Structural, electronic and optical properties of a series of oligofluorene–thiophene oligomers and polymers

Structural, electronic and optical properties of a series of oligofluorene–thiophene oligomers and polymers

Journal of Molecular Structure: THEOCHEM 758 (2006) 29–39 www.elsevier.com/locate/theochem Structural, electronic and optical properties of a series ...

403KB Sizes 1 Downloads 61 Views

Journal of Molecular Structure: THEOCHEM 758 (2006) 29–39 www.elsevier.com/locate/theochem

Structural, electronic and optical properties of a series of oligofluorene–thiophene oligomers and polymers Li Yanga, Ji-Kang Fenga,b,*, Ai-Min Rena 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 7 April 2005; revised 30 June 2005; accepted 30 June 2005

Abstract A significant drawback of thiophene oligomers are their low fluorescence and poor stability, especially in solid state. To overcome this problem, end-capped oligofluorene–thiophenes were synthesized. By adjusting the conjugation length of the thiophene units between the two fluorenes, it is possible to fine-tune the energy level and emission color of the resulting materials. In this contribution, we apply quantumchemical techniques to investigate a series of oligomers and polymers based on end-capped oligofluorene–thiophenes. The optimized structures, the characterization of frontier molecular orbitals, HOMO–LUMO gaps (DH–L), in addition to the ionic potentials (IP) and electron affinity (EA) were obtained by B3LYP/6-31G density functional theory (DFT) calculations. The lowest excitation energies (Eg) and the maximal absorption wavelength labs of the oligomers are studied employing the time dependent density functional theory (TD-DFT). The DH–Ls, Egs, IPs and EAs of the polymers were obtained by extrapolating those of the oligomers to the inverse chain length equal to zero (1/nZ0). The outcomes show that both the hole and electron accepting and transporting properties in polymers are better than that in oligomers. As the conjugation lengths increase the energy gaps decrease and thus the absorption spectra exhibit bathochromic shift. q 2005 Elsevier B.V. All rights reserved. Keywords: Fluorene; Thiophene; Oligomer; Polymer; DFT

1. Introduction Conjugated polymers are now considered as a very important class of electroactive and photoactive materials. Some of these polymers exhibit physical properties, which lend themselves to the development of display devices, transistors, sensors, etc. [1–3]. Among these applications, the development of flexible and tunable polymeric lightemitting diodes (PLEDs) has received a great deal of attention from both academic and industrial laboratories [4–7]. During the past decade, thiophene-based electronic materials have been extensively investigated. The ease in chemical modification of their structures can potentially allow us to fine-tune their optical and electronic properties [8–12]. These properties strongly depend on the degree of electronic delocalization present in these materials, effective conjugation length (ELC), and the introduction of * Corresponding author.

0166-1280/$ - see front matter q 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.theochem.2005.06.047

substituents at specific positions. However, a significant drawback of oligothiophenes is their low fluorescence and poor stability, especially in solid states [13]. On the other hand, oligofluorenes show much higher fluorescent efficiency and better stability due to their rigid structure and lower HOMO level compared to thiophene oligomers. These materials have been used for LED’s. Le´vesque et al. [14] demonstrated a series of fluorene-based copolymers and the incorporation with thiophene and phenylene moieties leads to the tenability of the electroluminescent poperties. Beaupre´ et al. [15] have successfully synthesized three processable copolymers by Suzuki coupling between functionalized fluorenes and oligothiophenes, which seemed to be a promising candidate for the fabrication of red-light-emitting diodes. In order to rationalize the experimentally observed properties of known materials and to predict those of unknown ones, theoretical investigations on the structures and electronic spectra and emissive properties of these materials are indispensable. In the past decades, ab initio and semiempirical levels were applied to analysis various properties of oligomers and polymers. Schulten et al. [16]

30

L. Yang et al. / Journal of Molecular Structure: THEOCHEM 758 (2006) 29–39

presents a multireference double excitation configuration interaction method (MRD-CI) and employ a Pariser-ParrPople (PPP) model Hamiltonian in polyenes. Bre´das [17] used HF semiemprical AM1 and INDO level to predict nonlinear optical response and simulate the frequencydependent response in poly(paraphenylenevinylene). Recently, a series of polymers were studied employing DFT/B3LYP/6-31CG(d) method by Jiang. [18] However, with the growing molecular size from monomer to oligomers, it is very difficult to use a high level of theory to treat these systems. Here, we report the electronic and optical properties of a series oligofluorene–thiophene derivatives [19] as shown in Fig. 1, including the ground-state conformation, ionization potentials and electronic affinities, as well as the excited states using density functional theory (DFT), time-dependent DFT (TDDFT) and singlet configuration interaction (CIS) methods. [20,21] By adjusting the conjugation length of the thiophene units between the two fluorenes, it is possible to fine-tune the energy level and emission color of the resulting materials and to finetune the optical and electronic properties, oligothiophenes ranging from one to eight moieties were introduced in conjugated linkage with two fluorene units. Through a lot of experimental studies, it can be concluded that many properties of polymers tend to vary linearly as functions of reciprocal chain lengths, such as IP and EA [23], Eg (energy gap) [24] and absorption wavelengths [25]. This experimentally well-known reciprocal rule has been successfully employed to investigate the properties for the oligomers and polymers in theory. [18,26–32] Because the thiophene segments in the series are not the repeated units of oligomers, the chain dependence of the electronic and optical properties in polymers including HOMO– LUMO gaps, the lowest excitation energies, IPs and EAs, do not follow the usual linear 1/n rule. We have used three plotted points closest to polymer to plot lines; and extrapolated the resultant linear relationship to infinite chain length, and finally obtained the relative properties of polymers [18,22]. Hutchison et al. [33] pointed out that this empirical relationship, however, provides an incomplete picture for very long oligomers and the infinite polymer since it does not correctly express the actual asymptotic behavior. Because when the oligomers having up to more unit cells, the bond-lengths alternation in the system converges to the infinite value, while the band gaps still decrease smoothly. Therefore, it can be suggested that the empirical 1/N relationship may yield

