Toward an Accurate Description of Thermally Activated Delayed

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Toward an Accurate Description of Thermally Activated Delayed Fluorescence: Equal Importance of Electronic and Geometric Factors Chao Wang, Keren Zhou, Shuping Huang, and Qisheng Zhang J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.9b01896 • Publication Date (Web): 12 Apr 2019 Downloaded from http://pubs.acs.org on April 12, 2019

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The Journal of Physical Chemistry

Toward an Accurate Description of Thermally Activated

Delayed

Fluorescence:

Equal

Importance of Electronic and Geometric Factors Chao Wang‡a, Keren Zhou‡a, Shuping Huangb,c and Qisheng Zhang*a a

MOE Key Laboratory of Macromolecular Synthesis and Functionalization, Department of

Polymer Science and Engineering, Zhejiang University, Hangzhou, China, 310027 b

College of chemistry, Fuzhou University, Fujian 350108, China

c

Fujian Provincial Key Laboratory of Theoretical and Computational Chemistry, Xiamen, Fujian,

361005, China

Abstract: Obtaining reasonable geometric and electronic structures of excited states are essential for accurately predicting the thermally activated delayed fluorescence (TADF) for the application in organic light-emitting diodes (OLEDs). Both electronic and geometric factors are evaluated using density functionals for reproducing the vertical emission (EVE(S1)) and singlet-triplet splitting energies (ΔEST) of 28 typical TADF molecules. It is found that most TADF molecules (charge transfer type) can easily twist upon excitation, indicating the importance of constructing a rigid molecular structure for improving the performance of TADF OLEDs. Functionals with insufficient exact exchange will result in the substantial underestimation of the relaxation energy of T1, suggesting that the hybrid functionals like B3LYP should not be used. Overall, the best

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approach for calculating EVE(S1) and ΔEST is the descriptor-tuned LC-ωPBELOL functional combining the CAM-B3LYP-optimized excited state geometries, which shows mean absolute deviations (MADs) of 0.21 and 0.10 eV, respectively.

Introduction Pure-organic thermally activated delayed fluorescence emitters have recently become a research hotspot because of their potential application in organic light emitting diodes (OLEDs).1-4 The vanishing energy difference (ΔEST) between the lowest singlet (S1) and triplet (T1) excited state is a key for efficiently up-converting no emissive triplet excitons to emissive singlet ones, which can realize nearly 100% internal quantum efficiency in OLEDs.5 A widely-used strategy for TADF molecule design is to construct a twisted donor-acceptor (D-A) molecular structure, which narrows the singlet-triplet energy splitting of the charge-transfer (CT) state and enhances the energy of the lowest locally excited triplet state (3LE).6-7 To develop new TADF emitters, molecular simulations of excited states are of the essence. Taking into account the relatively high molecular weight of TADF emitters (about 500-1000), the time-dependent density functional theory (TD-DFT) provides reasonable results at an acceptable cost.8 Various functionals lead to very different results, and one of the key factor is the percentage of Hartree-Fock exchange (HF) in the functionals. It was reported that functionals with low HF% result in a substantial twisting of a D-A molecule and an underestimation of the vertical emission energy of S1(EVE(S1)).9-10 The reason is the formation of the spurious CT in the S1 state when the functional suffers from the self-interaction error (SIE).11-13 The SIE also relates to the delocalization/localization error which can be relieved by the range-separation (RS) of exchange potential combined with the tuning of RS parameter (ω) in the hybrid functional.11, 14-15 Recently,


