The article information
 Jianzhong Fan, Shuai Qiu, Lili Lin, Chuankui Wang
 范建忠, 邱帅, 蔺丽丽, 王传奎
 FirstPrinciples Investigation on Triazine Based Thermally Activated Delayed Fluorescence Emitters
 三嗪基热活化延迟荧光发射体的第一性原理研究
 Chinese Journal of Chemical Physics, 2016, 29(3): 291296
 化学物理学报, 2016, 29(3): 291296
 http://dx.doi.org/10.1063/16740068/29/cjcp1508181

Article history
 Received on August 26, 2015
 Accepted on December 4, 2015
Organic light emitting diodes (OLEDs) have attracted much attention recently since some metalfree thermally active delayed fluorescent (TADF) emitters with internal quantum efficiency attending to 100% are reported [1, 2, 3]. The TADF emitters break the rule that the internal quantum efficiency of organic molecules in OLED can't exceed 25%,and are regarded as the third generation organic electroluminescent molecular materials. One common character of these TADF emitters is that they are composed of electronaccepting groups (A) and electrondonating groups (D),which results in small energy gap between the singlet excited states (S) and the triplet excited states (T). Consequently,triplet excitons can upconvert to singlet excitons by the reverse intersystem crossing (RISC) process,thus the exciton utilization efficiency and the internal quantum efficiency are enhanced significantly. It is indicated that separating the spatial distribution of the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) by introducing the donor groups and acceptor groups is an effective way to get a small ST energy gap [4]. Nevertheless,the fluorescence rate is decreased due to the significant chargetransfer property of S1 in the DA based systems. Thus a tradeoff strategy is highly required in the design of TADF emitters. Now some researches found that the fluorescent rate can be enhanced by adding an aromatic bridge between D and A to increase the DA separating length [5]. Furthermore,DAD type and ADA type based TADF emitters have also been designed in order to increase the fluorescent intensity [6, 7].
In this work,the triazine based TADF emitters are studied. The optimal HF method will be used to calculate the ST energy gap. Detail analysis of transition orbitals and the electronhole (eh) distribution as well as the eh overlap will be carried out. By quantitatively analysis of the charge transfer distance and the integral of the eh overlap for the S1 state,some design strategies for TADF emitters with high exciton utilization efficiency as well as high fluorescent rate will be provided. In the end,the energy state structure will be presented for further study of the dynamics of excited states.
Ⅱ. COMPUTATIONAL DETAILSIn this work,the geometries of three molecules are optimized with the density functional theory (DFT) method at the B3LYP/631G^{*} level. The excitation energy for several lowlying excited states is calculated with the optimal HF methods [8] and the 631G^{*} basis set is used. All the calculations above are realized in the Gaussian 09 program [9]. Further,the transition property such as the eh distribution and the overlap of eh of excited states are analyzed with the multifunctional wavefunction analyzer (Multiwfn) [10]. Here,we just list the main calculation steps. For more theoretical and computational details,one can refer to the manual of Multiwfn. In this work,the eh distribution is studied to analyze the excitation property of molecules. The density distribution of holes $\rho ^{{\rm{hole}}}$ and electrons $\rho ^{{\rm{ele}}}$ can be gracefully defined as:
$ {{\rho }^{\text{hole}}}\left( r \right)=\rho _{\text{loc}}^{\text{hole}}\left( r \right)+\rho _{\text{cross}}^{\text{hole}}\left( r \right) $  (1) 
$ {{\rho }^{\text{ele}}}\left( r \right)=\rho _{\text{loc}}^{\text{ele}}\left( r \right)+\rho _{\text{cross}}^{\text{ele}}\left( r \right) $  (2) 
$ \rho _{\text{loc}}^{\text{hole}}\left( r \right)=\sum\limits_{i\to l}{{{\left( w_{i}^{l} \right)}^{2}}}{{\rho }_{i}}\sum\limits_{i\leftarrow l}{{{\left( w_{i}^{l} \right)}^{2}}}{{\rho }_{i}} $  (3) 
$ \rho _{{\rm{loc}}}^{{\rm{ele}}} \left( r \right) = \sum\limits_{i \to l} {\left( {w_i^l } \right)} ^2 \rho _l  \sum\limits_{i \leftarrow l} {\left( {w_i^l } \right)} ^2 \rho _l $  (4) 
$ \begin{matrix} \rho _{\text{cross}}^{\text{hole}}\left( r \right)=\sum\limits_{i\to l}{\sum\limits_{i\ne i\to l}{w_{i}^{l}w_{j}^{l}}{{\varphi }_{i}}{{\varphi }_{j}}} \\ \text{ }\sum\limits_{j\ne i\leftarrow l}{\sum\limits_{i\leftarrow l}{w_{i}^{l}w_{j}^{l}}{{\varphi }_{i}}{{\varphi }_{j}}} \\ \end{matrix} $  (5) 
$ \begin{matrix} \rho _{\text{cross}}^{\text{ele}}\left( r \right)=\sum\limits_{i\to l}{\sum\limits_{i\to m\ne l}{w_{i}^{l}w_{i}^{m}}{{\varphi }_{l}}{{\varphi }_{m}}} \\ \sum\limits_{i\leftarrow l}{\sum\limits_{i\leftarrow m\ne l}{w_{i}^{l}w_{i}^{m}}{{\varphi }_{l}}{{\varphi }_{m}}} \\ \end{matrix} $  (6) 
In this work,three molecules composed of carbazol (D) and triazine (A) groups are theoretically studied.
