Substituent effect of fluorine ligand on spectroscopic properties of Pt(N^C^N)Cl complexes, a theoretical study

Substituent effect of fluorine ligand on spectroscopic properties of Pt(N^C^N)Cl complexes, a theoretical study

Organic Electronics 13 (2012) 2568–2574 Contents lists available at SciVerse ScienceDirect Organic Electronics journal homepage: www.elsevier.com/lo...

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Organic Electronics 13 (2012) 2568–2574

Contents lists available at SciVerse ScienceDirect

Organic Electronics journal homepage: www.elsevier.com/locate/orgel

Substituent effect of fluorine ligand on spectroscopic properties of Pt(N^C^N)Cl complexes, a theoretical study Baozhu Yang a, Qi Zhang a, Jing Zhong a,⇑, Shuang Huang b, Hongxing Zhang c a

School of Petrochemical Engineering, Jiangsu Province Key Lab of Fine Petrochemical Engineering, Changzhou University, Changzhou 213164, China School of Mathematics & Physics, Changzhou University, Changzhou 213164, China c State Key Laboratory of Theoretical and Computational Chemistry Institute of Theoretical Chemistry, Jilin University, Changchun 130023, China b

a r t i c l e

i n f o

Article history: Received 25 June 2012 Received in revised form 10 July 2012 Accepted 10 July 2012 Available online 1 August 2012 Keywords: Time-Dependent Density Functional Theory Substituent effect Spectroscopic properties Fluorine ligand

a b s t r a c t Time-Dependent Density Functional Theory (TDDFT) method was used to investigate the substituent effect of fluorine ligand on geometrical structures, electronic properties, electroluminescent properties, absorption and emission spectra of six tridentate cyclometalated Pt(II) complexes. M062X hybrid functional was proved to be suitable for calculating the lowest triplet excited state (T1) characters in TDDFT calculations. The energies of d–d transitions both in absorption and emission were larger than HOMO–LUMO energy gaps, so d–d transitions did not easily occur. With the introduction of fluorine ligand, the energy levels did not show regularity changes, while the IP (ionization potentials) values and EA (electron affinities) values increased correspondingly. The phosphorescence emissions of the complexes were all assigned as 3ILCT mixed with 3MLCT. In addition, one dimeric form of cyclometalated Pt(II) complexes have also been investigated. Ó 2012 Elsevier B.V. All rights reserved.

1. Introduction Recently, phosphorescent materials have been widely reported as organic electroluminescent devices, sensor materials, and bioimaging probes [1–5]. Pt(II) complexes with tridentate cyclometalated ligand, Pt(N^C^N)Cl, (N^C^N = 1,3-di(2-pyridyl)benzene) are typical phosphorescent materials with d8 electronic configuration, which have dsp2 hybridization and square-planar structure [6,7]. The planar structure is conductive to producing and separating electron–hole, and will lead to a dimeric form through conjugation effect between two molecules. The conjugated p bond of aromatic ligand mixed with dp(Pt)orbitals facilitates charge migration and energy transfer. If we adjust the extent of conjugation, then the spectrum and properties of excited state will be changed. Nowadays, Time-Dependent Density Functional Theory (TDDFT) [8–10] has emerged as the effective instrument

⇑ Corresponding author. E-mail address: [email protected] (J. Zhong). 1566-1199/$ - see front matter Ó 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.orgel.2012.07.018

for the calculation of excited state properties [11–13]. The computational cost is an intermediate between semiempirical theories and wave function approaches. But there is an important drawback: the quality of the obtained results is profoundly functional-dependent [14,15]. So the appropriate selection of the exchange–correlation functional is crucial to gain reasonable conclusions. In this paper, we tested a few functionals under TDDFT method to gain reliable excited state properties. We carried out the present work with two goals: (1) to provide an indepth theoretical understanding about the substituent effect of fluorine ligand on spectroscopic and photophysical properties of Pt(N^C^N)Cl complexes, and (2) to gain a sound process for calculating the excited states of pp-orbitals mixed with dp(Pt)-orbitals through p-conjugation.

