Theoretical study on electronic structure and optical properties of novel donor–acceptor conjugated copolymers derived from benzothiadiazole and benzoselenadiazole

Journal of Molecular Structure: THEOCHEM 816 (2007) 161–170 www.elsevier.com/locate/theochem

Theoretical study on electronic structure and optical properties of novel donor–acceptor conjugated copolymers derived from benzothiadiazole and benzoselenadiazole Li Yang a, Ji-Kang Feng a

a,b,*

, Ai-Min Ren

a

State Key Laboratory of Theoretical and Computational Chemistry, Institute of Theoretical Chemistry, Jilin University, Changchun 130023, China b College of Chemistry, Jilin University, Changchun 130023, China Received 12 September 2006; received in revised form 6 April 2007; accepted 11 April 2007 Available online 19 April 2007

Abstract One serious problem associated with luminescent polymers is the significant energy barrier for hole or electron injections and thus usually face charge injection and transport difficulties with the currently available cathode and anode materials. The incorporation of charge carriers is expected to improve the recombination of the charge carriers. In this contribution, we apply quantum-chemical techniques to investigate two carbazole-based donor–acceptor CT type copolymers, poly[4,7-(2,1,3-benzothiadiazole)-3,6-(N-(2-methyl)carbazole)] (PCzBTDZ) and poly[4,7-(2,1,3-benzoselenadiazole)-3,6-(N-(2-methyl)carbazole)) (PCzBSeDZ), in which the HOMO–LUMO gaps DH–L), the lowest excitation energies (Eg), ionization potentials (IP) and electron affinities (EA) are fine-tuned by the regular insertion of electron-accepting units, 2,1,3-benzothiadiazole (BTd) and 2,1,3-benzoselenadiazole (BSe), respectively. The results show that the alternated incorporation of electron-accepting moieties BTd and BSe significantly decrease the LUMO energy and thus enhance the EAs and consequently the electron-injection and transporting ability are greatly improved. Meanwhile, since carbazole has good hole transporting ability, the copolymers of a carbazolyl unit and BTd or BSe units possess high electron affinity and low ionic potential and achieve a relative balanced charge injection. In addition, due to the weak interactions between the two building blocks, the two copolymers have rather small energy gap and thus lead to a large bathochromic shift in absorption spectra compared with pristine polyfluorene and polycarbazoles.  2007 Elsevier B.V. All rights reserved. Keywords: Carbazole; Benzothiadiazole; Benzoselenadiazole; DFT; Optical

1. Introduction Materials suitable for application in organic light-emitting diodes have been actively researched in the past decade because of their potential application in flat-panel displays and the academic interest on the structure–property relationship of molecules featuring multiple functional moieties [1]. Recently, increasing interests have been paid to polymers based upon the 3,6-linked carbazole moiety because of their optical properties and good hole-trans-

*

Corresponding author. E-mail address: [email protected] (J.-K. Feng).

0166-1280/$ - see front matter  2007 Elsevier B.V. All rights reserved. doi:10.1016/j.theochem.2007.04.014

porting ability in light-emitting devices [2]. This unit in conjugated polymer chains serves as a conjugation break, which in turn leads to some useful properties. Polycarbazoles have been proved to efficiently suppress the keto defect emission, which leads to both a color instability and reduced efficiency [2a]. Another advantage of polymers containing 3,6-linked carbazole units is the elimination of color dependence on molecular weight [3]. On the other hand, the electrical and optical activity of these polymer electroluminescent materials relies on the ability of the materials to transport electrical charges: electrons and positive holes through their structures. It has been shown that the electron is transferred to the material with higher electron affinity and the hole to the material

162

L. Yang et al. / Journal of Molecular Structure: THEOCHEM 816 (2007) 161–170

with lower ionization potential [4]. p-Conjugated polymers with donor–acceptor architecture are currently of interest because the electron or hole affinities can be enhanced, and the intramolecular charge transfer can lead to small band gap semiconduction polymers for red emission. The polymers consisting of defined hole-transporting (donor) or electron-transporting (acceptor) segments are also interesting because the electron and hole affinities can be enhance simultaneously. Applications of such donor– acceptor copolymers to OLEDs and to bulk heterojunction photovoltaic devices have recently been studied [5]. Much of the motivation for studying polymers stems from the potential to tailor desirable optoelectronic properties and processing characteristics by manipulation of the primary chemical structure. Thus, it is easy to raise or lower the HOMO and LUMO levels including conjugation length control, as well as the introduction of elelctrondonating or -withdrawing groups to the parent chromophore. Regulating the HOMO and LUMO energy levels permits the fine-tuning of charge injection properties [6,7]. In LED, the HOMO/LUMO energy difference directly controls emission frequency, i.e., emission color. In this paper, various compound (Chart 1) [5], are chosen as the partner donor or acceptor and their various copolymers are calculated to optimize the appropriate donor and acceptor moieties. After optimizing, it has been shown that the copolymers derived from substituted-carbazole and Sand Se-containing heterocycles, benzothiadiazole and benzoselenadiazole have rather better charge transporting abilities than others. In this contribution, the electronic and optical properties of carbazole-based donor–acceptor p-conjugated copolymers containing new BTd and BSe units have been investigated by theoretical studies, where BTd and BSe units serves for electron-accepting units because of containing two electron-withdrawing imine