Fig. 1. Molecular structure of the oligofluorene–thiophene derivatives.

a better fit for very short oligomers because of the slight variations in the carbon-backbone bond lengths. The band gaps of the isolated, infinite-length polymers lie significantly higher in energy than the extrapolated values from oligomers, due to saturation effects as the band gap becomes roughly constant at some large length. It is also pointed out that TDDFT systematically underestimated the excitation energies by 0.2–0.5 eV comparing to the experimental results due to the limitation of the current approximate exchange-correlation functionals in correctly describing the exchange-correlation potential in the asymptotic region. [34,35] However, reasonable results can still be expected here, because (1) we use the HF/DFT hybrid functionals B3LYP, which could partially overcome the asymptotic problem [18,36,37] and because (2) we study the homologous fluorene-oligomer-based oligomers and polymers, with our interests in their modulation of electronic and optical properties by adjusting the conjugation length of the of the thiophene units between the two fluorenes.

2. Computational details All calculations on these oligomers studied in this work have been performed on the SGI origin 2000 server using Gaussian 03 program package [38]. The ground-state geometry of each oligomer has been determined by a full optimization of its structural parameters. There is no symmetric constraint on the geometric optimization. Calculations on the electronic ground state, as well as the cationic and anionic structures of oligomers were carried out using density functional theory (DFT), B3LYP/6-31G. These minimizations have been performed until the rms residual force is lower than 3!10K4 a.u. (this corresponds to the default threshold in Gaussian 03). Therefore, the optimized geometries were calculated for the various charged states (cationic, anionic, and neutral). Also, the energies for the different charged states in the relevant geometries were obtained for calculating various ionization potentials (IPs) and electronic affinities (EAs). The excited geometries were optimized by ab initio CIS/ 6-31G. The energy gap has been estimated from two ways, namely, HOMO–LUMO gap and the lowest excited energies. The transition energies will be calculated at the ground state and excite-state geometries using TD-DFT/ B3LYP calculations, and the results are compared with the available experimental data. Then we apply the experimentally well-known reciprocal rule for polymers. A distinct advantage of this approach is that it can provide the convergence behavior of the structural and electronic properties of oligomers, since the exact length distributions and geometries of long-length conducting polymers are usually not well characterized.

L. Yang et al. / Journal of Molecular Structure: THEOCHEM 758 (2006) 29–39

31

Fig. 2. The optimized geometries of DHF2TF (a) and DHF4TF using B3LYP (b).

3. Results and discussions 3.1. Ground-state geometry The sketch map of the structures for DHFnTF (nZ1–8) is depicted in Fig. 1. The side hexyl groups inserted on thiophene have been replaced by methyl, respectively, for the sake of reducing the time of calculation, which has been proved that the presence of alkyl groups does not significantly affect the equilibrium geometry and thus the optical properties [39,40]. To determine the minimum energy configuration as well as energy differences between the planar- and nonplanar-conformation, we perform geometrical optimizations on DHFnTF (nZ2 and 4) with B3LYP/6-31G with the geometry restricted to be planar. The results show that nonplanar conformation is more stable than the planar conformation by around 7.5 and 12.6 Kcal/ mol for DHF2TF and DHF4TF, respectively. Furthermore, the inter-ring distances are nearly unchanged between the planar and non-planar conformations. The calculated parameters in thiophene ring change little with the increase of chain length in the series of DHFnTF (nZ1–8). We take the DHF2TF and DHF4TF as examples and show the bond lengths and bond angles in Fig. 2. Comparing DHF2TF with DHF4TF, the increase of conjugation lengths of thiophene has little effect on the parameters in thiophenes and nearly unchanged in fluorene structures. Table 1 collects the torsion angles between two adjacent thiophenes and the angles between thiophene and fluorene units, as well as the dipole moments. As shown in Table 1, the torsion angles between thiophene and fluorene at the both ends of

the oligomers are largest in the range of 16.9–21.38. This result is consistent with the experimental observation of the similar systems reported by Wong et al., [41] in which the torsional angle is around 21.58, slightly larger than ours due to the steric effect induced by phenyl on 9 position of fluorene. With the increasing of the thiophene units, there is a significant reduction in the inter-ring torsional angles in the center of the oligomer compared to the outside. For example, the inter-ring torsional angle between the two adjacent thiophenes in DHF8TF is nearly zero degree at the center and 2.48 at the end. Similar variation trends have been found for polythieno[3,4-b]benzene and polythieno[3,4-b]pyrazine.[29] In general, crystalline oligothiophenes are found to be nearly planar as a result of more favorable crystal packing [42]. The DFT-optimized geometries are in excellent agreement with the solid-state structure. Fig. 3 reports the overall summations of the natural population analysis (NAP) atomic charges on different molecular domains. B3LYP/6-31G calculations reveals an interesting even/odd feature regarding the ‘electrostatic picture’ of the oligofluorene–thiophene systems even in the pristine state, two end fluorene moieties are dominantly charged positively, while the relay is charged negatively twice the amount, as if a intermolecular charge transfer (ICT) should take place between the end and central parts. On the other hand, we also observe that the outermost thienyl units (namely, the two thiophenes adjacent to fluorene) are always dominantly charged negatively, whereas the central thiophenes are weakly negatively charged to a similar amount with each other with

