Theoretical analysis on the geometries and electronic structures of coplanar conjugated poly(azomethine)s

(1)

Theoretical analysis on the geometries and electronic structures of

coplanar conjugated poly(azomethine)s

Cheng-Liang Liu

a

, Fu-Chuan Tsai

a

, Chao-Ching Chang

a

, Kuo-Huang Hsieh

a,b

,

Jen-Liang Lin

c

, Wen-Chang Chen

a,b,

*

a

Department of Chemical Engineering, National Taiwan University, Taipei 106, Taiwan, ROC

b

Institute of Polymer Science and Engineering, National Taiwan University, Taipei 106, Taiwan, ROC

c_{Union Chemical Laboratories, Industrial Technology Research Institute, Hsinchu 300, Taiwan, ROC}

Received 5 January 2005; received in revised form 16 March 2005; accepted 16 March 2005 Available online 19 April 2005

Abstract

In this study, theoretical analysis on the geometries and electronic properties of various conjugated poly(azomethine)s is reported. The theoretical ground-state geometry and electronic structure of the studied poly(azomethine)s are optimized by the hybrid density functional theory (DFT) method treated in periodic boundary conditions at the B3LYP level of theory with 6-31G basis set. The geometry and electronic structure of poly(1,4-phenylenemethylidyneitrilo-1,4-phenylene-nitrilomethylidyne) (PPI) are compared with those of poly(p-phenylene vinylene) (PPV) or polyazine (PAZ). The theoretical results suggest the non-coplanar conformation of PPI but PPV and PAZ with a coplanar conformation. The electronic properties of PPI are in the intermediate between PPV and PAZ. The non-coplanar conformation of PPIcould be released if the phenylene ring is replaced by the five-member ring of 3,4-ethylenedioxythiophene (PEEI), pyrrole (PYYI), thiophene (PTTI), furan (PFFI), or thiadiazole (PThThI). The theoretical Egof PEEI, PYYI, PFFI, and PTTI are in the range of 1.11–

1.67 eV, which is due to the coplanar configuration or donor–acceptor intrachain charge transfer. However, the large bond length alternation or lack of charge transfer characteristic makes the PThThI with a larger Egof 2.47 eV than others. The trend on the IP or EA of the studied

conjugated poly(azomethine)s are consistent with the electronic characteristic of the aromatic ring. The upper valence bandwidth of the studied five-member ring based poly(azomethine)s except PThThI is in the range of 562–613 meV, which is larger than that of PPI (247 meV) or PPV (373 meV). The results suggest that the electronic properties of conjugated poly(azomethine)s could be varied through various ring structure. The proposed new coplanar conjugated poly(zomethine)s can be potentially used as transparent conductors or thin film transistors.

Keywords: Poly(azomethine)s; Theoretical electronic properties; Planarity

1. Introduction

Conjugated polymers have been widely recognized as a new class of materials for electronic and optoelectronic

devices, such as light emitting diodes [1], thin film

transistors [2], and photovoltaic cells [3]. The intrinsic

electronic properties of conjugated polymers governing the device performance are the ionization potential (IP),

electronic affinity (EA), band gap (Eg), and band width

(BW). The electronic and optoelectronic properties of conjugated polymers can be tuned through the following

methodologies: [4,5] (1) donor (e.g. alkoxy) or acceptor

(e.g. cyano) side group substitution; (2) incorporating heteroatoms (N, O, S, etc.) into the conjugated polymer backbone or ring structure (e.g. pyridine, pyrrole, furan, or

thiophene); (3) solid state morphology[6,7].

Conjugated poly(azomethine)s have been widely studied for the last 20 years due to their excellent thermal, mechanical, electronic, optical, optoelectronic,

and fiber-forming properties [8–14]. The general

chemical structure of conjugated poly(azomethine)s is

www.elsevier.com/locate/polymer

* Corresponding author. Address: Department of Chemical Engineering, Polymer Science and Engineering, National Taiwan University, No1. Sec. 4, Roosevelt Rd, Taipei 106, Taiwan, ROC. Tel.: C886 2 23628398; fax: C886 2 23623040.