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the IP-tuned RS functional16-17, the descriptor-tuned hybrid functional18-19 and triplet-tuned RS functional20 have shown their reliability in predicting the lowest vertical absorption energy and ΔEST of TADF emitters. The nearly delocalization/localization-free nature of these functionals guarantees the reasonable description of excited states.21-24 Apart from the electronic structure, Jacquemin has pointed out that the geometric structure of S1 is also a key for obtaining accurate emissions.25 In many typical TADF emitters, the dihedral angle between the donor and acceptor is allowed to twist by 30° ~ 60° during the geometry relaxation in the S1 state,26-27 which may be driven by the molecular orbital energy gaps between the donor and acceptor fragments.28 Such a twisting not only decreases vertical emission energy but also the value of ΔEST.29-34 Unfortunately, it is still difficult to obtain reliable S1 molecular geometries in D-A systems.35-38 Combing both geometric and electric factors, a spurious CT nature of S1 will result in the vanishing oscillator strength and spin orbit-coupling underestimating the rate of reverse intersystem crossing (RISC), and vice versa for the spurious LE nature.39-41 The reliability of functionals in predicting both factors needs to be benchmarked towards successful design of TADF emitters. In this work, we carefully access the impact of geometric and electronic factor on EVE(S1) and ΔEST for 28 typical TADF emitters (Figure 1).1, 5, 18-19, 26, 42-45 The molecules are classified into 3 groups according to their dihedral angles (θ) between the donor and acceptor in the ground state (S0), i.e., S (θ < 40 °), M (40 °< θ < 80 °) and L (θ > 80 °) groups. The geometric optimization and the calculation of transition energies are thus separated into two individual steps using both default functionals with different HF% and tuned functionals, such as the K-OHF tuning18 for PBEα functional and IP16-17 and LOL46 tuning for LC-ωPBE functional. The functional and tuning methods are specified in the next section. Experimental results are directly adapted as references.18


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High level post-HF methods are not benchmarked in this work because of the huge computational costs.

Figure 1. Chemical structures of TADF emitters studied in this work. θ represents the dihedral angles between donor and acceptor fragments. Computational Details


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Typical TADF molecules have an acceptor core and one or several donor fragments, as shown in Scheme 1. For the molecules with multi-donors, the averaged bond length d and dihedral angle θ are defined as follows: (2)

(3)

Scheme 1. The simplified molecular skeleton of TADF emitters. Donor and acceptor fragments are labelled as D and A, respectively. In most cases, the donor fragments in each emitter are identical All DFT calculations are performed in a polarizable continuum model (PCM) with toluene solvation using Gaussian 0947 software. Although the state-specific (SS) formalism can improve the TDDFT performance on both excitation energies and state dipole moments,48-49 it is not used here because we use different functionals for geometry optimization and emission energy calculation, and the purpose of this work is to compare the different results obtained from different functionals. The Tamm−Dancoff approximation (TDA)50 is applied to all the TD-DFT calculations for avoiding triplet instabilities.51-52 The geometries of S0 and S1 are optimized at the B3LYP/631G(d) and TD-DFT/6-31G(d) levels, respectively, while the T1 is accessed with a spin-relaxed


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open-shell optimization at the UDFT/6-31G(d) level. The transition energies are calculated using different default and tuned functionals combined with the 6-311G(d) basis set. The calculated singlet-triplet splitting is defined as the energy difference between the S1 and T1 (ΔEST = E(S1) – E(T1)). In the IP tuning, the optimal range separation parameter (ωIP) of a RS functional is obtained by minimizing the square of the difference (J2) between the energy of the highest occupied molecular orbital (HOMO) and ionization potential (IP) of the n and n+1 electron systems: (4) The IP-tuned LC-ωPBE functional is labeled as LC-ωPBEIP. In descriptor tuning, the optimal proportion of the HF exchange (αo) in PBEα functional (K-OHF tuning)18 and the optimal range separation parameter (ωLOL) in a LC-ωPBE (LOL tuning)46 are obtained by calculating the descriptor and substituting it into an experimentally-determined equation, respectively: (5) (6) where K is defined as the negative growth rate of the exciton binding energy Eb with respect to α (K = −dEb/dα) for measuring the degree of CT18 and rLOL refers to the mean localization distance for determining the degree of the localization of the electron density46. The descriptor-tuned PBEα and LC-ωPBE is referred as PBEαo and LC-ωPBELOL, respectively. Since PBEαo is a tuned version of PBE0 with more flexible HF%, PBE0 is not included in our tests. It is reported that the optimal HF% for global hybrid functionals is usually under 44% in the system of TADF molecules,18-19 thus M062X (54%) is not included as well.