Table 1 Selected important dihedral angles and dipole moments of DHFnTF (nZ1–8) obtained by DFT//B3LYP/6-31G calculations Oligomer

F–T

T–T

DHFnTF nZ1 nZ2 nZ3 nZ4 nZ5 nZ6 nZ7 nZ8

21.3 18.8 19.3 19.7 17.4 19.4 16.9 18.4

0.1 2.8 0.9 3.6 0.9 3.4 2.4

T–T

2.2 0.1 0.7 0.1 0.5 0.9

T–T

0.8 1.2 0.0 1.0 0.3

T–T

1.3 0.0 0.1 0.0

T–T

1.0 0.9 0.3

T–T

1.5 0.9

T–T

T–F

2.5

20.9 18.8 18.3 20.0 19.5 19.2 19.7 18.2

32

L. Yang et al. / Journal of Molecular Structure: THEOCHEM 758 (2006) 29–39

Fig. 3. Overall summation (in e) of the B3LYP/6-31G natural population analysis (NAP) atomic charges on fluorene or thiophene domains for each oligomer.

the increasing thiophene conjugation lengths. This result indicates that the increasing thienyl units between the two fluorene has little contributions to the ICT. 3.2. Front molecular orbitals 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 excitation properties [43] and of the ability of electron or hole transport. Because the first dipole-allowed electron transitions, as well as the strongest electron transitions with largest oscillator strength correspond almost exclusively to the promotion of an electron from HOMO to LUMO, we have plotted the contour plots of HOMO and LUMO

orbitals of DHFnTF (nZ1–8) by B3LYP/6-31G in Fig. 4. As shown that the frontier orbitals spread over the whole p-conjugated backbone in the oligomers with relative short conjugation length (namely, nZ1–2), whereas with the increasing thiophene conjugation lengths (nZ3–8), the electron clouds on the fluorene dramatically decrease and dominantly localized on the thienyl units. These results can be ascribed to the structural characters: the relatively large torsion angles between the two adjacent subunits observed for these oligomers in their ground states; and with the increasing of the thienyl units, the conjugation becomes better presented in the decreasing torsion angles between the tow adjacent thiophenes. This also can be predicted from the NPA atomic charges analysis as above. In the HOMO the ‘CaC’ units are p bonding and have an alternating phase with respect to their neighboring CaC units, whereas

L. Yang et al. / Journal of Molecular Structure: THEOCHEM 758 (2006) 29–39

33

Fig. 4. The contour plots of HOMO and LUMO orbitals of the DHFnTF (nZ1–8).

in the LUMO the ‘CaC’ units are p antibonding and bonding in the bridge single bond. From these calculations, it also becomes apparent that the HOMO and LUMO topologies and sizes are almost identical with the increasing thienyl conjugation lengths, even to the infinite lengths. In experiment, the HOMO and LUMO energies were measured from empirical formula, based on the onset of the oxidation and reduction peaks measured by cyclic voltammetry, assuming the absolute energy level of ferrocene/ferrocenium to be 4.8 eV below vacuum [44– 47]. However, this method has considerable approximation, so theoretical calculations are indispensable and they will provide some useful information for the experiment. Fig. 5 sketches a diagram with the energies of the molecular orbitals around the gap within the series of oligomers.

From Fig. 5 it can be seen that although there are some deviations between the experimental data and calculated results with respect to HOMO and LUMO energies, they have the same trend that with the increasing conjugation lengths the HOMO energies increase, whereas the LUMO energies decrease. This is reasonable, since the HOMO shows inter-ring antibonding character and the LUMO shows inter-ring bonding character. Indeed, the increasing conjugation lengths should reduce the antibonding character between the two subunits and thus destabilize the HOMO. On the other hand, the increase of the planarity between the subunits should enhance the electronic conjugation over the whole molecule and thus stabilize the LUMO. It is noteworthy that the energies of HOMO and LUMO incline to change little with the increasing thienyl conjugation lengths, which indicates

34

L. Yang et al. / Journal of Molecular Structure: THEOCHEM 758 (2006) 29–39

Fig. 5. The frontier molecular orbital energies of DHFnTF (nZ1–8) around the band gap region by B3LYP/6-31G with the experimental data of HOMO and LUMO energies listed in parenthesis [19] for DHFnTF (nZ1–4).