2. Computational details The structures of complexes 1–6 are depicted in Fig. 1. To obtain more accurate data, the complexes were symmetry-restricted to C1 group and all the calculations were

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to calculate the absorption behavior for these small molecules, although they performed very well on big molecules [28]. TPSSh are good for the absorption calculation in CH2Cl2 solvent. For the optimization of excited states, we also tested the functionals as we did on absorption test, long range corrected functionals also did not perform well as we expected. M062X functional are suitable for the calculations of excited states, since the weak interaction is also considered in this functional. For excited state calculations in solution, there is a distinction between equilibrium and non-equilibrium calculations. Non-equilibrium is the default for TD-DFT energies using the default PCM procedure [17]. Therefore, we did the equilibrium corrections on the calculation of emissions. The results show that there is hardly any difference between the two ways. For saving computational resources, we used TD-DFT method with non-equilibrium calculations to describe the properties of excited states. 3. Results and discussion 3.1. The frontier molecular orbitals analysis and absorption properties

Fig. 1. Schematic structures of the investigated complexes.

performed in CH2Cl2 solvent with the polarized continuum model (PCM) [16], which creates the solute cavity via a set of overlapping spheres. The 6–31G(d) basis sets were adopted for C, N and H atoms, 6-311+G(d) for Cl and F atom, and the SDD basis sets associated with the pseudopotential were adopted for Pt atom. All the calculations were accomplished by using the Gaussian 09 software package [17]. To find the appropriate functional, we taken complexes 1 and 2 for example to do functional tests. For the ground state, PBEPBE [18,19] and three hybrid functionals PBE0 [20], B3LYP [21–23] and M062X [24] were tested. From the comparison of structure parameters, PBE0 tended to outperform other functionals, which has 25% exchange and 75% correlation weighting. For the absorption calculation in CH2Cl2, we tested M062X, PBE0, TPSSh [25], and two long range corrected functionals CAM-B3LYP [26] and xB97XD [27]. Comparing the absorption date we obtained, long range corrected functionals were not suitable

The structures of complexes 1–6 in ground state were optimized by PBE0 functional and shown in Fig. 1. The optimized structural parameters of the complexes in ground state has been listed in Table 1, which are in general agreement with the corresponding experimental values [6]. With the changes of fluorine ligand, the bond lengths have no obvious changes. The bond length of Pt – Cl in complex 1 is longer than the others, which indicated that the interaction between Pt and Cl were enhanced with the increasingly introduction of fluorine ligand. The absorption spectra for complexes 1–6 in CH2Cl2 solution were explored using TDDFT method under TPSSh level with PCM model. Table 2 gives the absorption data in terms of the transition states, excitation energies, excitations with maximum CI coefficients, oscillator strengths and experimental values. For clarity, complexes 2–6 only listed the lowest energy absorptions and the absorptions with the biggest oscillator strength. As shown in Table 2, the calculated absorptions are agree well with the experimental results. The excitation configurations of HOMO ? LUMO are responsible for all the lowest-lying dipole-allowed absorptions. In Table 3, the compositions of frontier molecular orbitals were revealed. The HOMOs of the complexes

Table 1 Optimized geometric structural parameters of complexes in the ground state, together with the experimental values of complex 1.

a

Parameter

1

2

3

4

5

6

Expa

Bond length (Å) Pt – N(1) Pt – C Pt – N(2) Pt – Cl

2.042 1.908 2.042 2.414

2.042 1.909 2.042 2.410

2.042 1.908 2.041 2.409

2.041 1.908 2.041 2.404

2.040 1.909 2.041 2.406

2.040 1.909 2.040 2.400

2.041 1.907 2.041 2.417

Bond angle (deg) N(1) – Pt – N(2) C – Pt – Cl

161.2 180.0

161.1 180.0

161.5 179.8

161.9 180.0

161.4 179.8

161.8 180.0

Ref. [6].

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Table 2 Absorptions of complexes 1–6 in CH2Cl2 solution according to TDDFT calculations, together with the experimental values.

1

S1 S2 S3 S5 S8 S10 S11 S1 S11 S1 S10 S1 S10 S1 S11 S1 S10

2 3 4 5 6 a

Excitation

Coeff.