(2)

[–(Ar1)–CHaN–(Ar2)–NaCH–]n. The CaN linkages of

poly(1,4-phenylenemethylidyneitrilo-1,4-phenylenenitrilo-methylidyne) (PPI) is isoelectronic with the CaC linkages of poly(p-phenylene vinlyene) (PPV). The incorporating the CaN linkage results in a non-planar conformation of

PPI and thus the p-electronic delocalization is poor in

comparison with PPV [8,9]. However, the CaN linkage

also allows the complexation with acid or metal ion and thus

could be used as fluorescence sensing device[15]or

hole-transporting layer of light-emitting device [16]. A recent

report on thiophene-based azomethine oligomers also shows that the CaN linkage considerably improves the self-assembly properties and thus high carrier mobility up to

w10K2cm2VK1SK1 is achieved [17]. The control of

conformation and their electronic structures are keys to the above technology applications. One strategy to improve the p-electron delocalization of PPI is to replace one of the phenylene rings by a thiophene ring, which has been

reported by us[18]and other studies[10,13]. However, the

development of coplanar conjugated poly(azomethine)s

with the Eg less than 2.0 eV remains challenging, which

can be potentially used as transparent conductors or thin film transistors.

Theoretical analysis on the electronic structures of various conjugated polymers has been extensively reported [19–26]. We have successfully used the hybrid density functional theory (DFT) method to predict conjugated

poly(azomethine)s [18]. In this study, the theoretical

analysis on the geometries and electronic properties of conjugated poly(azomethine)s (1,2), PPV (3), and

poly-azine (PAZ, 4) is reported, as shown in Fig. 1. The

theoretical ground-state geometry and electronic structure of the studied poly(azomethine)s are optimized by the DFT method treated in periodic boundary conditions at the

B3LYP level of theory with 6-31G basis set[19,24,25]. The

geometry and electronic structure of PPI are compared with those of PPV and polyazine (PAZ) to address the role of the CaN linkage. Then, the effects of the p-electron donor or acceptor ring based backbone on the electronic properties of conjugated poly(azomethine)s were studied, including 3,4-ethylenedioxythiophene (PEEI, 2a), pyrrole (PYYI, 2b), thiophene (PTTI, 2c), furan (PFFI, 2d), and thiadiazole (PThThI, 2e). The effects of the ring structure on the conformation and electronic properties are discussed in this study.

2. Methodology

The ground-state geometry and electronic structure of the studied poly(azomethine)s are optimized by means of the hybrid density functional theory (DFT) method treated in periodic boundary conditions at the B3LYP level of theory

(Becke-style 3-parameter density functional theory [27]

using the Lee–Yang–Parr correlation functional[28]) with

6-31G basis set performed on Gaussian 03 program package

[29]. This method B3LYP//B3LYP (started with B3LYP

geometry optimization followed by B3LYP electronic structure calculation) is more reliable than other method-ology when applied to the system where the equilibrium

geometries deviate substantially from planar structures[19].

It has been reported in the literature [30] that the 6-31G

basic set yields a similar result on the prediction of dihedral angle of conjugated materials as that of 6-31G* (6-31G basis set with added augmentation of polarization function). Since the calculation of B3LYP/6-31G* is time consuming for conjugated polymers, the 6-31G is chosen as the basis set for the present study. Besides, the theoretical electronic properties of PPV and PPI based on B3LYP/6-31G energy level are in a good agreement with those reported in the literature by other method or experimentally.

In this analysis, one full unit cell was used for the calculation of an isolated, infinite, and one-dimensional polymer in the gaseous phase, starting from the geometry of the central portion (two repeat units) of the corresponding polymer. Full geometry optimization was performed inside a given lattice length, and the lattice parameters were then varied to locate both the equilibrium lattice parameters and the lowest-energy structure in that unit cell.

3. Results and discussion

3.1. Influence of the linkage on the electronic structures: PPI, PPV, and PAZ

The optimized geometries and electronic structures of

PPI, PPV, and PAZ are shown inFig. 2andTable 1. The

bond length of the CaN linkage in PPI and that of the CaC

linkage in PPV are 1.293 and 1.355 A˚ , respectively.