that the last a few points approach the characters of polymers. 3.3. HOMO–LUMO gaps and the lowest excitation energies There are two theoretical approaches for evaluating the energy gap in this paper. One way is based on the groundstate properties, from which the energy gap is estimated from the energy difference between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO), when nZN, termed the HOMO–LUMO gaps (DH–Ls). The TDDFT, which has been used to study systems of increasing complexity due to its relatively low computational cost and also to include in its formalism the electron correlation effects, is also employed to extrapolate energy gap of polymers from the calculated first dipole-allowed excitation energy of their oligomers. In fact, the theoretical quantity for direct comparison with experimental band gap should be the transition (or excitation) energy from the ground state to the first dipoleallowed excited state. The approach to get band gap with orbital energy difference between the HOMO and LUMO is crude considering experimental comparison. The implicit assumption underlying this approximation is that the lowest singlet excited state can be described by only one singly excited configuration in which an electron is promoted from HOMO to LUMO. In addition, the orbital energy difference between HOMO and LUMO is still an approximate estimate to the transition energy since the transition energy also contains significant contributions from some two-electron integrals. However, because the HOMO–LUMO gap is easy

to get, the approach can also be used to provide valuable information on estimate band gaps of oligomers and polymers, especially treating even larger systems. Here, the HOMO–LUMO gaps and lowest singlet excited energies are all listed in Table 2. The relationships between the calculated DH–Ls and the lowest excitation energies and the inverse chain length are plotted in Fig. 6. As a whole, all plotted data do not show a good linearity since the fluorene ring is not in the repeated unit. However, with the increase of conjugation length, the linearity becomes more obvious as shown in Table 2 and Fig. 6. So in order to get the polymeric information, we use the last three points (nZ6–8) to perform a linearity fitting and extrapolate the linear to the infinite chain length. Table 2 The HOMO–LUMO gaps (DH–L)(eV) and the lowest excitation energies (Eg)(eV) of DHFnTF (nZ1–8) and comparison with experimental data DHFnTF

DH–L/eV

Eg(TD)/eV

Eg (exp)/ eV/UVa

Eg (exp)/ eV/Echemb

nZ1 nZ2 nZ3 nZ4 nZ5 nZ6 nZ7 nZ8 nZN

3.86 3.46 2.72 2.53 2.39 2.29 2.21 2.15 1.76

3.15 2.73 2.56 2.37 2.21 2.10 2.02 1.97 1.60

2.77 2.65 2.31 2.25

2.92 2.83 2.43 2.26

a HOMO–LUMO gap (Eg) measured according to the onset of UV absorption of the deposited films. b HOMO–LUMO gap (Eg) measured according to the equation reported by de Leeuw et al. [19].

L. Yang et al. / Journal of Molecular Structure: THEOCHEM 758 (2006) 29–39

35

Fig. 6. The HOMO–LUMO gaps by B3LYP and lowest excitation energies Eg by TD-DFT as a function of reciprocal chain length n in oligomers of DHFnTF (nZ1–8).

In the following parts, we also use the three points closest to polymer to plot lines and extrapolate the resultant linear relationship to infinite chain length; and finally obtained the relative properties (namely, various IPs, EAs, HEPs, and EEPs, et al.) of polymers. As shown in Table 2, in all cases the band gaps extrapolated by not only the lowest excitation energies Egs but also the HOMO–LUMO gaps DH–Ls have the same trend: as the conjugation length increase the energy gaps decrease, which also agree with the trend observed in experiment. Obviously, the TDDFT results presented in Table 2 yield a good agreement with the experimental data than HOMO– LUMO gaps in this study, with the discrepancies within 0.4 eV. As shown in Table 2 the extrapolated energy gaps from TDDFT excitation energies systematically underestimate the actual band gap derived from the solid-state data due to the inherent limitation in TDDFT calculations as mentioned in Section 1. Other two factors may also be responsible for deviations by both methods from experimental. One 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. Another is that it should be borne in mind that solid-state effects (like polarization effects and intermolecular packing forces) have been neglected in the calculations [48]. Furthermore, Kudin et al. [49] pointed out that the idea of fitting a generic oligomer property to a power series in 1/N has been proposed long ago and the alternative extrapolation schemes should be proposed and implemented. They presented a new model to describe linear polarizablility of long polymeric chains. Although in the system under study, the optical properties basically hold the classical empirical ‘1/N’ trend, there still exist limitations of oligomer extrapolation

approximations, such as the extrapolation from the electronic structures of the oligomers cannot accurately model the full band structures of the corresponding polymers, and not readily provide information on the shapes and dispersions of the bands, reveal overlapping bands, or take saturation effects into account and underestimate the band gaps, discussed above. However, as mentioned in the Introduction, our interest is to investigate the variation trend in the modulation of electronic and optical properties by adjusting the conjugation length of the of the thiophene units between the two fluorenes, so in despite of these limitations of the extrapolation methods, it is possible to provide reasonable information. 3.4. Ionization potentials and electron affinities As mentioned in the introduction, efficient injection and transport of both holes and electrons are important parameters for the rational design of optimized lightemitting diodes. Ionization potentials (IPs) and electron affinities (EAs) are used to estimate the energy barrier for the injection of both holes and electrons into the polymer. Table 3 contains the ionization potentials (IPs), electron affinities (EAs), both vertical (v; at the geometry of the neutral molecule) and adiabatic (a; optimized structure for both the neutral and charged molecule), and extraction potentials (HEP and EEP for the hole and electron, respectively) that refer to the geometry of the ions [50– 52]. Fig. 7 displays plots of IPs, EAs, HEPs and EEPs as functions of reciprocal chain lengths for DHFnTF (nZ1–8). As far as the whole trend is concerned, the linearity between them in not perfect because the fluorene is fixed, not the repeated units. But with the increase of thiophene ring, the trend in linearity is observed. So we still considered the last