2,4bis(3(9Hcarbazol9yl)9Hcarbazol9yl)6phenyl1,3,5triazine[11, 12, 13],2(12phenylindolo(2,3a) carbazole11yl)4(3(9Hcarbazol9yl)9Hcarbazol9yl)6phenyl1,3,5triazine and 2,4bis(3(9Hcarbazol9yl)9phenyl9Hcarbazole)6phenyl1,3,5triazine are marked with No.1,No.2,and No.3 respectively (shown in Fig. 1). It is significant that No.1 is a typical DAD molecule,while No.2 is a D'AD type with different donor groups connected to the A group. No.3 is a generalized system of No.1,with an aromatic benzene ring inserted between D and A groups,which is a typical D $\pi$ A $\pi$ D molecule. The dihedral angles between D and A in three molecules optimized at B3LYP/631G^{*} level are different with each other (see Table Ⅰ). In No.1,the angles between D and A are 19.79° and 21.12°. While the angles between D' and A in No.2 changed to 47.06° and the DA angle becomes 13.54°. For No.3,the insert of the benzene ring between D and A makes the angles between the D group and the $\pi$ unit become 51.40° and 52.50°. The significant increase of the angle between D and A will obstacle the charge transfer from D to A,thus less charge transfer will be expected for No.2 and No.3 in comparison with No.1. From Table Ⅰ,we can also see that the insert of the benzene rings decreases the angle between the benzene ring and A (a5). In addition,the three benzene rings connected to the A group keep good planarity as illustrated in Fig. 1.
For TADF emitters,small energy gap between the S1 state and the T1 state is a necessary condition. Theoretical calculations of excited states usually adopt the time dependent density functional theory (TDDFT) methods for large and medium systems. However,some researches have shown that TDDFT with nonhybrid functional always underestimates transition energies for chargetransfer (CT) states due to the neglecting of longrange Columbic attraction between the separated electrons and holes [14, 15]. While TDHF usually suffers from the socalled electron correlation problem and it may overestimate transition energies. It is found that the excited state calculation is largely depent on the HF% in functionals [16, 17]. Therefore,an optimal HF% (OHF) in TDDFT calculation should be determined. It has been proven that OHF is proportional to the CT amount $q$ with a relationship of OHF=42 $q$ . The CT amount for No.1,No.2 and No.3 are 0.886,0.860 and 0.870 respectively (shown in Table Ⅱ). Correspondingly,the OHF calculated for three molecules are 37.2,36.0 and 36.5. According to the results,the PBE38 (OHF=37.5) functional [18, 19] is adopted to calculate the excitation energy for all the three molecules. For comparison,the calculation is also performed using the BMK (OHF=42) functional (see Table Ⅱ). It is found that the excited energy is influenced significantly by the functional used. The excited energy calculated with the PBE38 functional for all the three molecules are smaller than that calculated with the BMK functional.
To calculate the zerozero excited energy for the S1 and T1 states theoretically is quite timeconsuming. Here,we adopt the useful formula as follows which has been proven correct and convenient [8].
$ E_{0  0} \left( {\textrm{S1}} \right) = E_{\textrm{VA}} \left( {\textrm{S1},\textrm{OHF}} \right)  \Delta E_\textrm{V}  \Delta E_{\textrm{stokes}} $  (7) 
$ \begin{matrix} {{E}_{00}}\left( 3\text{CT} \right)={{E}_{00}}\left( \text{S1} \right)[{{E}_{\text{VA}}}\left( \text{S1},\text{OHF} \right) \\ 0.12cmC{{E}_{\text{VA}}}\left( \text{T1},\text{BLYP} \right)] \\ \end{matrix} $  (8) 
$ {{E}_{00}}\left( 3\text{LE} \right)=\frac{{{E}_{\text{VA}}}\left( \text{T1},\text{OHF} \right)}{\omega }\Delta {{E}_{\text{stokes}}} $  (9) 
$ C=\frac{{{E}_{\text{VA}}}\left( \text{S1},\text{OHF} \right)}{{{E}_{\text{VA}}}\left( \text{S1},\text{BLYP} \right)} $  (10) 
The natural transition orbitals (NTOs) and the eh distributions of the S1 states for three molecules are shown in Fig. 2 (a) and (b). For No.1,holes are mainly located at two peripheral bicarbazole groups,while electrons are mainly distributed at the triazine and benzene groups. It means that electrons transfer from two D groups to the A group when the molecule is excited to the S1 state. It can also be confirmed by the NTO diagram,which shows that 96% of the excitation mainly happens from two D groups to the A group. Comparing No.2 with No.1,one can see that the replacement of one bicarbazole group with the indolocarbazole group breaks the symmetry of the molecule and also influences the excitation property. As illustrated,holes are only distributed on one bicarbazole group for No.2. Thus one can also deduce that electrons transfer mainly from one bicarbazole group to the triazine and benzene group in No.2,which is also in consistence with the NTO diagram. In comparison with the NTO of No.1,the transition orbital of No.2 is less delocalized. As mentioned above,the ST energy gap of No.2 is much larger than that of No.1. This is consistent with the conclusion that the more delocalized the transition orbital is,the smaller the ST energy gap will be [20]. For No.3,the transition happens from the two carbazole groups to the triazine group and the benzene groups between