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The functional tuning of PBEαo for optimizing the S1 geometry is done based on the S0 geometry. The functional tuning of PBEαo, LC-ωPBEIP and LC-ωPBELOL for calculating the EVE(S1) and ΔEST is performed based on the S1 geometry. A home-made python code is used to perform the automation of the tuning scheme. The natural transition orbitals (NTOs)53 and distance of charge transfer (DCT)54 are calculated using Multiwfn 3.4.0.55 Results and Discussion Three functionals, namely B3LYP, PBEαo and CAM-B3LYP, are selected to compare the influence of HF exchange on molecular geometries. The B3LYP holds a global hybrid of 20% HF exchange, while the CAM-B3LYP mixes the short range with 20% HF exchange and the long range with 60% HF exchange. PBEαo has an optimally-tuned global hybrid from about 25% to 50% regarding different molecules. The optimal HF% values are listed in Table S1. As listed in Table S2, the stretching of d and twisting of θ in S1 is suppressed with the increase in the proportion of HF exchange. The constraint of d is more pronounced in the molecules of M group than S group, while those of θ is of similar magnitude in L group. For the molecules in L group, the constraint of molecular geometry is so strong that negative deviations are found in d. Hence, we deduce that the default RS functionals mixing 100% HF at the long range may be inappropriate for the optimization because the relaxation of S1 might be underestimated. Generally, there are strong dipole-dipole interactions between the TADF emitters and the external environment, i.e., the polar solvents or host molecules in the thin films, leading to the substantial broad emission bands.56-60 Interestingly, it is difficult to relieve the issue by building the nonpolar central symmetric molecular geometry.61-64 Taking DPA-AQ as an example, we plot the rigid scan of the potential surface of the S1 with respect to θ1 and θ2 in Figure 2. It is observed that the potential surface of S1 is very flat and barrierless. Meanwhile, the CAM-B3LYP


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suppresses the twisting of the θ1 and θ2 by preserving the equivalence of each other. On the other hand, the B3LYP and PBEαo result in the substantial twisting of θ2 and the inequivalence of θ1 and θ2 because of the obtained different Δd1 and Δd2. Our calculation indicates that the high HF% can constrain the excessive geometric relaxation in S1 and help maintain the symmetry in the unrestricted geometric optimizations. The flat potential surface and the asymmetric S1 geometry can be responsible to the broad emission bands because they give rise to a wide distribution of the molecular geometries, especially under the perturbation of an external molecular environment which leads to the significant polarization of S1. Therefore, constructing a rigid molecular structure is particularly useful in improving the color purity and efficiency of OLEDs.65

Figure 2. The color-filled map of relative energy (in eV) as a function of θ1 and θ2 on the potential surface of S1 for DPA-AQ. The diamond relates to the optimized S1 geometry and the cycle corresponds to the S0 geometry. Then we exam the electronic factors based on the CAM-B3LYP geometry which is one of the most frequently used functional in the geometry optimization of S1 for TADF emitters.16-17, 66-68 As displayed in Figure 3a (detailed calculated values are given in Table S3 ~ S4), the default functionals with low HF exchange percentage significantly underestimate the emission energies,


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while the default RS functionals with high proportion of HF exchange substantially overestimate them. The BMK performs relatively well among the default functionals with somewhat overestimation because of the fixed amount of HF exchange, especially in S group. In contrast, tuning methodologies provide flexible ways of changing the HF exchange according to the geometric structures of molecules, which results in relatively better predictions than functionals with fixed proportion of HF exchange. In Figure 3b, a normal distribution of the errors can be found in LC-ωPBELOL which performs the best with a MAD of 0.21 eV. Our result suggests that the tuning methodology is necessary for predicting the emission energies but the error is larger than the lowest absorption based on the S0 geometry as reported previously (with a MAD of about 0.1 eV).16-17 Interestingly, the BMK also provides somewhat good result with slight overestimation or even exceeds the optimally-tuned functionals on average.