Enm (eV)

Oscillator

Assignment

Exptl (nm)a

H?L H?L+1 H – 1?L H – 2?L H – 2?L+1 H?L+3 H – 4?L H?L H – 1?L+1 H?L H – 4?L H?L H – 4?L H?L H – 4?L H?L H – 4?L

0.70 0.69 0.71 0.70 0.62 0.68 0.66 0.70 0.62 0.70 0.64 0.70 0.66 0.69 0.53 0.70 0.66

414 408 376 359 335 309 306 427 303 409 309 399 309 421 307 408 307

0.0065 0.1111 0.0076 0.0306 0.0390 0.0191 0.2506 0.1195 0.1381 0.0243 0.2438 0.0076 0.2851 0.0641 0.1731 0.0080 0.2325

MLCT/ILCT MLCT/ILCT MLCT MLCT/ILCT MLCT/ILCT MLCT/ILCT MLCT/ILCT MLCT/ILCT MLCT MLCT/ILCT MLCT/ILCT MLCT/ILCT MLCT/ILCT MLCT/ILCT MLCT/ILCT MLCT/ILCT MLCT/ILCT

402

(2.99) (3.04) (3.30) (3.46) (3.70) (4.02) (4.05) (2.91) (4.09) (3.03) (4.02) (3.11) (4.02) (2.95) (4.04) (3.04) (4.04)

379

319 421 290 380 286 375 287 – – 403 268

Ref. [6].

were consisted of N^C^N ligand and Pt atom orbitals, and the LUMOs were mainly located on N^C^N ligand, so all the absorptions have MLCT (metal-to-ligand charge transfer) character mixed with ILCT (intra-ligand charge transfer). The absorptions with the biggest oscillator strength can be also assigned as the combination of MLCT/ILCT, which all Table 3 Partial molecular orbital compositions in the ground state of complexes 1–4 in CH2Cl2 solution. MO

E (eV)

Contribution (%) N^C^N

Pt

0.2718 2.1391 2.1867 5.4374 5.9509

52.0 97.7 79.7 37.7

45.8

1

DE (eV)

H–L d–d

3.2507 5.6791

L + 4 (d) L+1 L H H – 1 (d)

0.3616 2.2605 2.3173 5.4532 6.0126

55.7 85.6 97.8 45.7

42.2 10.4

3.1359 5.6510

L + 4 (d) L+1 L H H – 1 (d)

0.4180 2.1639 2.2787 5.5650 6.0412

57.4 96.3 89.6 42.8

40.3

3.2863 5.6232

L + 4 (d) L+1 L H H – 1 (d)

0.5785 2.2090 2.3249 5.6877 6.1136

53.2 91.4 79.6 52.5

43.4

3.3628 5.5351

L + 4 (d) L+1 L H H – 1 (d)

0.5350 2.2934 2.3734 5.5634 6.0915

50.5 92.2 93.9 45.9

47.0

3.1900 5.5565

L + 4 (d) L+1 L H H – 1 (d)

0.7880 2.3551 2.3873 5.6744 6.1588

52.1 94.8 87.2 44.4

43.8

3.2871 5.3708

L + 4 (d) L+1 L H H – 1 (d)

2

H–L d–d 3

H–L d–d 4

H–L d–d 5

H–L d–d 6

H–L d–d

10.7 45.3 93.9

43.2 94.2

44.7 94.0

Cl

11.7

11.1

12.6

20.1 46.2 90.0

42.4 94.2

10.9 42.8 94.3

coming from HOMO-4 ? LUMO transitions. Furthermore, the absorption spectra of 1–6 simulated with a Gaussiantype curve were shown in Figs. 2 and 3 together with the experimental absorption spectra of complexes 1 and 4. The absorption spectra can be simulated by the mathematP ical expression: i f  exp ð0:5  ððka  kf ðiÞ Þ=10Þ2 Þ, where f is the oscillator strength, kf is the absorption wavelength, ka is x axis value which means absorption range from 200 nm to 500 nm, and the peak width at half height estimated from the experiment is 10 nm. In our calculation, we calculated forty lower-energy absorptions for each complex. In Fig. 2, we could find the simulated spectra accorded with the experimental absorption. To help us understand the orbitals described above, the energy level diagrams of the partial molecular orbitals were presented in Fig. 4. With the changes of fluorine ligand, the energy levels did not show regularity changes, complex 4 which have two fluorine ligand on the two sides of phenyl group, shown the biggest HOMO–LUMO energy gap. When the fluorine ligand located at the para-position of the Pt atom, such as in complex 2, the HOMO–LUMO energy gap was the smallest. The d–d state is usually regarded as the intrinsic reason for the nonemission of square-planar Pt(II) complexes in solution. Therefore, stabilizing and deactivating the d–d state is of great significance in experiments. Table 3 shows that HOMO-1 and LUMO+4 are mainly consisted of d orbitals of Pt atom, and the energy gaps of d–d state are about 5.5 eV, which are bigger than the charge transfer energies. Therefore, the d–d transitions are difficult to happen. 3.2. Electroluminescent (EL) properties