(C@N) nitrogens. Then, we discuss the optical properties of the polymers under study based the longest oligomers. We were particularly interested in exploring the donor– acceptor p-conjugated structural properties and the potential of BTd and BSe units as electron-accepting moieties and the influence of replacement of sulfur atom in the BTd unit with selenium on electronic materials through comparing the energies of HOMO and LUMO and the variation of IPs, EAs and energy gaps of copolymers PCzBTd and PCzBSe with those of the PCz [9] or PF [10] homopolymer. The possible consequences of mixtures of electronaccepting and hole-accepting polymers for the photophysics, light-emitting properties, molecular aggregation and charge transport are very intriguing to us and thus motivated our studies. 2. Computational details Calculations on electronic ground state, cationic and anionic geometries described in this paper were performed at the DFT levels of theory as implemented within the Gaussian 03 software package [11] on the SGI origin 2000 server. Becke’s three-parameter hybrid method using the Lee–Yang–Parr correlation functional was employed (denoted as B3LYP) here, which are have been proved very useful to predict geometries [12] and calculate molecular orbital distributions for the interpretation of electrochemical and photochemical results [13]. Correlation effects can be very important for the study of electronic structure of molecules and should be taken into account particularly when one is interested in the evaluation of the energy gap. In the B3LYP functional, the exchange potential includes some percentage of the exact HF exchange, with the remaining part being described by the Slater functional plus a weighted Becke gradient correction. Furthermore,

Chart 1. CT-type polymers.

L. Yang et al. / Journal of Molecular Structure: THEOCHEM 816 (2007) 161–170

density functional theory (DFT), due to its feature of including the electronic correlation in a computationally efficient manner, can be used in larger molecular systems. In its formalism, the ionization potential and electron affinity are well-defined properties than can be calculated. Since the anionic system whose electron charge distribution becomes much more diffuse and requires the use of a larger basis set (usually including at least one set of diffuse functions). So, we have investigated the basis set by optimizing the geometry of monomer CzBSe with the ‘‘full’’ 6-31G*, hybrid atomic basis set (6-31G* for C, N and H atoms and S and Se with the 6-31+G*) and ‘‘full’’ 6-31+G* basis set, respectively. The results show that the total energies with 6-31G* basis set and with hybrid atomic basis set differ 238.75 kcal/mol and 43.69 kcal/mol from that much larger basis set 6-31+G*, respectively. Moreover, the HOMO–LUMO gaps calculated by 6-31G* basis set and by hybrid atomic basis set differ 0.047 eV and 0.014 eV from that much larger basis set 6-31+G*, respectively. In addition, the CPU time consumed for calculation with hybrid atomic basis set and larger 6-31+G* basis set are about twice and even 11 times, respectively, compared with that with 6-31G* basis set. Considering the huge computational efforts for dimer, trimer and tetramer with larger molecular size, thus, hybrid atomic basis set of 6-31G(d) (C, N and H)/6-31+G(d) (S or Se) was utilized in all calculations, which denoted as 6-31G(d)/6-31+G(d) (S or Se). The investigated polymer (CzBTd)n correspond to copolymers in literature 14, and the main difference is that the oligomers under study substitute ethylhexyl with methyl at 9-position in carbazole, for the sake of reducing the time of calculation. It has been proved that the presence of alkyl groups does not significantly affect the equilibrium geometry and thus the electronic and the optical properties [15]. And PCzBSe is new designed copolymer by our optimal calculations. As already mentioned before, one of the most important features of the p-conjugated polymers is their ability to become highly conducting after oxidative (p-type) or reductive (n-type) [16] doping. So, the optimized cationic and anionic geometries of oligomers in both series of (CzBTDZ)n and (CzBSeDZ)n (n = 1–4) were used to calculate the ionization potential and electron affinity energies which can be used to estimate the ability to accept holes and electrons. There are two widely used theories for describing the charge mobilities in organic materials. One is the formulizm of Gaussian disorders first proposed by Ba¨ssler and co-worker [17]. In this formulizm, the mobilities depend on two key parameters: energy disorder and position disorder. It is difficult to relate these two disorder parameters to molecular properties to provide practical guidelines on the molecular level for designing suitable hole or electron transport material. The transport of charge carriers can also be viewed as an electron hopping process, which can be accounted for by the Marcus electron transfer theory [18]. The intermolecular transfer of hole and electron can be represented by Eq. (1):

163

Fig. 1. The reorganization energy for hole transport (khole) is given by k+ + k0.