Besides, the C–C bond length between the CaN linkage

(3)

and the N-phenylene in PPI is 1.410 A˚ , while that between

the CaC linkage and the phenylene in PPV is 1.462 A˚ . The

shorter bond lengths of CaN and C–N than those of CaC and C–C are due to the larger electro-negativity of the nitrogen than carbon. If the bond length alternation (d) is defined as the difference on the bond length between the double and single bond, it shows similar d of PPI and PPV,

as illustrated inTable 1. However, a significant difference is

shown on the dihedral angles (F1and F2) between aromatic

ring and linkage. The dihedral angles (F1and F2) in PPV

are almost zero but F2of PPI is 30.48, as shown inFig. 2.

The repulsion force between the adjacent hydrogen atoms on the CaN linkage and the N-phenylene of PPI results in a non-coplanar conformation. Besides, the bond angle q

shown inFig. 2is 122.48 for PPI and 127.08 for PPV. Both

the differences of bond length and bond angle between PPV

and PPI result in the distance between H1 and H2 much

shorter in PPI than that in PPV. Consequently, it results in a much smaller (and negligible) H–H repulsion force for PPV than that of PPI. It explains why PPV is coplanar but PPI is twisted instead. The non-coplanar conformation of PPI was also verified from the X-ray diffraction results of small

(4)

molecule trans-N-benzylideneaniline [31], in which the CaN plane twists 558 from the N-phenylene and 108 from the benzylidene ring in the opposite direction. It leads to the conjugation between the CaN nitrogen lone-pair electrons and p-electrons on the N-phenylene, which suggests the twisted nature of PPI. For the case of PAZ, both the

dihedral angles (F1and F2) are almost zero since there is no

H–H repulsion force as shown inFig. 2(c). The very small

dihedral angles suggest that both PPV and PAZ exhibit the coplanar conformation.

The calculated electronic properties of PPI, PPV, and

PAZare shown inTable 1. The calculated (IP, EA, Eg) of

PPI, PPV and PAZ are (5.47, 2.64, 2.83) eV, (4.78, 2.31, 2.47) eV, and (5.92, 3.61, 2.31) eV, respectively. Note that

the experimental (IP, EA, Eg) of PPI and PPV are (5.12,

2.60, 2.52) eV and (5.11, 2.71, 2.40) eV, respectively[9]. It

indicates that the (IP, EA) is underestimated in the coplanar PPV, while that is overestimated in the non-coplanar PPI. The deviation between the experimental and theoretical results might be due to the polymer packing in solid state or the condition of cyclic voltammetry measurements. How-ever, the trend on the order of calculated electronic properties is in agreement with that of the experimental results.

The effect of the linkage between the phenylene rings on the electronic structures can be further illustrated by the

HOMO and LUMO energy levels ofFig. 3. The (IP, EA) of

PPIis intermediated between PPV and PAZ. It shows the

asymmetric stabilization of the HOMO and LUMO levels when the CaC linkage in PPV is replaced by the CaN linkage. This stabilization is attributed to not only the electron-withdrawing CaN linkage but also the twisted conformation of PPI. It is known that the substitution of an electron-withdrawing group can lead to the stabilization of

