The article information
 Minglang Wang, Jianzhong Fan, Lili Lin
 王明朗, 范建忠, 蔺丽丽
 Influence of Electron Donating Ability on Reverse Intersystem Crossing Rate for One Kind of Thermally Activated Delayed Fluorescence Molecules
 供电子能力对一类热活化延迟荧光分子反系间窜越速率的影响
 Chinese Journal of Chemical Physics, 2018, 31(3): 291299
 化学物理学报, 2018, 31(3): 291299
 http://dx.doi.org/10.1063/16740068/31/cjcp1710191

Article history
 Received on: October 19, 2017
 Accepted on: December 22, 2017
b. Department of Electronics, Peking University, Beijing 100871, China
Since the milestone work of Tang et al. in 1987, organic lightemitting diodes (OLEDs) have attracted extensive attentions because of their potential application in flatpanel display and solidstate lighting [13]. In OLEDs, the singlet to triplet exciton formation ratio is 1:3 due to the spin statistics. For normal fluorescence emitters, radiative decay of the triplet excitons that account for 75% is spin forbidden and only the singlet excitons (25%) can be used for light emitting. To realize the goal of fully harvesting the triplet excitons, phosphorescent materials are developed and have achieved great success [47]. However, the phosphorescent materials are limited to Ir and Pt complexes, thus both fluorescence and phosphorescence OLEDs have advantages and disadvantages. Recently, Adachi et al. successfully achieved 100% internal quantum efficiency (IQE) by the use of pure organic thermally activated delayed fluorescence (TADF) OLEDs [812]. For effective TADFOLEDs, a small energy gap (
As we know, molecular structures determine their photophysical properties. In order to illustrate the influence of modification in donor groups of TADF molecules on their transition properties,
The geometry optimizations and frequency calculations are performed for the ground and excited states by using density functional theory (DFT) and timedependent density functional theory (TDDFT) with the B3LYP functional and 631G(d) basis set respectively. No imaginary frequencies are found which can help one to ensure the structure is stabilized. All calculations are carried out by Gaussian 16 package [18]. Besides, we not only draw the distribution of HOMO and LUMO but also analyze the overlap between them by Multiwfn (a multifunctional wavefunction analyzer) [19]. Moreover, based on the analysis of the excitation component of S
Finally, the intersystem crossing rate constant from initial singlet/triplet to triplet/singlet states can be calculated based on the perturbation theory as
$ \begin{eqnarray} K_{\text{f}\leftarrow \text{i}}^{\text{ISC}}=K_{\text{f}\leftarrow\text{i}}^{(0)}+K_{\text{f}\leftarrow \text{i}}^{(1)}+K_{\text{f}\leftarrow \text{i}}^{(2)} \end{eqnarray} $  (1) 
Where
$ K_{\text{f}\leftarrow \text{i}}^{(0)}\equiv \frac{1}{\hbar^2}H_{\text{fi}}^{\text{SO}} ^2 \int_{\infty}^\infty \text{d}t \text{e}^{iw_{\text{if}}t} \rho_{\text{fi}}^0 (t) $  (2) 
$ K_{\text{f}\leftarrow \text{i}}^{(1)}\equiv\text{Re}\left [\frac{2}{\hbar^2}\sum\limits_k H_{\text{fi}}^{\text{SO}} T_{\text{if}, k} \int_{\infty}^\infty \text{d}t\text{e}^{iw_{\text{if}} t}\rho_{\text{fi}, k}^1 (t) \right ] $  (3) 
$ K_{\text{f}\leftarrow i}^{(2)}\equiv\frac{1}{\hbar^2} \sum\limits_{k, l}T_{\text{if}, k} T_{\text{fi}, l} \int_{\infty}^\infty \text{d}t\text{e}^{iw_{\text{if}} t} \rho _{\text{fi}, kl}^2 (t) $  (4) 
$ \begin{eqnarray} T_{\text{if}, k(l)}=\sum\limits_n\left(\frac{H_{\text{in}}^{\text{SO}}\langle \phi_n\hat{P}_{fk}\phi_f\rangle} {\Delta E_{nf}}+\frac{H_{nf}^{\text{SO}}\langle\phi_i\hat{P}_{nk}\phi_n \rangle}{\Delta E_{\text{in}}}\right) \end{eqnarray} $  (5) 
$ \rho_{\text{fi}, k}^1 (t)=Z_i^{1)}\text{Tr}[\hat{P}_{fk}\text{e}^{i\tau_f \hat{H}_f}\text{e}^{i\tau_i \hat{H}_i }] $  (6) 
$ \rho_{\text{fi}, kl}^2 (t)=Z_i^{1} \text{Tr}[\hat{P}_{fk}\text{e}^{i\tau_f \hat{H}_f}\hat{P}_{fl}\text{e}^{i\tau_i \hat{H} _i }] $  (7) 
Eq.(6) and Eq.(7) are from Ref.[23] and Ref.[24] respectively.