11.7

12.1

In this section, we have calculated the ionization potentials (IP), electron affinities (EA), and reorganization energy (k), together with the hole extraction potential and electron extraction potential (HEP, EEP). The results are listed in Table 4 and the computation details could be obtained from previous reports [29]. As we know, a smaller ionization potential (IP) value means hole injection easier;

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Fig. 2. Simulated absorption spectra of complexes 1 and 4 in CH2Cl2 solution. Inside were the experimental spectra.

Fig. 4. Energy level diagrams of partial molecular orbitals for the complexes.

Table 4 Ionization potentials (IP), electron affinities (EA), extraction potentials (HEP and EEP) and internal reorganization energies (k) for the investigated complexes (eV).

1 2 3 4 5 6

IP (v)

IP (a)

HEP

khole

EA (v)

EA (a)

EEP

kelectron

7.1127 7.1922 7.2811 7.4516 7.3369 7.4874

7.0336 7.0912 7.2023 7.3745 7.2372 7.3916

6.9554 6.9887 7.1240 7.2980 7.1353 7.2924

0.1573 0.2035 0.1570 0.1536 0.2015 0.1950

0.5454 0.7770 0.6250 0.7199 0.8213 0.8481

0.6949 0.9446 0.7770 0.8458 0.9972 1.0256

0.8268 1.0854 0.9204 0.9472 1.1458 1.1751

0.2814 0.3084 0.2953 0.2273 0.3245 0.3269

Table 5 Optimized geometric structural parameters of complexes in the lowest triplet excited state.

Fig. 3. Simulated absorption spectra of complexes 2, 3, 5 and 6 in CH2Cl2 solution.

whereas larger electron affinity (EA) value will facilitate electron injection. According to Marcus/Hush model [30–33], the charge (hole or electron) transfer rate k can be expressed by the following formula:



( ) 4p2 V2 ðDG0 þ kÞ2 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi exp  h 4kK b T 4pkK b T

where DG0 is the free energy difference between the initial and final states, k is the reorganization energy, Kb is the Boltzmann constant, and V is the electronic coupling matrix element between the two species M and M+/. Due to the limited intermolecular charge transfer range in solid-state, it has been proved that the charge mobility is dominantly related to the internal reorganization energy for OLED materials [34–36]. Therefore, the lower reorganization energy is necessary for an efficient charge transport process. In Table 4, the IP values of complex 1 is the smallest. With the fluorine ligand introduction, the IP values increased correspondingly. This means that the hole injection is much easier in complex 1 than others. When the fluorine

Parameter

1

2

3

4

5

6

Bond length (Å) Pt – N(1) Pt – C Pt – N(2) Pt – Cl

2.094 1.875 2.046 2.524

2.095 1.870 2.049 2.515

2.096 1.880 2.043 2.526

2.089 1.881 2.043 2.514

2.094 1.876 2.045 2.514

2.090 1.877 2.046 2.506

Bond angle (deg) N(1) – Pt – N(2) C – Pt – Cl

162.4 179.4

162.6 179.4

162.4 179.4

162.6 179.6

162.7 179.4

162.8 179.6

Table 6 Emissions of complexes 1–6 in CH2Cl2 solution under TDDFT calculations. Excitation (coeff)

Enm (eV)

Phosphorescence 1 H?L (0.65) 2 H?L (0.65) 3 H?L (0.66) 4 H?L (0.66) 5 H?L (0.65) 6 H?L (0.65)

spectra 519 (2.39) 536 (2.31) 513 (2.42) 500 (2.48) 531 (2.34) 513 (2.42)

Assignment

Exptl (nm)

U

s (ls)