frontier orbitals [4,5]. However, the twisted conformation

would result in the stabilization of the HOMO level but the

Tabl e 1 The optimi zed geom etries and electronic propert ies of the studied conjugat ed polym ers RC1–C2 (A ˚) RC2 a N (A ˚) RC3–N (A ˚) d a (A ˚) F1 b (8 ) F2 b (8 ) V alence bandwi dth (meV) and ef fectiv e mass Conduct ion bandwi dth (meV) and ef fectiv e mass IP (eV) EA (eV) Eg (eV) 1 (PPI ) 1.46 3 1.293 1.41 0 0.02 1 0.9 30.4 247 (0.742 me ) 298 (0.688 me ) 5.47 2.64 2.83 2a (PEEI ) 1.41 4 1.314 1.34 5 0.02 3 0.2 0.6 613 (0.233 me ) 644 (0.223 me ) 4.25 3.14 1.11 2b (PYYI ) 1.42 7 1.309 1.37 1 0.00 6 1.8 12.1 562 (0.406 me ) 552 (0.403 me ) 4.40 2.73 1.67 2c (PFF I) 1.42 4 1.309 1.34 8 0.02 5 0.3 0.1 590 (0.376 me ) 556 (0.343 me ) 4.89 3.33 1.56 2d (PTTI ) 1.42 3 1.308 1.35 7 0.01 8 0.3 0.3 572 (0.278 me ) 583 (0.275 me ) 5.03 3.61 1.42 2e (PT hThI ) 1.43 6 1.296 1.36 3 0.04 0 0.6 0.8 318 (0.530 me ) 287 (0.504 me ) 7.19 4.72 2.47 3 (PPV ) 1.46 2 c 1.355 d 1.46 2 e 0.02 5 0.5 0.3 373 (0.466 me ) 392 (0.446 me ) 4.78 2.31 2.47 4 (PAZ ) 1.41 8 f 1.128 g 1.41 8 h 0.02 0 0.3 0.3 347 (0.474 me ) 405 (0.464 me ) 5.92 3.61 2.31 a Ave rage bond leng th alt ernation. b F1 and F2 are de fined in Fi gs. 1 and 2 . c RC1–C2 . d RC2 a C3 . e RC3–C4 . f RC1–N1 . g RN1 a N2 . h RN2–C2 .

Fig. 3. Effect of linkage between the phenylene rings on the HOMO and LUMO energy levels.

(5)

destabilization of the LUMO level, and increases the Eg

consequently[32]. Therefore, the degree of the stabilization

of the HOMO level is more than that of the LUMO level when the CaC linkage in PPV is replaced by the CaN linkage, leading to the larger bandgap of PPI. The replacement of CaC linkage by NaN linkage leads to the asymmetric stabilization of the HOMO and LUMO levels since the NaN linkage is an electron-withdrawing segment. Therefore, the IP and EA of the PAZ are larger than those of

PPV. Besides, the calculated Egof PPV and PAZ are 2.47

and 2.31 eV, respectively. The smaller Eg of PAZ is

probably attributed to the intrachain charge transfer from the withdrawing NaN linkage and the electron-donating phenylene ring. The bond length alternation of PPI, PPV, and PAZ shows an insignificant variation but not in the case of electronic properties. It suggests that the dihedral angle plays a major role on the electronic properties of poly(azomethine)s.

3.2. Influences of the electron donor/acceptor five-member ring on the electronic properties of conjugated

poly(azomethine)s

As mentioned previously, the six-membered ring based poly(azomethine)s, PPI, has a non-coplanar conformation and affects its electronic properties significantly. If the phenylene ring is replaced by the five-member heterocyclic ring in the backbone of conjugated poly(azomethine)s, the geometries and electronic structures would change dramati-cally. The optimized geometries and calculated electronic properties of conjugated poly(azomethine)s, PEEI (2a),

PYYI(2b), PFFI (2c), PTTI (2d), and PThThI (2e) are

shown inTable 1, respectively.Fig. 4shows the calculated

geometries of PEEI (2a), PTTI (2d), and PThThI (2e). The five-member ring based conjugated poly(azomethine)s

show a very small dihedral angle(F1or F2), which suggests

a coplanar conformation. It is attributed to the absence of the repulsion force between the adjacent hydrogen atoms on the CaN linkage and the N-substitued phenlyene. The planar configurations are in agreement with a recent report on a model compound of thiophene-based monazomethine, as

evidenced by X-ray crystal analysis[33]. The bond length

alternation of the studied five member ring based conjugated

poly(azomethine)s are in the range of 0.006–0.040 A˚ , in

which PThTh with the largest of 0.040 A˚ .