For the firstorder contribution
$ \begin{eqnarray} K_{\text{ISC}}=\frac{1}{\hbar^2}\langle\phi_f\hat{H}^{\text{SO}}\phi_i \rangle \int_{\infty}^\infty \text{d}t[\text{e}^{i\omega_{\text{if}}t} Z_i^{} \rho_{\text{ISC}}(t, T)] \end{eqnarray} $  (8) 
All these calculations for ISC and RISC rates are performed by MOMAP (molecular materials property prediction package) promoted by the Institute of Chemistry Chinese Academy of Sciences and Department of Chemistry in Tsinghua University. Both the methodology and application of this formalism can be found in Peng et al's and Shuai et al's. works [2530].
Ⅲ. RESULTS AND DISCUSSION A. Geometry structuresAccording to the method discussed in computational details, the geometry structures of S
Moreover, the electrondonating ability affects molecular photophysical properties. Atomic charges of the S
Composition of frontier molecular orbital (FMO) is closely related to the molecular excitation properties such as absorption and emission properties. Moreover, ultrafast excited state dynamics investigation is a research hotspot [31, 32]. In order to get a deep understanding of photophysical behavior of all investigated compounds, analysis of FMO at S
$ \begin{eqnarray} \Delta E_{\text{S}_1\text{T}_1}\hspace{0.1cm}=\hspace{0.1cm}2\int \int \phi_L(1)\phi_H (2)\frac{\text{e}^2}{r_1\hspace{0.1cm}\hspace{0.1cm}r_2 } \phi_L (2)\phi_H (1)\text{d}r_1 \text{d}r_2 \nonumber\\ \end{eqnarray} $  (9) 
a small
In order to determine the dominant factor in decreasing the
In order to investigate the electronic transition nature of all studied compounds, TDDFT calculations are performed based on their optimized S
As we all know, ISC and RISC processes play a crucial role in efficient TADFOLEDs. Through abovementioned results, we know that
In this work, the electronic structures, molecular orbital properties, energy gaps, excitation properties and RISC process of all eight molecules are investigated by DFT and TDDFT methods. Through our investigations, the diphenylamine substitution in the donor unit has little effect on the dihedral angle between donor and acceptor unit, but can decrease the bond length between them except for the T
This work was supported by the National Natural Science Foundation of China (No.11374195 and No.21403133), the Taishan Scholar Project of Shandong Province, the Promotive Research Fund for Excellent Young and Middleaged Scientists of Shandong Province (No.BS2014CL001), and the General Financial Grant from the China Postdoctoral Science Foundation (No.2014M560571). Great thanks to Professor Yi Luo at University of Science and Technology of China, Professor Zhigang Shuai at Tsinghua University and Qian Peng at Institute of Chemistry, Chinese Academy of Sciences for their helpful suggestions in our calculation. Thanks to Professor Yingli Niu at Beijing Jiaotong University for his great help in the usage of MOMAP.