36

L. Yang et al. / Journal of Molecular Structure: THEOCHEM 758 (2006) 29–39

Table 3 Ionization potentials, electron affinities and extraction potentials for each molecular (in eV) (eV)

IP(v)

IP(a)

HEP

EA(v)

EA(a)

EEP

DHFnTF nZ1 nZ2 nZ3 nZ4 nZ5 nZ6 nZ7 nZ8 nZN

6.41 5.95 5.81 5.71 5.62 5.56 5.49 5.45 5.12

5.99 5.80 5.68 5.58 5.50 5.45 5.40 5.36 5.13

5.86 5.68 5.55 5.45 5.39 5.33 5.30 5.26 5.08

0.42 0.81 1.09 1.29 1.47 1.60 1.71 1.80 2.40

0.61 0.98 1.23 1.43 1.58 1.71 1.81 1.89 2.42

0.74 1.11 1.36 1.55 1.70 1.82 1.91 1.98 2.44

The suffixes (v) and (a), respectively, indicate vertical and adiabatic values.

three points to plot the lines and extrapolating the resulting linear relationship to infinite chain length. The outcomes show that as the fraction of thiophene increases the IPs decrease, indicating the hole injection properties significantly improved, which consists with the estimation of the energies of HOMO. As in the case of IPs,

Fig. 7. IP (v,a)s and HEP (a), EA(v,a) and EEP (b) of DHFnTF (nZ1–8) as a function of reciprocal chain length in oligomers.

with the content of thiophene increase the EAs increase, suggesting the ability to accept electron is also improved as expectation of the energy of LUMO. In general, the energy required to create a hole is w5.1 eV and the extraction of an electron from the anion requires w2.4 eV in the polymer. All in all, both the hole and electron accepting and transporting properties in polymers are better than that in oligomers. 3.5. Absorption spectra The TDDFT//B3LYP/6-31G has been used on the basis of the optimized geometry to obtain the nature and the energy of the singlet–singlet electronic transitions of all the oligomers in the series under study. The first three singlet excited states in DHFnTF (nZ1–8) are listed in Table 4 and compare with the corresponding experimental results. As shown, all electronic transitions are of the pp* type and involve both subunits of the molecule. In other words, no localized electronic transitions are calculated among the first three singlet–singlet transitions. Excitation to the S1 state corresponds almost exclusively to the promotion of an electron from the HOMO to the LUMO. The oscillator strengths (f) of S0/S1 electronic transition are largest. The excitation energies of the next two states are calculated to have considerably weak oscillator strengths. And the oscillator strengths in S0/S2 and S0/S3 are almost zero in the oligomers with even thiophene units due to the transition forbidden resulted from the centrosymmetry. Obviously, the strongest absorption peaks are all assigned to pp* electronic transition character arising exclusively from S 0/S1 electronic transition mainly composed by HOMO/LUMO transition. We can find that with the conjugation lengths increasing, the absorption wavelengths and the oscillator strengths of S0/S1 electronic transition increase progressively. It is reasonable, since HOMO/ LUMO transition is predominant in S0/S1 electronic transition and as analysis above that with the extending molecular size, the HOMO–LUMO gaps decrease. Since the first allowed transitions are also the absorption maximum, they have the same variation trend, which we would not say more than is needed. From Table 4 we find that our absorption spectra by calculations of TDDFT deviates the experimental data. Of course the different medium is one of the reasons, the drawback of TDDFT itself is also the reason. Many investigations show that TDDFT is a good predictive tool for absorption spectra of molecules. However, this method cannot yet be used to study extended systems. It is well known that the failure of TDDFT in the large systems is attributed to the fact that the exchange-correlation potentials generated by the current approximate exchange-correlation functionals decay too rapidly in the asymptotic region. Of course, the simple extrapolation of oligomer optical properties is also responsible for this deviation as described above. However, because the atomic structures of

L. Yang et al. / Journal of Molecular Structure: THEOCHEM 758 (2006) 29–39

37

Table 4 Electronic transition data obtained by the TDDFT//B3LYP/6-31G DHFnTF

Electronic transitions

Wavelengths/ nm

f

MO/character

Coefficient

Wavelengths (exp.)/nm

nZ1

S1)S0 S2)S0

394.20 324.99

1.8152 0.0006

300.55

0.0583

S1)S0 S2)S0

454.27 368.62

2.0816 0.0000

S3)S0

335.76

0.0000

S1)S0 S2)S0

484.94 402.90

2.4423 0.0008

S3)S0

360.02

0.0322

S1)S0 S2)S0

522.89 438.25

2.7139 0.0000

S3)S0

300.55

0.0000

S1)S0 S2)S0

559.95 471.03

3.0842 0.0004

S3)S0

421.68

0.0144

S1)S0 S2)S0

589.05 498.65

3.3744 0.0003

S3)S0

447.49

0.0000

S1)S0 S2)S0

614.86 522.23

3.7532 0.0003

S3)S0

473.25

0.0087

S1)S0 S2)S0

629.51 544.50

4.0123 0.0001

S3)S0

489.51

0.0000

0.66 0.56 0.43 0.47 0.36 0.65 0.57 0.41 0.53 0.36 0.64 0.58 0.41 0.52 0.36 0.64 0.57 0.42 0.52 0.35 0.64 0.57 0.41 0.52 0.35 0.64 0.57 0.41 0.52 0.34 0.65 0.58 0.40 0.53 0.33 0.65 0.59 0.39 0.53 0.32