The electronic properties (IP, EA, Eg) of PPI are also

significantly modified by the five-member ring based

conjugated poly(azomethine)s, as shown in Table 1. The

HOMO and LUMO energy levels of the studied coplanar

conjugated poly(azomethine)s are illustrated in Fig. 5. As

shown inTable 1andFig. 5, the calculated IP increases in

the following order: PEEI!PYYI!PFFI!PTTI! PPI!PThThI, while the order of calculated EA is PPI! PYYI!PFFI!PEEI!PTTI!PThThI. The smallest IP of PEEI is as expected since 3,4-ethylenedioxythiophene shows stronger p-donating strength than the others.

Similarly, the largest EA of PThThI is due to the better p-accepting ability of thiadiazole, which indicates PThThI

might be more stable in the n-doped form[25]. The relative

order on IP/EA of PYYI, PFFI and PTTI is consistent with the electron donating ability of the heteroatom. The smallest IP and EA of PYYI among three above conjugated polymers indicate that pyrrole might be sensitive in the neutral form and stable in the p-doped form since nitrogen

shows less electro-negativity than sulfur and oxygen[24].

Weaker donor strength of heteroatom (sulfur compared to

oxygen)[34]leads to a larger IP of PTTI than that of PFFI

by 0.14 eV.

The calculated Egof the studied conjugated

poly(azo-methine)s increases in the following order: PEEI!PTTI! PFFI!PYYI!PThThI!PPI. The five-membered ring heterocyclic poly(azmothine)s is almost coplanar and thus

the calculated Egis much smaller (0.3–1.7 eV) than that of

PPI. Besides, the electron-withdrawing imine group, CaN could have a significant intramolecular charge transfer with the electron-donating heterocyclic rings (3,4-ethylenediox-ythiophene, pyrrole, furan and thiophene) and thus result in

a very small band gap[34]. The 3,4-ethylenedioxythiophene

based conjugated poly(azomethine)s, PEEI, has a Eg of

1.11 eV, which is among the smallest among

poly(azo-methine)s. The small Eg of PEEI is also close to other

classes of small bandgap polymers reported in the literature,

including poly(isothianaphthene)s [35,36], poly(thiophene

methine)s. Hence, they could have the potential applications

as transparent conductors[37,38]. Although the thiadiazole

based conjugated poly(azomethine)s, PThThI, also shows a

coplanar structure, the Egis much larger (about 1 eV) than

the other five-member ring based polymers. It might be due to the large bond length alternation or lack of the intrachain charge transfer as that of polymers 2a–2d. The charge transfer ability could be investigated by calculating total

atomic Mulliken charge [39]. As for the case of PThThI,

the calculated net orbital atomic charge on the electron-rich thiadiazole and electron-deficient imine moiety amount 0.131 and K0.131e, respectively. However, the correspond-ing values are 0.231 and K0.231e for those of PTTI. The smaller charge values on the alternating donor–acceptor unit indicate less intrachain charge transfer ability for PThThI than that for PTTI. PYYI has a larger bandgap among these four electron-donating heterocyclic ring based polymers since PYYI shows a small torsional angle (12.18) between the imine linkages and pyrrole group.

Fig. 6 shows the one-dimensional band structure along the polymer chain of PPI and PEEI. The bandwidths (BWs) and electron effective mass of the studied conjugated

polymers are also summarized inTable 1. The BW values

(or electron effective mass) were calculated on the upper valence band and lower conduction band, which are good parameters for predicting the hole and electron transporting

ability, respectively [40–42]. The effective mass of the

(6)

(7)

upper valence band is defined as 1 mZ 1 h v2EðkÞ vk2 (1) The larger curvature of the energy with the function of momentum reaches a maximum at the inflection point corresponding to diverging mass and thus decreases the effective mass. The kinetic model of mobility (m) is given by

the Drude form[40,43],

m Z_met (2)

When the BW is larger, the effective mass of hole (or electron) should be smaller leading to a higher carrier mobility. Specifically, the effective mass equals the free

hole or electron mass at the broad band[44]. The calculated

upper valence BW of poly(azomethine)s (2a–2d) is 562– 613 meV, which is higher than that of PPI with 246 meV or

PPVwith 373 meV. Besides, the calculated effective mass

of valence band edge of poly(azomethine)s (2a–2d) which is lower than that of PPI and PPV is consistent with the trend of the upper valence BW. Thus, the hole mobility of the coplanar p-type poly(azomethine)s (2a–2d) is expected to be higher than that of non-coplanar PPI. The high bandwidths (small electron effective mass) of the proposed conjugated poly(azomethine)s could have the potential applications as thin film transistors for organic electronics. The high mobility of thiophene based azomethine oligomers

reported in the literature [17] also suggested the above

prediction.