[1]  C. W. Tang, and S. A. VanSlyke, Appl. Phys. Lett. 51 , 913 (1987). DOI:10.1063/1.98799 
[2]  J. H. Jou, S. Kumar, A. Agrawal, T. H. Li, and S. Sahoo, J. Mater. Chem. C 3 , 2974 (2015). DOI:10.1039/C4TC02495H 
[3]  S. Xu, R. F. Chen, C. Zheng, and W. Huang, Adv. Mater. 28 , 9920 (2016). DOI:10.1002/adma.201602604 
[4]  C. Adachi, M. A. Baldo, M. E. Thompson, and S. R. Forrest, J. Appl. Phys. 90 , 5048 (2001). DOI:10.1063/1.1409582 
[5]  Z. Kuang, X. Wang, Z. Wang, G. He, Q. Guo, L. He, and A. Xia, Chin. J. Chem. Phys. 30 , 259 (2017). DOI:10.1063/16740068/30/cjcp1703058 
[6]  C. Li, L. Duan, D. Zhang, and Y. Qiu, Acs. Appl. Mater.Inter. 7 , 15154 (2015). DOI:10.1021/acsami.5b04090 
[7]  S. Cao, L. Hao, W. Y. Lai, H. Zhang, Z. Yu, X. Zhang, X. Liu, and W. Huang, J. Mater. Chem. C 4 , 4709 (2016). DOI:10.1039/C6TC00856A 
[8]  H. Uoyama, K. Goushi, K. Shizu, and H. Nomura, C.Adachi, Nature 492 , 234 (2012). 
[9]  J. Guo, X. L. Li, H. Nie, W. Luo, R. Hu, A. Qin, Z. Zhao, S. J. Su, and B. Z. Tang, Chem. Mater. 29 , 3623 (2017). DOI:10.1021/acs.chemmater.7b00450 
[10]  J. Guo, X. L. Li, H. Nie, W. Luo, S. Gan, S. Hu, R. Hu, A. Qin, Z. Zhao, S. J. Su, and B. Z. Tang, Adv. Funct.Mater. 27 , 1606458 (2017). DOI:10.1002/adfm.v27.13 
[11]  L. Yu, Z. Wu, C. Zhong, G. Xie, K. Wu, and D. Ma, C.Yang, Dyes. Pigments. 141 , 325 (2017). DOI:10.1016/j.dyepig.2017.02.035 
[12]  J. Luo, S. Gong, T. Zhang, C. Zhong, G. Xie, Z. H. Lu, and C. Yang, Dyes. Pigments. 147 , 350 (2017). DOI:10.1016/j.dyepig.2017.08.030 
[13]  T. Sato, M. Uejima, K. Tanaka, H. Kaji, and C. Adachi, J.Mater. Chem. C 3 , 870 (2015). DOI:10.1039/C4TC02320J 
[14]  Q. S. Zhang, H. Kuwabara, W. J. Potscavage Jr, S. P. Huang, Y. Hatae, T. Shibata, and C. Adachi, J. Am.Chem. Soc. 136 , 18070 (2014). DOI:10.1021/ja510144h 
[15]  J. Z. Fan, S. Qiu, L. L. Lin, and C. K. Wang, Chin. J. Chem.Phys. 29 , 291 (2016). DOI:10.1063/16740068/29/cjcp1508181 
[16]  J. Fan, L. Cai, L. Lin, and C. Wang, Chem. Phys. Lett. 664 , 33 (2016). DOI:10.1016/j.cplett.2016.10.009 
[17]  M. Y. Wong, ZysmanColman E., J. Mater. Chem. C 29 , 1605444 (2017). 
[18]  M. J. Frisch, G. W. Trucks, H. B. Schlegel, G. E. Scuseria, M. A. Robb, J. R. Cheeseman, G. Scalmani, V. Barone, B. Mennucci, G. A. Petersson, H. Nakatsuji, M. Caricato, X. Li, H. P. Hratchian, A. F. Izmaylov, J. Bloino, G. Zheng, J. L. Sonnenberg, M. Hada, M. Ehara, K. Toyota, R. Fukuda, J. Hasegawa, M. Ishida, T. Nakajima, Y. Honda, O. Kitao, H. Nakai, T. Vreven, J. A. Montgomery Jr., J. E. Peralta, F. Ogliaro, M. Bearpark, J. J. Heyd, E. Brothers, K. N. Kudin, V. N. Staroverov, R. Kobayashi, J. Normand, K. Raghavachari, A. Rendell, J. C. Burant, S. S. Iyengar, J. Tomasi, M. Cossi, N. Rega, N. J. Millam, M. Klene, J. E. Knox, J. B. Cross, V. Bakken, C. Adamo, J. Jaramillo, R. Gomperts, R. E. Stratmann, O. Yazyev, A. J. Austin, R. Cammi, C. Pomelli, J. W. Ochterski, R. L. Martin, K. Morokuma, V. G. Zakrzewski, G. A. Voth, P. Salvador, J. J. Dannenberg, S. Dapprich, A. D. Daniels, Ö. Farkas, J. B. Foresman, J. V. Ortiz, J. Cioslowski, and D. J. Fox, Gaussian 16, Revision A. 03, Wallingford CT, USA: Gaussian Inc. (2016). 