Mþ= +M ! M + Mþ=

ð1Þ

+/

indicates the molecule in a cationic In this equation, M or anionic state. M* is a neighboring molecule in a neutral state. According to the semiclassical electron-transfer theory, the rate of electron-transfer Ket can be described to a good approximation as   kþ= 4p2 1 2 DH ab pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi exp  K hole ¼ h 4K b T 4pkþ= T   kþ= ¼ A exp  ð2Þ 4K b T where k is the reorganization energy, DHab is the electronic coupling matrix element between donor and acceptor, Kb is the Boltzman constant, and h is the Planck constant. Besides the terms involving k+/, the DHab term also appears to be important for determining relative hole/electron transfer rate. However, experimentally determined DHab show a rather narrow range of values [19]. Because the intermolecular charge-transfer processes considered in OLEDs involve direct contacts in amorphous solids, an even more limited range of DHab is expected. Therefore, based on this electron-transfer model, the mobilities of electrons and holes should be dominated by their respective reorganization energies k+ and k in the exponential term in Eq. (2) which needs to be small for the efficient transport. We take the cationic molecule as an example to calculate the reorganization energies k+ and the potential energy curve of this reaction is shown in Fig. 1. Thus, khole is given by k+ + k0 = [E+(M*)  E+(M+)] + [E(M+)E(M*)]. Similarly, kelectron is given by k + k0 = [E(M)  E(M)]  [E(M*)  E(M*)]. 3. Results and discussion 3.1. Ground state Among p-conjugated polymers, those containing benzene-fused heteroaromatic rings with nitrogen atom(s),

164

L. Yang et al. / Journal of Molecular Structure: THEOCHEM 816 (2007) 161–170

Fig. 2. Relative HOMO and LUMO energy levels.

so-called poly(benzazole)s (Chart 1), are a class of materials that has shown interesting electrical and optical properties. To test the electron or hole-transporting ability, these benzazoles are incorporated with fluorene and carbazole and the relative HOMO and LUMO energy levels are listed in Fig. 2. For molecules FBTd and FBSe, HOMOs are dramatically lowered compared with molecules FBIm and FBTa, suggesting the electron-transporting properties in the former two have been greatly improved. When fluorene is replaced with carbazole, HOMOs are elevated, but LUMOs are lowered, which facilitate both the hole and electron-transporting ability. The results of Fig. 2 can be easily rationalized by analyzing how the nature of the frontier electronic levels is affected by the incorporation of different benzazoles units (Take molecules CzBSe as examples as shown in Fig. 3). In CzBSe, the LUMO is localized on BSe units; whereas

Fig. 3. Energies and shapes of the HOMO (top) and LUMO (bottom) orbitals of carbazole (Cz), 2,1,3-benzoselenadiazole (BSe) and CzBSe.