4. Conclusions

In this study, the theoretical geometries and electronic properties of varies aromatic ring based conjugated

poly(azomethine)s are investigated. The comparison on the geometry of PPI with those of PPV and PAZ reveals that the non-coplanar conformation of PPI is resulted from the repulsion force between the adjacent hydrogen

Fig. 5. Effects of the ring structure on the HOMO and LUMO energy levels of conjugated poly(azomethine)s.

(8)

atoms on the CaN linkage and N-phenylene. The electronic properties of PPI are in the intermediate between PPV and PAZ. The non-coplanar conformation of PPI could be overcome by the five member ring based conjugated poly(azomethine)s, including 3,4-ethylenedioxythiophene (PEEI), pyrrole (PYYI), or thiophene (PTTI), furan (PFFI), and thiadiazole (PThThI). The coplanar configur-ation or donor–acceptor intrachain charge transfer resulted

in small Egof PEEI PYYI, PFFI, and PTTI. The trend on

the IP or EA of the studied conjugated poly(azomethine)s are consistent with the ring characteristic. The upper valence bandwidth of the studied five-member ring based poly(azomethine)s except PThThI is larger than that of PPI. The results suggest that the electronic properties of conjugated poly(azomethine)s could be varied through various ring structure and can be potentially used as transparent conductors or thin film transistors.

Acknowledgements

We thank the financial supports of the National Science Council, Industrial Technology Research Institute, and the Ministry of Economic Affairs of Taiwan for this work.

References

[1] Gross M, Mu¨ller DC, Nothofer HG, Scherf U, Neher D, Bra¨uchle C, et al. Nature 2000;405:661.

[2] Sirringhaus H, Tessler N, Friend RH. Science 1998;280:1741. [3] Yu G, Gao J, Hummelen JC, Wudl F, Heeger AJ. Science 1995;270:

1789.

[4] Roncali J. Chem Rev 1997;97:173.

[5] Lu HF, Chan HSO, Ng SC. Macromolecules 2003;36:1543. [6] Chen SH, Su AC, Chou HL, Peng KY, Chen SA. Macromolecules

2004;37:167.

[7] Lin WJ, Chen WC, Wu WC, Niu YH, Jen AKY. Macromolecules 2004;37:2335.

[8] Yang CJ, Jenekhe SA. Chem Mater 1995;7:1276. [9] Yang CJ, Jenekhe SA. Macromolecules 1995;28:1180.

[10] Wang C, Shieh S, Legoff E, Kanatzidis MG. Macromolecules 1996; 29:3147.

[11] Thomas O, Inganas O, Andersson MR. Macromolecules 1998;31: 2676.

[12] Olinga TE, Destri S, Botta C, Porzio W, Consonni R. Macromolecules 1998;31:1070.

[13] Destri S, Pasini M, Pelizzi C, Porzio W, Predieri G, Vignali C. Macromolecules 1999;32:353.

[14] Krebs FC, Jorgensen M. Synth Met 2004;142:181. [15] Giuseppone N, Lehn JM. J Am Chem Soc 2004;126:11448.

[16] Kimoto A, Cho JS, Higuchi M, Yamamoto K. Macromolecules 2004; 37:5531.

[17] Kiriy N, Bocharova V, Kiriy A, Stamm M, Kreb FC, Adlder HJ. Chem Mater 2004;16:4765.

[18] Tsai FC, Chang CC, Liu FC, Chen WC, Jenekhe SA. Macromolecules 2005;38:1958.

[19] Yang S, Olishevski P, Kertesz M. Synth Met 2004;141:171. [20] Cornil J, dos Santos DA, Beljonne D, Bre´das JL. J Phys Chem 1995;

99:5604.