3

490

0.60

7.2

504

0.39

7.0

481

0.52

6.5

MLCT/3ILCT

3

3

MLCT/ ILCT

3

MLCT/3ILCT

3

MLCT/3ILCT

471

0.60

6.8

3

3







3

3

481

0.46

7.8

MLCT/ ILCT MLCT/ ILCT

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Table 7 Partial molecular orbital compositions in the lowest triplet excited state in CH2Cl2 solution. MO

E (eV)

Contribution (%) N^C^N

1 H–L d–d

DE (eV) 5.5781 8.2478

L + 3 (d) L H H – 2 (d)

0.0683 1.5075 7.0856 8.1795

94.7 68.4

5.4338 8.2951

L + 4 (d) L H H – 2 (d)

0.0424 1.6580 7.0918 8.2527

95.6 67.5

5.6679 8.3139

L + 3 (d) L H H – 2 (d)

0.0444 1.5110 7.1789 8.2695

94.8 63.8

5.7536 8.3765

L + 3 (d) L H H – 2 (d)

0.0109 1.6074 7.3610 8.3656

93.7 72.6

5.5312 8.3621

L + 4 (d) L H H – 2 (d)

0.0093 1.6610 7.1922 8.3528

95.7 71.7

5.6293 8.3786

L + 4 (d) L H H – 2 (d)

0.0520 1.7325 7.3618 8.4306

94.6 69.4

2 H–L d–d 3 H–L d–d 4 H–L d–d 5 H–L d–d 6 H–L d–d

Pt

Cl

79.1

18.1

27.3 89.0 80.3

16.7

28.0 89.7 81.1

15.8

22.6 89.4 83.8

12.4

23.2 88.6 83.0

13.4

24.2 89.8 86.8

7.3

25.6 90.4

ligand located at 4-position of phenyl ligand, the IP values increased much more than that at 3-position and 5-position. The EA values of complex 6 is the biggest, which means the electron injection is much easier than the other complexes. By comparison with complexes 2 and 3, we also found the effect of 4-position on electron injection is greater than the other positions. With respect to complex 4, when the fluorine ligand located at both 3-position and 5position, the khole and kelectron were the smallest. This means complex 4 is suitable for charge transport process. 3.3. Emission spectrum The lowest triplet excited state (T1) of the complexes were optimized by TDDFT method at m062X level. The phosphorescence were calculated in CH2Cl2 solution with polarized continuum model. The main geometry parameters of 1–6 in T1 state were presented in Table 5 and the

spectra information were listed in Table 6. Compared with the ground states, the bond lengths of Pt–N1, Pt–N2 and Pt–Cl were elongated, while Pt–C bonds were shortened. This implied that the electrons were promoted from pyridine to phenyl ligand and the metal–phenyl interaction was strengthened in excited state. The calculated phosphorescence emissions in CH2Cl2 solution were 519 nm, 536 nm, 513 nm, 500 nm, 531 nm and 513 nm for complexes 1–6, respectively. The compositions of corresponding molecular orbitals were revealed in Table 7. The emissions were mainly from the transitions of HOMO ? LUMO. As revealed in Table 7, the HOMOs of the complexes have about 70% N^C^N and 25% metal compositions, while the LUMOs of the complexes were mainly localized on N^C^N ligand. Therefore, the transitions of complexes were all assigned as 3ILCT mixed with 3MLCT. Table 7 shows that HOMO-2 of the complexes are mainly consisted of Pt atom, while LUMO+3 of complexes 1, 3, 4 and LUMO+4 of complexes 2, 5, 6 are localized on Pt atom. The energy gaps of d–d state are about 8.3 eV, which are far higher than HOMO–LUMO energy gaps (about 5.5 eV). Therefore, d–d nonradiative transitions are difficult to happen. By comparison with complexes 1, 2 and 3, we found the HOMO–LUMO energy gap in complex 2 is smaller than that in complex 1, while the gap of complex 3 is bigger than that in complex 1. This indicated that when the electron-withdrawing ligand localized at 4-position of phenyl, the HOMO–LUMO energy gap will decrease; while the opposite case will occur at 3-position and 5-position of phenyl. 3.4. The properties of dimer As we know, Pt(II) complexes with a plane structure are facilitate to form dimers. Therefore, the complex 1 were taken as an example to simulate the properties of dimers. The optimized structure of the dimer was shown in Fig. 5. The two molecules packed neither head-to-tail nor head-tohead, they formed a 103.9° angle as shown in Fig. 5. The Pt    Pt distance is 5.4144 Å and plane-to-plane distance is 3.7771 Å. The lowest energy absorption and phosphorescence emission of the dimer in CH2Cl2 was 422 nm and 534 nm, respectively, which were mainly from the transitions of HOMO ? LUMO. The partial molecular orbital diagrams of the dimer were shown in Fig. 6. The electroluminescent properties has also been calculated, which are IP(v)(6.7545 eV), khole (0.2147 eV), EA(v)(0.7681 eV) and

Fig. 5. Optimized structures of complex 1 in a dimeric form. The hydrogen atoms are omitted for clarity.