L. Yang et al. / Journal of Molecular Structure: THEOCHEM 816 (2007) 161–170

the HOMO remains localized on Cz units in the copolymer which is different from FBSe. The reason is that the energy separations between both the HOMO (1.22 eV) and LUMO (1.92 eV) of Cz and BSe are larger than that of FBSe and lead to rather weaker interactions between the two building blocks (Fig. 3). This charge transfer implies that Cz [9] unit is a better electron-donating charge carrier than F and the BSe serves as electron-accepting functionalities by the presence of the selenium and nitrogen heteroatoms. It is also the reason why the HOMO level of CzBSe is close to that of Cz, whereas the LUMO level is similar with BSe. The results show that such mixtures of electron-accepting and hole-accepting copolymers, could lead to cost-effective, efficient, large-area photodiodes and full color displays by improving both electron and hole-transporting abilities. After comparison and analysis, it can be concluded that carbazole-based copolymers consisting of the 2,1,3-benzothiadiazole and 2,1,3-benzoselenadiazole are the best candidates for the applications of such donor– acceptor copolymers. In this paper, we mainly study the two series of copolymers, namely, PCzBTd and PCzBSe. The selected important inter-ring bond lengths and torsion angles which are between the adjacent carbazole and benzothiadiazole or benzoselenadiazole rings in (CzBTd)n and (CzBSe)n (n = 1  4) in the neutral ground state obtained by B3LYP/6-31G(D)/6-31+G(D) (S or Se) calculations are listed in Table 1. Because the dihedral angle between two phenyl rings in carbazole is fixed by ring bridged-atoms which tend to keep their normal tetrahedral angles in their ring linkage, the carbazole keeps their quasi planar conformation. The biggest torsion angels in (CzBTDZ)n and (CzBSeDZ)n are the inter-ring torsion angles between carbazole and benzothiadiazole or benzoselenadiazole rings. Compared with pristine polycarbazole in which the intra-ring torsion angle is 38, a slightly large twisted angle is observed in both copolymers (39). The ground-state geometry of each oligomer in (CzBTDZ)n is slightly less twisted than that in (CzBSeDZ)n by replacement of sulphur atom in the BTd unit with selenium. The average bond alternation parameters, dinter and dring may furnish useful information relevant to the structures of oligomers and denote the degree of the electronic delocalization. Four bond alternation parameters dring, dinter, d0ring and d0inter , are defined as dring = (raa  rab)/[(raa + rab)/2], dinter = (rbb  rab)/[(rbb + rab)/2], d0ring ¼ ðrcc  rbc Þ=½ðrcc þ rbc Þ=2 and d0inter ¼ ðrbb  rbc Þ=½ðrbb þ rbc Þ=2, respectively, where rbb denotes the inter-ring bond length, and raa and rab are the intra-ring bond lengths in carbazole and rbc and rcc are the intra-ring bond lengths in benzothiadiazole (or benzoselenadiazole) as being labeled in Fig. 4. To facilitate discussing the effects of the introduction of benzothiadiazole and benzoselenadiazole into carbazole, the average interand intra-ring bond alternation parameters for pure polycarbazole [9] are also listed in Table 2. As shown in Table 2, when benzothiadiazole rings are replaced by benzoselenadiazole rings, it is found two

165

Table 1 Selected inter-ring bond distances and torsion angles of (CzBTDZ)n and (CzBSeDZ)n (n = 1–4) calculated by B3LYP/6-31G(d)/6-31+G(d) (S or Se) Oligomer

C–T

T–C

C–T

(CzBTDZ)n n=1 r U

1.482 37.1

n=2 r U

T–C

C–T

1.481 36.3

1.481 37.4

1.482 36.5

n=3 r U

1.480 36.3

1.480 37.1

n=4 r U

1.480 36.9

T–C

C–T

1.480 35.6

1.481 37.2

1.481 37.0

1.481 37.4

1.480 37.4

1.481 37.2

1.480 37.3

1.481 38.8

1.481 37.1

S–C

C–S

S–C

C–S

S–C

C–S

1.481 39.0

1.482 38.9

(CzBSeDZ)n

C–S

n=1 r U

1.482 39.2

n=2 r U

1.481 38.6

1.482 39.0

1.482 38.5

n=3 r U

1.481 39.1

1.481 39.4

1.481 38.7

1.482 39.8

1.482 38.7

n=4 r U

1.482 38.2

1.482 39.4

1.481 38.2

1.481 38.9

1.481 38.0

Note: C means the carbazole ring and T and S are the BTd and BSe rings in every molecule.

Fig. 4. Definition of bond length alternation (BLA).

Table 2 Average bond alternation parameters (d)a Oligomer

dring

dinter

d0inter

d0ring

(CzBTDZ)n (CzBSeDZ)n (Cz)n

0.006 0.006 0.006

0.054 0.055 0.057

0.069 0.072

0.032 0.037

a dring and d0ring are the average intra-ring bond alternation parameters over carbazole and benzothiadiazole (or benzoselenadiazole) rings, dinter and d0inter are the average inter-ring bond alternation parameters, respectively.

L. Yang et al. / Journal of Molecular Structure: THEOCHEM 816 (2007) 161–170

influences on the ring geometries. One effect is that the bond alternations over benzoselenadiazole rings in (CzBSeDZ)n become larger. It is reflected by the larger d0ring (0.037) in (CzBSeDZ)n than that of the (CzBTDZ)n ðd0ring ¼ 0:035Þ. Another effect is that d0inter in (CzBSeDZ)n (0.072) also tends to be larger than that of (CzBSeDZ)n (0.059). That explicates the reason the inclusion of benzoselenadiazole (BSe) group lowers the band gap compared with the copolymers with benzothiadiazole (BTd). In addition, compared with polycarbazole, it is obvious that the inter-ring bond alternation parameter in both (CzBTDZ)n (0.069) and (CzBSeDZ)n (0.072) are larger than that in polycarbazole (0.057), and therefore, the introduction of benzothiadiazole (or benzoselenadiazole) rings gives rise to the local geometrical distortions along the backbones of copolymers, making it possible to form the conjugational defects and to provoke a significant decrease in the band gaps of such acceptor/donor systems (see Section 3.3). It will be useful to examine the highest occupied orbitals and the lowest virtual orbitals for these oligomers and polymers because the relative ordering of the occupied and virtual orbitals provides a reasonable qualitative indication of the subsequent excitation properties [20] and of the ability of electron or hole transport. The electron density isocontours of HOMO and LUMO of the oligomers in (CzBTDZ)4 and (CzBSeDZ)4 (n = 1–4) are plotted in Fig. 5. It can be seen that an asymmetric character prevails for the HOMO in (CzBTDZ)4 and (CzBSeDZ)4 and the localization of electronic cloud distributing in the side part of HOMOs is typically expected due to chain-end effects. In contrast, the shapes of the LUMOs become different, are localized on the benzothiadiazole or benzoselenadiazole units, as a result of the weak interactions between the two building blocks. When replace of sulfur atom in the