[19]  T. Lu, and F. W. Chen, J. Comput. Chem. 33 , 580 (2012). DOI:10.1002/jcc.v33.5 
[20]  Dalton, a Molecular Electronic Structure Program, http://daltonprogram.org. 
[21]  Y. L. Niu, Q. Peng, C. M. Deng, X. Gao, and Z. G. Shuai, J. Phys. Chem. A 114 , 7817 (2010). 
[22]  Q. Peng, Q. H. Shi, Y. L. Niu, Y. P. Yi, S. R. Sun, W. Li, and Q W., Z. G Shuai, J. Mater. Chem. C. 4 , 6829 (2016). DOI:10.1039/C6TC00858E 
[23]  Q. Peng, Y. L. Niu, Q. H. Shi, X. Gao, and Z. G. Shuai, J.Chem. Theory. Comput. 9 , 1132 (2013). DOI:10.1021/ct300798t 
[24]  T. Zhang, H. L. Ma, Y. L. Niu, W. Q. Li, D. Wang, Q.Peng, Z. G. Shuai, and W. Z. Liang, J. Phys. Chem. C 119 , 5040 (2015). DOI:10.1021/acs.jpcc.5b01323 
[25]  Z. G. Shuai, and Q. Peng, Phys. Rep. 537 , 123 (2014). DOI:10.1016/j.physrep.2013.12.002 
[26]  J. Z. Fan, L. Cai, L. L. Lin, and C. K. Wang, J. Phys. Chem.A 120 , 9422 (2016). 
[27]  J. Fan, L. Lin, and C. K. Wang, J. Mater. Chem. C 5 , 8390 (2017). DOI:10.1039/C7TC02541F 
[28]  L. Lin, Z. Wang, J. Fan, and C. Wang, Org. Electron. 41 , 7 (2017). 
[29]  J. Fan, L. Lin, and C. K. Wang, Phys. Chem. Chem. Phys. 19 , 30147 (2017). DOI:10.1039/C7CP05451C 
[30]  J. Fan, L. Cai, L. Lin, and C. K. Wang, Phys. Chem. Chem.Phys. 19 , 29872 (2017). DOI:10.1039/C7CP05009G 
[31]  X. C. Li, N. Sui, Q. H. Liu, Q. L. Yuan, and Y. H. Wang, Chin. J. Chem. Phys. 29 , 389 (2016). DOI:10.1063/16740068/29/cjcp1512251 
[32]  Y. P. Wang, S. Zhang, S. m. Sun, K. Liu, and B. Zhang, Chin. J. Chem. Phys. 26 , 651 (2013). DOI:10.1063/16740068/26/06/651655 
[33]  M. K. Etherington, J. Gibson, H. F. Higginbotham, T. J. Penfold, and A. P. Monkman, Nat. Commun. 7 , 13680 (2016). DOI:10.1038/ncomms13680 
[34]  Y. Gao, S. Zhang, Y. Pan, L. Yao, H. Liu, Y. Guo, Q. Gu, B. Yang, and Y. Ma, Phys. Chem. Chem. Phys. 18 , 24176 (2016). DOI:10.1039/C6CP02778D 
[35]  J. Gibson, A. P. Monkman, and T. J. Penfold, ChemPhysChem 17 , 2956 (2016). DOI:10.1002/cphc.201600662 
[36]  J. Gibson, and T. J. Penfold, Phys. Chem. Chem. Phys. 19 , 8428 (2017). DOI:10.1039/C7CP00719A 
b. 北京大学电子学系, 北京 100871