them. Consequently,significant charge transfer property for the S1 states of all the three molecules can be found. Nevertheless,there is still some component from localized excitation (LE) for the S1 state. In Fig. 2(c),the overlap between electrons and holes can be directly seen. For No.1,the overlap mainly happens in the triazine group and two neighbor carbazole groups. It is similar for No.2,which is located at one carbazol group and the triazine group. For No.3,the benzene groups inserted between D and A groups are the main area for eh overlap. As the oscillator strength of one molecule is proportional to the transition orbital overlap. The larger the eh overlap is,the greater the transition orbital overlap will be,and the lager the oscillator strength will be. The fluorescent rate is also proportional to the oscillator strength. Thus a higher fluorescent intensity may be obtained for the system with larger eh overlap. Nevertheless,large overlap of transition orbitals may also enlarge the ST energy gap. Consequently,the tradeoff of the CT and LE component in S1 will be important for highly efficient TADF emitters.
For quantitative comparison,the $\Delta r$ index and the integral of the overlap of eh ( $S$ ) are introduced. The $\Delta r$ index was proposed to measure chargetransfer length during electron excitation and the holeparticle pair interactions could be related to the distance covered during the excitations,and it is defined as follows [21]:
$ \Delta r = \frac{{\displaystyle\sum\limits_{ia} {K_{ia}^2 \left {\left\langle {\varphi _a } \rightr\left {\varphi _a } \right\rangle  \left\langle {\varphi _i } \rightr\left {\varphi _i } \right\rangle } \right} }}{{\displaystyle\sum\limits_{ia} {K_{ia}^2 } }} $  (11) 
The energy level structure and their dynamics determine the photophysical property of the molecules. The energy level structures of excited states for No.1,No.2 and No.3 are shown in Fig. 3. All the calculations are performed with the optimal HF method at the PBE38/631G^{*} level. For No.1,the first triplet excited state (T1) and the second triplet excited state (T2) are degenerate. The energy of the third triplet excited state (T3) is about 72 meV higher than that of T2. All the three triplet states are lower in energy than the S1 state and the energy gap between S1 and T1 is 184 meV. As shown in the energy level diagram,S2 are much higher than S1. For No.2 and No.3,there are also three triplet states lower than S1 in energy. The gap between S1 and T1 is as large as 607 meV for No.2 and 856 meV for No.3. In comparison with the 00 energy gaps between S1 (T1) and S0,the vertical excitation energy gaps are much larger. This also indicates that there is significant relaxation between S1 (T1) and S0 in geometric structures. Generally,the internal conversion (IC) is much more quickly than the intersystem crossing (ISC) when the energy gap between the states with the same spin multiplicity is not large enough. We can deduce that the RISC process for all the three systems should mainly happens between the T1 state and the S1 state. Of course,the S2 state should also be in consideration when S2 is quasidegenerate with S1 such as in No.2. However,the ISC process may mainly happen between the S1 state and the T3 state for both No.1 and No.2. For No.3,the ISC from S1 to T2 and T3 should be with the same importance. Based on the energy level structures,the theoretical model can be established and the dynamics of the excited states will be studied then. We will present our investigation on the dynamics of the excited states in the future work.
Ⅳ. CONCLUSIONIn summary,firstprinciples investigations on three triazine based molecules designed for TADF emitters are performed. An optimal HF method with PBE38 functional is adopted to predict the ST energy gap. The analysis of NTO,the eh distribution and the eh overlap indicated that the ST energy gap is closely related to the CT and LE component in S1. Quantitative calculation reflects that effective separation of electron and hole by inserting aromatic groups between D and A can significantly enhance the oscillator strength. Symmetric geometry is a necessary condition for TADF emitters,which can provide more delocalized transition orbitals and consequently a small ST energy gap. The arrangement with D groups as many as possible connected with the A group may be a useful way to obtain both small ST energy gap and large fluorescent rate,which is quite important for highly efficient TADF emitters. The geometryproperty relationship will provide some enlightenment on the design of high efficient TADF emitters. The energy level structures calculated with the PBE38 functional will provide the basis for the study of the dynamics of the excited states.
Ⅴ. ACKNOWLEDGMENTSThis work is supported by the National Natural Science Foundation of China (No.11374195 and No.21403133),Taishan Scholar Project of Shandong Province and the Scientific Research Foundation of Shandong Normal University,and 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 USTC for his helpful suggestion and discussion in the detail calculation.
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