325

S3)S0

HOMO/LUMO HOMO-1/LUMO HOMO/LUMOC1 HOMO/LUMOC1 HOMO-1/LUMO HOMO/LUMO HOMO-1/LUMO HOMO/LUMOC1 HOMO/LUMOC1 HOMO-1/LUMO HOMO/LUMO HOMO-1/LUMO HOMO/LUMOC1 HOMO/LUMOC1 HOMO-1/LUMO HOMO/LUMO HOMO-1/LUMO HOMO/LUMOC1 HOMO/LUMOC1 HOMO-1/LUMO HOMO/LUMO HOMO-1/LUMO HOMO/LUMOC1 HOMO/LUMOC1 HOMO-1/LUMO HOMO/LUMO HOMO-1/LUMO HOMO/LUMOC1 HOMO/LUMOC1 HOMO-1/LUMO HOMO/LUMO HOMO-1/LUMO HOMO/LUMOC1 HOMO/LUMOC1 HOMO-1/LUMO HOMO/LUMO HOMO-1/LUMO HOMO/LUMOC1 HOMO/LUMOC1 HOMO-1/LUMO

nZ2

nZ3

nZ4

nZ5

nZ6

nZ7

nZ8

350

360

375

The experimental values measured in thin film [19].

the molecules are alike and are calculated with the same methods and basis sets, the results can still reflect some variation trend. As observed in experiment, the calculated results show that with the increasing contents of thiophene the absorption spectra exhibit bathochrome, which also consists with the trend of energy gaps [53,54]. 3.6. The properties of excited structures and the emission spectra It is well known that up to now, the standard for calculating excited state equilibrium properties of larger molecules is the configuration interaction singles (CIS) method. However, due to the neglect of electron correlation, CIS results are not accurate enough in many applications. In this study, we hope to investigate

the excited state properties by this method and in despite of not accurate, we believe it can give some useful information. Because the calculation of excited-state properties typically requires significantly more computational effort than is needed for the ground states and dramatically constrains by the size of the molecules, we only optimize the monomer by CIS/6-31G. In Fig. 8 we compare the excited structures (S1) of DHFTF by CIS/631G with their ground structures by HF/6-31G. Interestingly, the main characters of the front orbitals by HF/631G are same to that by B3LYP/6-31G. As shown, some of the bond lengths lengthened, but some shortened. We can predict the differences of the bond lengths between the ground (S0) and singlet excited state (S1) from MO nodal patterns. Due to the singlet state corresponds to an excitation from the HOMO to the LUMO in

38

L. Yang et al. / Journal of Molecular Structure: THEOCHEM 758 (2006) 29–39

Fig. 8. Comparison of the excited structure (S1) with the ground geometry (S0) of DHFTF.

the considered oligomers, we can explore the bond lengths variation by analyzing the HOMO and LUMO. The HOMO has a node across the r(4,9), r(5,6), r(10,11), r(8,13), r(12,14), r(15,16), r(17,19), r(20,21), r(24,23) and r(22,25) bonds in DHFTF, while the LUMO is bonding. The data confirm the anticipated contraction of these bonds. On the contrary, the HOMO is bonding across r(1,2), r(3,4), r(4,5), r(8,9 0 ), r(9,10), r(11,12), r(12,13), r(14,15), r(16,17), r(19,20), r(19,24), r(21,22), r(22,23), r(25,26), r(25,28) and r(29,30) bonds in DHFTF, but the LUMO has nodes in these regions. Therefore one would expect elongation of these bonds; the data in the figure shows that these bonds are in fact considerably longer in the excited state. The bridge bonds between each conjugation segment rotate to some extent when excited from ground to excited states. The biggest dihedral angle F(11,12,14,15) and F(16, 17,19,20) in DHFTF reduced from 37 and 368 obtained by HF/6-31G method to nearly zero degree by CIS/6-31G, respectively. It is obvious that the excited structure has a strong coplanar tendency in both the series, that is, the conjugation is better in the excited structure, which further approves the predictions from frontier orbitals. On the optimized excited geometries, the emission spectra of the monomer DHFTF are computed by TDDFT. As the case of the absorption spectra, for DHFTF the calculated fluorescence (458 nm) with strongest intensity (1.9540) for S1 arising from HOMO/LUMO pp * excitation is close to the experimental result of 485 nm [19].

4. Conclusion A series of oligomers and polymers based on end-capped oligofluorene–thiophenes are investigated by DFT and TDDFT approaches. With the increasing of the thiophene units, there is a significant reduction in the inter-ring torsional angles in the center of the oligomer compared to the outside. All decisive molecular orbitals are delocalized on both subunits of the oligomers. The HOMO possesses an antibonding character between subunits, which may explain

the nonplanarity observed for these oligomers in their ground state. On the other hand, the LUMO shows bonding character between the two adjacent rings, in agreement with the more planar S1 excited state. Importantly, as the fraction of thiophene increase, the IPs decrease and EAs increase, indicating both the hole and electron accepting properties significantly improved. Excitation to the S1 state corresponds almost exclusively to the promotion of an electron from the HOMO to the LUMO. Accordingly, the energy of the S0/S1 electronic transition follows the HOMO–LUMO energy gap of each oligomer. The first electronic transition gives rise to the largest values of the oscillator strength in each oligomer. The absorption spectra of the alternating oligomers were red-shifted with the adding of the thiophene content. Furthermore, with the thiophene content increasing, energy gap turns to narrow and the absorption spectra exhibits red-shifted. Finally, the good agreement between theoretical electronic transitions and experimental spectra seems to indicate that a rational design the tunable light-emitting fluorene derivatives and related polymers is possible and should then contribute to the development of organic light-emitting diodes.