BTd unit with selenium, LUMOs become rather strongly confined to one benzoselenadiazole unit due to the rather large electronegative. This implies that benzothiadiazole and benzoselenadiazole units serve as electron-accepting functionalities and it is anticipated that (CzBTDZ)n and (CzBSeDZ)n have enhanced electron affinities. In experiment, the HOMO and LUMO energies were calculated from one empirical formula proposed by Bre´das et al., based on the onset of the oxidation and reduction peaks measured by cyclic voltammetry, assuming the absolute energy level of ferrocene/ferrocenium to be 4.4 eV below vacuum [16]. Whereas the HOMO and LUMO energies can be calculated accurately by density functional theory (DFT) in this study. Fig. 6 describes the evolution of the B3LYP/6-31G(d)/631+G(d) (S or Se) calculated highest occupied molecular

-1.0 -1.5 LUMO

-2.0 -2.5 Energy (eV)

166

-3.0 -3.5 -4.0 -4.5 HOMO

-5.0 -5.5 -6.0 -6.5 0.0

0.2

0.4

0.6 1/n

0.8

1.0

1.2

Fig. 6. B3LYP/6-31G(d)/6-31+G(d) (S or Se) calculated HOMO and LUMO energies of (CzBTDZ)n (. . ... . .) and (CzBSeDZ)n (. . .m. . .) and PCz (. . .n. . .) oligomers as a function of the inverse number of monomer units.

Fig. 5. The HOMO and LUMO orbitals of (CzBTDZ)n and (CzBSeDZ)n (n = 4) by B3LYP/6-31G(d)/6-31+G(d) (S or Se).

L. Yang et al. / Journal of Molecular Structure: THEOCHEM 816 (2007) 161–170

orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) energies as a function of the inverse number of monomer units in (CzBTDZ)n and (CzBSeDZ)n. For the sake of comparison, the frontier energy levels of (Cz)n (n = 2–7) are also listed in Fig. 6. As is usual in p-conjugated systems, the energy of the frontier electronic levels evolves linearly with inverse chain length in the four systems: the HOMO energies increase, whereas the LUMO energies decrease [21]. Similar energies are obtained for the HOMO energy level of PCzBTDZ and PCzBSeDZ and PCz [9], indicating hole-accepting properties do not worsen. Turning to the evolution of the LUMO levels, the LUMO of PCzBTDZ and PCzBSeDZ are generally stabilized by about 1.7 eV with respective to PCz chains due to the incorporation with the electron-accepting benzothiadiazole and benzoselenadiazole moieties, indicating that the electron-accepting BTd and BSe units significantly improve the electron-accepting properties and result in more efficient charge carrier balance. 3.2. Ionization potentials and electron affinities One general challenge for the application of polymers in PLEDs is achievement of high electron affinity (n-type) conjugated polymers for improving electron injection/ transport and low ionization potential (p-type) conjugated polymers for better hole injection/transport in polymer electronic devices. For PCzBTDZ and PCzBSeDZ, the energies required to create a hole in the polymers are both around 5.4 eV. While the extraction of an electron from the anion requires average 2.16 eV and 2.23 eV by three methods for PCzBTDZ and PCzBSeDZ, respectively, which dramatically decreased about 1 eV than PF (1.2 eV)