[21] Choi CH, Kertesz M, Karpfen A. J Chem Phys 1997;107:6712. [22] Logdlund M, Salaneck WR, Meyers F, Bre´das JL, Arbuckle GA,

Friend RH, et al. Macromolecules 1993;26:3815.

[23] Cornil J, Gueli I, Dkhissi A, Sancho-Garcia JC, Hennebicq E, Calbert JP, et al. J Chem Phys 2003;118:6615.

[24] Salzner U, Lagowski LB, Pickup PG, Poirier RA. Synth Met 1998;96: 177.

[25] Kwon O, McKee ML. J Phys Chem A 2000;104:7106.

[26] Hutchison GR, Ratner MA, Marks TJ. J Phys Chem A 2002;106: 10596.

[27] Becke AD. J Chem Phys 1993;98:5648.

[28] Lee C, Yang W, Parr RG. Phys Rev B 1998;37:785.

[29] Frisch MJ, Trucks GW, Schlegel HB, Scuseria GE, Robb MA, Cheeseman JR, Montgomery JA, Vreven T, Kudin KN, Burant JC, Millam JM, Iyengar SS, Tomasi J, Barone V, Mennucci B, Cossi M, Scalmani G, Rega N, Peterssonp GA, Nakatsuji H, Hada M, Ehara M, Toyota K, Fukuda R, Hasegawa J, Ishida M, Nakajima T, Honda Y, Kitao O, Nakai H, Klene M, Li X, Knox JE, Hratchian HP, Cross JB, Adamo C, Jaramillo J, Gomperts R, Stratmann RE, Yazyev O, Austin AJ, Cammi R, Pomelli C, Ochterski JW, Ayala PY, Morokuma K, Voth GA, Salvador P, Dannenberg JJ, Zakrzewski VG, Dapprich S, Daniels AD, Strain MC, Farkas O, Malick DK, Rabuck AD, Raghavachari K, Foresman JB, Ortiz JV, Cui Q, Baboul AG, Clifford S, Cioslowski J, Stefanov BB, Liu G, Liashenko A, Piskorz P, Komaromi I, Martin RL, Fox DJ, Keith T, Al-Laham MA, Peng CY, Nanayakkara A, Challacombe M, Gill PMW, Johnson B, Chen W, Wong MW, Gonzalez C, Pople JA. Gaussian Inc., Pittsburgh PA; 2003.

[30] Lin BC, Cheng CP, Lao ZP. J Phys Chem A 2003;107:5241. [31] Manecke G, Wille WE, Kossmehl G. Makromol Chem 1972;160:111. [32] Bre´das JL, Street GB. J Chem Phys 1985;83:1323.

[33] Skene WG. Polym Prepr 2004;45:253.

[34] Yamamoto T, Zhou ZH, Kanbara T, Shimura M, Kizu K, Maruyama T, et al. J Am Chem Soc 1996;118:10389–99.

[35] Wudl F, Kobayashi M, Heeger AJ. J Org Chem 1984;49:3382. [36] Meng H, Wudl F. Macromolecules 2001;34:1810.

[37] Chen WC, Jenekhe SA. Macromolecules 1995;28:465.

[38] Chen WC, Liu CL, Yen CT, Tsai FC, Tonzola CJ, Olson N, et al. Macromolecules 2004;37:5959.

[39] Delgado MCR, Hernandez V, Navarrete JTL, Tanaka S, Yamashita Y. J Phys Chem 2004;108:2516.

[40] Haddon RC, Siegrist T, Fleming RM, Bridenbaugh PM, Laudise RA. J Mater Chem 1995;5:1719.

[41] Cornil J, Calbert JP, Bre´das JL. J Am Chem Soc 2001;123:1250. [42] Cheng YC, Sibley RJ, da Silba Filho DA, Calbert JP, Bre´das JL.

J Chem Phys 2003;118:3764.

[43] Beleznay FB, Bogar F, Ladik J. J Chem Phys 2003;119:5690. [44] Karl N. Synth Met 2003;133–134:649.