Acknowledgements This work is supported by the Major State Basis Research Development Program (No. 2002CB 613406).

References [1] H. Shirringhaus, N. Tessler, R.H. Friend, Science 280 (1998) 1741. [2] J.J. Halls, C.A. Walsh, N.C. Greenham, E.A. Marseglia, R.H. Friend, S.C. Moratti, A.B. Holmes, Nature 376 (1995) 498. [3] P.N. Prasad, D.J. Williams, Introduction to Nonlinear Effects in Monomers and Polymers, Wiley, New York, 1991. [4] J.H. Burroughes, D.D.C. Bradley, A.R. Brown, Nature 347 (1990) 539. [5] G. Gustafsson, Y. Cao, G.M. Treacy, F. Klavetter, N. Colaneri, A.J. Heeger, Nature 357 (1992) 477.

L. Yang et al. / Journal of Molecular Structure: THEOCHEM 758 (2006) 29–39 [6] P.L. Burn, A.B. Holmes, A. Kraft, D.D.C. Bradley, A.R. Brown, R.H. Friend, R.W. Gymer, Nature 356 (1992) 47. [7] A. Kraft, A.C. Grimsdale, A.B. Holmes, Angew. Chem., Int. Ed. 37 (1998) 402. [8] D. Fichou (Ed.), Handbook of Oligo- and Polythiophenes, Wiley, New York, NY, 1999. [9] M. Kobayashi, J. Chem, T.C. Chung, F. Moraes, A.J. Heeger, F. Wudl, Synth. Met. 9 (1984) 77–86. [10] T.C. Chung, J.H. Kaufman, A.J. Heeger, F. Wudl, Phys. Rev. B 30 (1984) 702–710. [11] S. Hotta, Molecular conductive materials: polythiophenes and oligothiophenes in: H.S. Nalwa (Ed.), Handbook of Organic Conductive Molecules and Polymers vol. 2, Wiley, Chichester, England, 1997, pp. 309–387. [12] C. Ziegler, Thin film properties of oligothiophenes in: H.S. Nalwa (Ed.), Handbook of Organic Conductive Molecules and Polymers vol. 3, Wiley, Chichester, 1997, pp. 677–743. [13] W. Yu, H. Meng, J. Pel, W. Huang, J. Am. Chem. Soc. 120 (1998) 11808. [14] A. Donat-Bouillud, I. Le´vesque, Y. Tao, M. D’Iorio, Chem. Mater. 12 (2000) 1931–1936. [15] S. Beaupre´, M. Leclerc, Adv. Funct. Mater. 12 (2002) 192. [16] P. Tavan, K. Schulten, J. Chem. Phys. 85 (1986) 6602–6609. [17] D. Beljonne, Z. Shuai, J. Cornil, D.A. dos Santos, J.L. Bre´das, J. Chem. Phys. 32 (1999) 267–276. [18] J. Ma, S.H. Li, Y.-S. Jiang, Macromolecules 35 (2002) 1109–1115. [19] H. Meng, J. Zheng, A.J. Lovinger, B.C. Wang, P.G. Van Patten, Z.N. Bao, Chem. Mater. 15 (2003) 1778–1787. [20] L. Yang, A.M. Ren, J.K. Feng, X.D. Liu, Y.G. Ma, H.X. Zhang, Inorg. Chem. 43 (2004) 5961; L. Yang, A.M. Ren, J.K. Feng, Y.G. Ma, M. Zhang, X.D. Liu, J.C. Shen, H.X. Zhang, J. Phys. Chem. A108 (2004) 6797. [21] L. Yang, A.M. Ren, J.K. Feng, J. Comput. Chem. 26 (2005) 969; L. Yang, A.M. Ren, J.K. Feng, J. Org. Chem. 70 (2005) 3009. [22] J.F. Wang, J.K. Feng, A.M. Ren, X.D. Liu, Y.G. Ma, P. Lu, H.X. Zhang, Macromolecules 37 (2004) 3451. [23] J.L. Bre´bdas, R. Silbey, D.S. Boudreaux, R. Chance, J. Am. Chem. Soc. 105 (1983) 6555–6559. [24] W.K. Ford, C.B. Duke, A. Paton, J. Chem. Phys. 77 (1982) 4564. [25] G. Klaerner, D. Miller, Macromolecules 31 (1998) 2007–2009. [26] J.L. Bre´das, R. Silbey, D.S. Boudreaux, R.R. Chance, J. Am. Chem. Soc. 22 (1983) 6555. [27] W.K. Ford, C.B. Duke, A. Paton, J. Chem. Phys. 77 (1982) 4564. [28] W.K. Ford, C.B. Duke, W.R. Salaneck, J. Chem. Phys. 77 (1982) 5030. [29] O. Kwon, M.L. McKee, J. Phys. Chem. A 104 (2000) 7106. [30] P. Otto, Int. Quantum Chem. 52 (1994) 353. [31] P. Lathi, J. Obrzut, F.E. Karasz, Macromolecule 20 (1987) 2023. [32] G. Zotti, S. Martina, G. Wegner, A. Schlu¨ter, Adv. Mater. 4 (1992) 798; G. Zotti, X. Zhou, A.-M. Ren, J.-K. Feng, Polymer 45 (2004) 7747. [33] G.R. Hutchison, Y.-J. Zhao, B. Delley, A.J. Freeman, M.A. Ratner, T.J. Marks, Phys. Rev. B 68 (2005) 035204. [34] D.-J. Tozer, N.-C. Handy, J. Chem. Phys. 109 (1998) 10180.