167

[10]. Thus, electron injection and transportation PCzBTDZ and PCzBSeDZ are expected to be enhanced compared to PF and as a consequence the charge carrier balance is better in the devices constructed from the copolymers. We take (CzBSe)4 as an example to plot the spin densities of cation and anion in Fig. 7. As shown in the cation spin density, the spin density largely shares on the whole molecule. This is consistent with the HOMO being primarily the p* orbitals. In the two series of polymers, the unpaired spin density is totally on moiety BSe, which basically consists with the analysis of LUMO composition. Our calculations of the reorganization energy khole and kelectron associate with different geometries of these two states are based on the hopping model schematically illustrated in Fig. 8. In PCzBTd, the reorganization energy computed for hole khole is 0.28 eV, while for electron kelectron is 0.14 eV. The value of khole in PCzBSe is slightly smaller than that of PCzBTd. This indicates that PCzBSe has better hole transport ability than PCzBTd from the standpoint of reorganization energy. The value of kelectron in PCzBSe is smaller than that in PCzBTd, indicating that the former one is a better electron transporter. The smaller kelectron in both PCzBSe and PCzBTd would suggest that the carrier mobilities of electron are larger than that of the hole. This indicates that BTd and BSe moieties are functioned as a electron transport group and carbazole as a hole transport group, which can be rationalized by HOMO and LUMO orbital character and ionic spin density. A crucial feature is that the LUMO and anionic spin density are strongly localized on BTd or BSe moieties, due to the involving of two electron-withdrawing imine(C@N) nitrogens. Furthermore, PCzBSe has superior hole and electron mobilities than PCzBTd by replacement

Fig. 7. Spin density of cation (up) and anion (down) of (CzBSeDZ)4.

168

L. Yang et al. / Journal of Molecular Structure: THEOCHEM 816 (2007) 161–170

solid-state effects (like polarization effects and intermolecular packing forces) have been neglected in the calculations. The latter can be expected to result in a decreased inter-ring twist and consequently a reduced gap in a thin film compared to an isolated molecule as considered in the calculations [22,23]. Comparing the calculated values of PCz with PCzBTdDZ and PCzBSeDZ, we can find the influence of BTd and BSe onto carbazole. The energy gaps obtained by HOMO–LUMO gaps and TD-DFT are 3.42 and 3.08 eV for PCz [9], respectively, which are both higher than that in (CzBTdDZ)4 with the values of 2.70 and 2.38 eV and that in (CzBSeDZ)4 of 2.56 and 2.23 eV with the same corresponding methods, suggesting electronaccepting moieties BTd and BSe significantly decrease the energy gaps of carbazole-based copolymers. Furthermore, on all accounts, the results of both methods indicate that the energy gaps in PCzBTdDZ are all higher than that of PCzBSeDZ, due to the larger inter-ring torsional angels between the two adjacent units in the latter one and it can be concluded that the breaking of the conjugation in the backbone narrowed its energy gap. 3.4. Absorption spectra Fig. 8. Sketch map of reorganization energy for copolymers PCzBTd and PczBSe.

of sulfur atom in the BTd unit with selenium atom. The results indicate that PCzBSe would act as both charge transport and emitter materials. 3.3. HOMO–LUMO gaps and the lowest excitation energies The energy gap has been estimated from two ways, namely, HOMO–LUMO gaps (DH–Ls) and the lowest excited energies (Egs). Obviously, the Egs presented in Table 3 yield a good agreement with the experimental data than DH–L in both oligomers in this study [8]. However, there are still errors between the calculated results and the experimental values from the edge of the electronic band; this discrepancy is in part due to the relatively large size of the studied systems and the reciprocal dependence of the energy gap on the number of repeat units usually observed in organic systems. Another factor responsible for deviations by both methods from experimental is that the predicted band gaps are for the isolated gas-phase chains, while the experimental band gaps are measured in the liquid phase where the environmental influence may be involved. Additionally, it should be borne in mind that Table 3 The HOMO–LUMO gaps (DH–Ls) (eV) by B3LYP and the lowest excitation energies (Egs) (eV) by TDDFT of (CzBTDZ)n and (CzBSeDZ)n Oligomers (CzBTd)n n=4

DH–L 2.70

Eg (TD) 2.38

Expl. [14]

Oligomers

DH–L

Eg (TD)

2.30

(CzBSe)n n=4

2.56

2.23

The TDDFT has been used on the basis of the optimized geometry to obtain the nature and the energy of absorption spectra in PCzBTd and PCzBSe, as reported in Table 4. Two interesting trends can be observed in both series of oligomers: (1) the oscillator strengths (f) of the lowest S0 fi S1 electronic transition are the largest in both series of oligomers, except for the monomer of PCzBTd and PCzBSe; (2) the oscillator strength coupling the lowest CT p–p* singlet excited state to the ground state increase strongly when going from an isolated molecule to a molecular group and this trend goes along with the conjugation lengths increasing; (3) the absorption wavelengths arising from S0 fi S1 electronic transition increase progressively with the conjugation lengths increasing. The results show that slightly longer maximal absorption wavelength in the series of PCzBSe are observed than that of PCzBTd. Compared with PCz (379 nm by TDDFT), [9] the absorption spectra of PCzBTd and PCzBSe exhibit bathochromic shift by the introduction of moieties BTd and BSe. 4. Conclusion The introduction of BTd and BSe units into p-conjugated polycarbazole backbone has improved the electrontransporting ability due to the presence of two electronwithdrawing imine(C@N) nitrogens. The more nonplanar structural properties in PCzBSe are observed than that in PCzBTd by replacement of sulfur atom with selenium. All decisive molecular orbitals are delocalized on all subunits of the oligomers. An asymmetric character prevails for the HOMO and the localization of electronic cloud