B. Yang et al. / Organic Electronics 13 (2012) 2568–2574

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Fig. 6. Partial molecular orbital diagrams of the dimer.

kelectron (0.4491 eV). Comparison with complex 1, the dimer is more suitable for charge and hole transport processes.

4. Conclusions In this article, we reported the detailed investigation of structures, spectra, and electroluminescent (EL) properties for a series of tridentate cyclometalated Pt(II) complexes. The calculated results revealed that TDDFT method with M062x functional was appropriate to optimize the lowest triplet excited states. With fluorine ligand increasing, the IP values and EA values of the complexes increased correspondingly. From complex 1 to complex 6, the difficulties of hole injection gradually increased, and the electron injection became easier. By comparison with complexes 2 and 3, we found the effect of 4-position on electroluminescent properties is greater than the other positions. All the absorptions of the complexes in CH2Cl2 were assigned as MLCT character mixed with ILCT and the emissions were all assigned as 3ILCT mixed with 3MLCT. The energy gaps of d–d state are bigger than the charge transfer energies. Therefore, the d–d transitions are difficult to happen. For the dimer of complex 1, the two molecules packed neither head-to-tail nor head-to-head, they formed a 103.9° angle. The Pt    Pt distance is 5.4144 Å and plane-to-plane distance is 3.7771 Å. Comparison with complex 1, the dimer is more suitable for charge and hole transport processes. We hope that the exploration of these characteristic properties for the Pt(II) metal complexes will help us design good functional materials.

Acknowledgements This work is supported by the Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD), Basic Research Program of Jiangsu Natural Science Foundation (BK2011240), Scientific Research Projects of Jiangsu Province Environmental Protection Department (201126), Science and Technology Support Program of Jiangsu Province (Social Development) (BE2011651), and the Innovation Foundation of Jiangsu for Postgraduate (CXZZ11_0374). Thanks the Foundation of State Key Laboratory of Theoretical and Computational Chemistry. References [1] Y. Shirota, H. Kageyama, Chem. Rev. 107 (2007) 953. [2] G.S.M. Tong, C.M. Che, Chem. Eur. J. 15 (2009) 7225. [3] A.B. Powell, C.W. Bielawski, A.H. Cowley, J. Am. Chem. Soc. 132 (2010) 10184. [4] V. Krishnan, A. Tronin, J. Strzalka, H.C. Fry, M.J. Therien, J.K. Blasie, J. Am. Chem. Soc. 132 (2010) 11083. [5] K.Y. Zhang, K.K.W. Lo, Inorg. Chem. 48 (2009) 6011. [6] Z. Wang, E. Turner, V. Mahoney, S. Madakuni, T. Groy, J. Li, Inorg. Chem. 49 (2010) 11276. [7] D.J. Cárdenas, A.M. Echavarren, M.C. Ramírez de Arellano, Organometallics 18 (1999) 3337. [8] Dreuw, M. Head-Gordon, Chem. Rev. 105 (2005) 4009. [9] V. Barone, A. Polimeno, Chem. Soc. Rev. 36 (2007) 1724. [10] D. Jacquemin, E.A. Perpète, I. Clofini, C. Adamo, Acc. Chem. Res. 42 (2009) 326. [11] D. Jacquemin, V. Wathelet, E.A. Perpète, C. Adamo, J. Chem. Theory Comput. 5 (2009) 2420. [12] D. Jacquemin, E.A. Perpète, G.E. Scuseria, I. Ciofini, C. Adamo, J. Chem. Theory Comput. 4 (2008) 123. [13] L. Goerigk, J. Moellmanna, S. Grimme, Phys. Chem. Chem. Phys. 11 (2009) 4611.

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