inter-ring bonds (C3-C4) of 1.356 and 1.357 Å are clearly CdC double bonds and the adjacent C2C3 bonds of 1.466 and 1.458 Å can be viewed as C-C single bonds in π-conjugated systems. This is in remarkable contrast to the bond alternation patterns in the other oligomer models mentioned above. The C1-C2 bonds (1.478 and 1.474 Å) are

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Figure 4. Band structures of the one-dimensional polymers. EF, HO, and LU represent the Fermi levels and the highest occupied and the lowest unoccupied bands, respectively. The shaded areas in the DOS indicate the contribution from the pz orbitals which is perpendicular to the molecular plane.

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TABLE 1: Band Gaps and Energy Levels of the HOCOs and the LUCOs of the Polymers in Figure 1 (units in ev)

a

TABLE 2: Bandwidths of the HO and the LU Bands of the Polymers in Figure 1 (units in ev)

polymer

band gap

HOCO

LUCO

polymer

HO band

LU band

(T)na (ATT)n (APP)n (AT)n (AP)n (A)n (BTT)n (BPP)n (BT)n (BP)n (B)n

2.05 0.47 0.33 0.34 0.22 0.10 0.50 0.36 0.37 0.24 0.14

-10.87 -10.59 -10.45 -10.46 -10.34 -10.21 -10.56 -10.43 -10.43 -10.31 -10.17

-8.82 -10.12 -10.12 -10.12 -10.12 -10.11 -10.06 -10.07 -10.06 -10.07 -10.03

(T)na (ATT)n (APP)n (AT)n (AP)n (A)n (BTT)n (BPP)n (BT)n (BP)n (B)n

0.35 0.12 0.24 0.63 0.80 0.85 0.12 0.24 0.63 0.84 0.87

0.90 0.00 0.00 0.01 0.00 0.02 0.00 0.00 0.01 0.01 0.03

(T)n: Polythiophene.

longer than the C2-C3 bonds (1.466 and 1.458 Å), but the difference between C1-C2 and C2-C3 is small in (A)10 and (B)10. The aromatic character of polythiophene is decreased as an increase in the ratio of nonclassical thiophenes involved. The nonclassical thiophene polymers (A)n and (B)n show quinoid characters which will lead to distinct electronic properties of these polymers. B. Band Structures and Band Gaps. We show in Figure 4 computed band structures and density of states (DOS) of the polymers. The broken line shows the Fermi level (EF); the shaded areas in the DOS indicate the contribution from the p-orbitals perpendicular to the molecular plane (pz). All the HOCOs (the highest occupied crystal orbital) and the LUCOs (the lowest unoccupied crystal orbital) consist of the pz-orbitals. We list in Table 1 calculated band gaps and energy levels of the HOCOs and the LUCOs. All the band gap values in Table 1 correspond to the direct transition at k ) 0 because in any case the HO (the highest occupied) band is highest at k ) 0 and the LU (the lowest unoccupied) band is almost flat or lowest at k ) 0, as seen in Figure 4. The band gap of polythiophene was calculated to be 2.05 eV, being in excellent agreement with an experimental value of 2.1 eV.15 A calculated band gap of 0.47 eV for (ATT)n is also consistent with a measured optical band gap of