L. Yang et al. / Journal of Molecular Structure: THEOCHEM 816 (2007) 161–170

169

Table 4 Electronic transition data for (CzBTd)n and (CzBSe)n Electronic transitions

Wavelengths (nm)

f

MO/character

Coefficient

CzBTd S2 ‹ S0

443.10

0.1628

HOMO1 fi LUMO

0.67

(CzBTd)2 S1 ‹ S0

495.04

0.6770

HOMO fi LUMO

0.60

(CzBTd)3 S1 ‹ S0

514.78

1.1907

HOMO fi LUMO

0.61

(CzBTd)4 S1 ‹ S0

520.88

1.7161

HOMO fi LUMO HOMO fi LUMO + 1

0.56 0.304

474.56

0.1348

HOMO1 fi LUMO

0.65

529.04

0.5452

HOMO fi LUMO HOMO fi LUMO + 1

0.59 0.31

(CzBSe)3 S1 ‹ S0

544.55

0.9248

HOMO fi LUMO HOMO fi LUMO + 1

0.57 0.32

(CzBSe)4 S1 ‹ S0

556.90

1.4245

HOMO fi LUMO HOMO fi LUMO + 1

0.54 0.33

CzBSe S2 ‹ S0 (CzBSe)2 S1 ‹ S0

a

Experiment wavelengths (nm)

465a

UV–visible absorption spectra measured for thin films in Ref. [14].

distributing in the side part of HOMOs is typically expected due to chain-end effects. In contrast, the shapes of the LUMOs are localized on the benzothiadiazole or benzoselenadiazole units, as a result of the weak interactions between the two building blocks. The spin densities in the cations show that the electron prevails over the whole molecule, which is basically consistent with the analysis of HOMO character. The lowest virtual orbitals are totally BTd and BSe in character, as also reflected in the spin densities in the anion. Importantly, the donor–acceptor copolymers not only enhance the optical stability and thus increase fluorescence quantum yields, but also improve the electron injection and more efficient charge carrier balance due to the lower LUMO levels, the higher EAs and small reorganization energies, compared with those of conventional polyfluorene or polycarbazole materials. These two points are both essential for light-emitting polymers, and provide the opportunity of tuning the electronic and optical properties of the resulting polymers. Our calculated results also indicate that the incorporation with electron-withdrawing moieties CzBTd and CzBSe will reduce the band gaps of carbazole-based copolymers due to the nonplanar structure in PCzBTd and PCzBSe. The absorption spectra of (CzBSe)n exhibit red-shifted compared with (CzBTd)n ascribed to the replacement of sulphur atom with selenium. Acknowledgement This work is supported by the Major State Basis Research Development Program (No. 2002CB 613406).

References [1] S.A. Jenekhe, J.A. Osaheni, Science 265 (1994) 765; J.-F. Morin, S. Beaupre´, M. Leclerc, et al., Appl. Phys. Lett. 80 (2002) 341; M. Grell, D.D.C. Bradley, M. Inbasekaran, et al., Adv. Mater. 9 (1997) 798; D. Sainova, T. Miteva, H. Nothofer, et al., Appl. Phys. Lett. 76 (2000) 1810; Q. Peng, Z.Y. Lu, Y. Huang, et al., Macromolecules 37 (2004) 260; W. Yu, Y. Cao, J. Pei, et al., J. Appl. Phys. Lett. 76 (2000) 2502. [2] J.P. Lu, Y. Tao, M. D’Iorio, et al., Macromolecules 37 (2004) 2442; J.F. Morin, M. Leclerc, Macromolecules 3 (2001) 4680; J.F. Morin, M. Leclerc, Macromolecules 35 (2002) 8413; G. Zotti, G. Schiavon, S. Zecchin, et al., Macromolecules 35 (2002) 2122; M. Belleteˆte, J. Bouchard, M. Leclerc, et al., Macromolecules 38 (2005) 880. [3] D. Witker, J.R. Reynolds, Macromolecules 38 (2005) 7636. [4] (a) X.–C. Li, Y. Liu, M.S. Liu, A.K.-Y. Jen, Chem. Mater. 11 (1999) 1568–1575; (b) K. Oyaizu, T. Iwasaki, Y. Tsukahara, E. Tsuchida, Macromolecules 37 (2004) 1257; (c) Q. Peng, Z.Y. Lu, ; Y. Huang, M.G. Xie, S.H. Han, J.B. Peng, Y. Cao, Macromolecules 37 (2004) 260; (d) N.C. Yang, S.M. LEE, Y.M. Yoo, J.K. Kim, D.H. Suh, J. Poly. Science: Part A 2 (2004) 1058. [5] T. Yasuda, T. Imase, T. Yamamoto, Macromolecules 38 (2005) 7378. [6] R.Q. Yang, R.Y. Tian, W. Yang, Y. Cao, Macromolecules 36 (2003) 7453; A. Bonat-Bouillud, L. Mazerolle, P. Gagnon, et al., Chem. Mater. 9 (1997) 2815; R.K. Khanna, Y.M. Jiang, B. Srinivas, et al., Chem. Mater. 5 (1993) 1792; S.J. Wang, W.J. Oldham, R.A. Hudack, G.C. Bazan, J. Am. Chem. Soc. 122 (2000) 56951;