39

[35] M.-E. Casida, C. Jamorski, K.-C. Casida, D.-R. Salabub,, J. Chem. Phys. 108 (1998) 4439. [36] Y. Gao, C. Liu, Y. Jiang, J. Phys. Chem. A 106 (2002) 5380. [37] C. Hsu, S. Hirata, H. Martin, J. Phys. Chem. A 105 (2001) 451. [38] M.J. Frisch, G.W. Trucks, H.B. Schlegel, G.E. Scuseria, M.A. Robb, J.R. Cheeseman, J.A. Montgomery, T. Vreven, Jr., K.N. Kudin, J.C. Burant, J.M. Millam, S.S. Iyengar, J. Tomasi, V. Barone, B. Mennucci, M. Cossi, G. Scalmani, N. Rega, G.A. Petersson, H. Nakatsuji, M. Hada, M. Ehara, K. Toyota, R. Fukuda, J. Hasegawa, M. Ishida, T. Nakajima, Y. Honda, O. Kitao, H. Nakai, M. Klene, X. Li, J.E. Knox, H.P. Hratchian, J.B. Cross, C. Adamo, J. Jaramillo, R. Gomperts, R.E. Stratmann, O. Yazyev, A.J. Austin, R. Cammi, C. Pomelli, J.W. Ochterski, P.Y. Ayala, K. Morokuma, G.A. Voth, P. Salvador, J.J. Dannenberg, V.G. Zakrzewski, S. Dapprich, A.D. Daniels, M.C. Strain, O. Farkas, D.K. Malick, A.D. Rabuck, K. Raghavachari, J.B. Foresman, J.V. Ortiz, Q. Cui, A.G. Baboul, S. Clifford, J. Cioslowski, B.B. Stefanov, G. Liu, A. Liashenko, P. Piskorz, I. Komaromi, R.L. Martin, D.J. Fox, T. Keith, M.A. AlLaham, C.Y. Peng, A. Nanayakkara, M. Challacombe, P.M.W. Gill, B. Johnson, W. Chen, M.W. Wong, C. Gonzalez, J.A. Pople, GAUSSIAN 03, Revision B.04, Gaussian, Inc., Pittsburgh PA, 2003. [39] J.B. Foresman, M. Head-Gordon, J.A. Pople, J. Phys. Chem. 96 (1992) 135. [40] M. Belleteˆte, S. Beaypre´, J. Bouchard, P. Blondin, M. Leclerc, G. Durocher, J. Phys. Chem. B 104 (2000) 9118. [41] K.-T. Wong, C.-F. Wang, C.H. Chou, Y.O. Su, G.-H. Lee, M. Peng, Org. Lett. 4 (2002) 4439. [42] G. Horowitz, B. Bachet, A. Yassar, P. Lang, F. Demanze, J.-L. Fave, F. Garnier, Chem. Mater. 7 (1995) 1337. [43] M.A. De OliveiraHe´lio, A. DuartePernaut, J.M. Wagner, B. De Almeida, J. Phys. Chem. A 104 (2000) 8256–8262. [44] J. Lu, Y. Tao, M. D’iorio, Y. Li, J. Ding, M. Day, Macromolecules 37 (2004) 2442. [45] X. Zhan, S. Wang, Y. Liu, X. Wu, D. Zhu, Chem. Mater. 15 (2003) 1963. [46] P.-H. Aubert, M. Knipper, L. Groenendaal, L. Lutsen, J. Manca, D. Vanderzande, Macromolecules 37 (2004) 4087. [47] N.C. Yang, S.M. Lee, Y.M. Yoo, J.K. Kim, D.H. Suh, J. Polym. Sci., Part A 42 (2004) 1058. [48] P. Puschning, C. Ambrosch-Draxl, G. Heimel, E. Zojer, R. Resel, G. Leising, M. Kriechbaum, W. Graupner, Synth. Met. 116 (2001) 327; V.J. Eaton, D. Steele, J. Chem. Soc., Faaraday Trans. 2 (1973) 1601. [49] K.N. Kudin, R. Car, R. Resta, J. Chem. Phys. 122 (2005) 134907. [50] B.-C. Lin, C.-P. Cheng, Z.-P. Michael Lao, J. Phys. Chem. A 107 (2003) 5241–5251. [51] A. Curioni, M. Boero, W. Andreoni, Chem. Phys. Lett. 294 (1998) 263–271. [52] I. Wang, B.A. Estelle, S. Olivier, I. Alain, L.B. Patrice, J. Opt. A: Pure Appl. Opt. 4 (2002) S258–S260. [53] S. Grimme, M. Parac, Chem. Phys. Chem. 3 (2003) 292. [54] R.P. Ortiz, M.C.R. Delgado, J. Casado, V. Herna´ndez, O.K. Kim, H.Y. Woo, L. Lo´pez Navarrete, J. Am. Chem. Soc. 126 (2004) 13363.