170

[7]

[8] [9] [10] [11] [12] [13]

[14] [15]

L. Yang et al. / Journal of Molecular Structure: THEOCHEM 816 (2007) 161–170 C. Roux, J.Y. Bergeron, M. Leclerc, Macromol. Chem. 194 (1993) 869; P. Blondin, J. Bouchard, S. Beaupre´, et al., Macromolecules 33 (2000) 5874. X. Zhou, A.M. Ren, J.K. Feng, Polymer 45 (2004) 7705; K.T. Wong, C.F. Wang, C.H. Chou, Y.O. Su, et al., Org. Lett. 4 (2002) 4439–4442. J. Huang, Y.H. Niu, W. Yang, Y.Q. Mo, M. Yuan, Y. Cao, Macromolecules 35 (2002) 6080. L. Yang, J.K. Feng, A.M. Ren, J.Z. Sun, Polymer 47 (2005) 1397. J.F. Wang, J.K. Feng, A.M. Ren, X.D. Liu, Y.G. Ma, et al., Macromolecules 37 (2004) 3451. M.J. Frisch et al., Gaussian 03, Revision B.04, Gaussian, Inc., Pittsburgh, PA, 2003. S. Lee, B.H. Boo, J. Phys. Chem. 100 (1996) 15073–15078. J. Zhang, G. Frenking, J. Phys. Chem. A 108 (2004) 10296–10301; J. Ma, S. Li, Y. Jiang, Macromolecules 35 (2002) 1109–1115; J.K. Yu, W. Chen, C. Yu, J. Phys. Chem. A 107 (2003) 4268–4275. J. Huang, Y.-H. Niu, W. Yang, et al., Macromolecules 35 (2002) 6080–6082. J.B. Foresman, M. Head-Gordon, J.A. Pople, J. Phys. Chem. 96 (1992) 135;

[16] [17]

[18]

[19]

[20] [21]

[22] [23]

M. Belleteˆte, S. Beaypre´, J. Bouchard, et al., J. Phys. Chem. B 104 (2000) 9118. J.-L. Bre´bdas, R. Silbey, D.-S. Boudreaux, R.-R. Chance, J. Am. Chem. Soc. 105 (1983) 6555–6559. H. Ba¨ssler, Phys. Stat. Sol. B 175 (1993) 15; E. Lebedev, T. Dittrich, V. Petrova-Koch, et al., Appl. Phys. Lett. 71 (1997) 2686; S. Barth, P. Muller, H. Riel, et al., J. Appl. Phys. 89 (2001) 3711. R.A. Marcus, J. Chem. Phys. 24 (1956) 966; R.A. Marcus, J. Chem. Phys. 43 (1956) 679; P.F. Barbara, T.J. Meyer, M.A. Ratner, J. Phys. Chem. 100 (1996) 13148. S.F. Nelsen, D.A. Trieber, R.F. Ismagilov, Y. Teki, J. Am. Chem. Soc. 123 (2001) 5684–5694; S.F. Nelsen, F. Blomgren, J. Org. Chem. 66 (2001) 6551–6559. A.DeO. Marcos, A.D. He´lio, J.M. Pernaut, B. De. Wagner, J. Phys. Chem. A 104 (2000) 8256–8262. J. Cornil, I. Gueli, A. Dkhissi, J.C. Sancho-Garcia, E. Hennebicq, J.P. Calbert, V. Lemaur, D. Beljoone, J.L. Bre´das, J. Chem. Phys. 118 (2003) 6615–6623. P. Puschning, C. Ambrosch-Draxl, G. Heimel, et al., Synth. Met. 116 (2001) 327. V.J. Eaton, D. Steele, J. Chem. Soc. Faraday Trans. 2 (1973) 1601.