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Figure 3. (a) The color-filled map of the signed deviation of EVE(S1) with respect to the experimental emission energy as a function of the molecules calculated by different DFT functionals. (b) The number of molecules as a function of various signed deviation of EVE(S1) calculated using the 4 best functionals. We are now in the position to explore geometric factors (S1) by using different functionals. Figure 4a presents the comparison of the performance of different functionals on EVE(S1) at optimized S1 geometries using various functionals (detailed calculated values are given in Table S3 ~ S8). In general, functionals show similar performance when different molecular geometries are used. It can be found that PBE and B3LYP significantly underestimates EVE(S1) for all emitters. However, B3LYP performs relatively well in S group using the CAM-B3LYP-optimized geometry, in which excessive twisting relaxations in S1 are successfully suppressed. BMK exceeds


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other default functionals except the above case, while the RS functionals substantially overestimate the EVE(S1). Inversely, the tuned functionals provide similar good results with MADs less than 0.3 eV, regardless of the geometries optimized by different functionals. Figure 4b compares the absolute deviation (AD) of calculated ΔEST using different functionals at various optimized S1 geometries (detailed calculated values are given in Table S9 ~ S14). In general, the TADF molecules whose donor and acceptor fragments are perpendicularly linked (L group) can potentially have very small ΔEST owing to the vanishing exchange integral between the hole and electron wavefunctions, if the triplet energies of all fragments are high enough.43 Such a configuration is immune to the twisting relaxation in a CT state. Therefore L group is less affected with smaller deviations in the geometric change than the other two groups. PBE and B3LYP basically provide negative ΔEST for all emitters owing to the insufficient HF exchange. BMK predicts ΔEST with small deviations at CAM-B3LYP-optimized geometry. The RS functionals result in substantial overestimation on ΔEST at all geometries due to the redundant HF exchange. As expected, the optimally-tuned functionals provide small deviations for different geometries. It should be noted that the MAD calculated at B3LYP-optimized geometry is larger than those at the PBEαo and CAM-B3LYP-optimized geometries for all tuned functionals, especially the LCωPBEIP and LC-ωPBELOL by ~0.1 eV. Since the magnitude of ΔEST is small (less than 0.3 eV for most TADF molecules),61 such difference is already large enough to confirm that the sensitivity of geometric factor is huge even if the electronic structures can be correctly described. Therefore, our calculations suggest that CAM-B3LYP is reliable in the optimization of the S1 geometry for TADF emitters and B3LYP introduces geometric errors that cannot be relieved even by the functional tuning schemes.


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Figure 4. The absolute deviation (AD) of (a) EVE(S1) and (b) ΔEST calculated using default functionals (left) and tuned functionals (right) at B3LYP, PBEαo, and CAM-B3LYP-optimized S1 geometries.


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Figure 5. The distribution of natural transition orbitals (NTOs) of DPA-Ph-AQ with corresponding weights (w) and charge transfer length (DCT) at B3LYP and CAM-B3LYP-optimized S1 geometries. DCT represents the distance between the positive (Δρ+) and negative (Δρ−) barycenters. In Figure 5, the S1 transition described by PBE (pure GGA) is very susceptive to the molecular geometries predicted by different functionals, i.e., B3LYP and CAM-B3LYP, because the lack of HF exchange in PBE results in a spurious CT excited state (DCT = 9.37 Å). BMK also suffers from the B3LYP-optimized geometry (DCT = 9.41 Å) but performs better in the CAM-B3LYPoptimized geometry showing a mixed CT+LE nature (DCT = 4.49 Å). Such a trend is relieved when the optimally-tuned functional is used, because the spurious CT issue is fixed by mixing the LE character into the S1 excitation according to different geometries. The difference of the nature of transitions (CT or LE) caused by different geometries vanishes when the LC-ωPBE functional is applied to different geometries, in which the LE excitation becomes dominant (DCT around 0.2 Å). Our result indicates that the pure functionals (or hybrid functionals with low HF%) is sensitive to the variation of S1 geometry due to the spurious CT excitation, while the RS functionals are insensitive to the S1 geometries since the LE excitation is dominated. The optimally-tuned


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functionals are also less affected by the geometric factor showing a universal usage in different type of molecules. The key to obtain a vanishing ΔEST is to maintain a vanishing conjugation between the donor and acceptor fragments and to have a high 3LE state approach to (or even higher than) S1.43 This means the relaxation energy of T1 (λT) should be sufficient small or smaller than that of S1 (λS). Although the IP-tuned RS and doubly hybrid functionals have proven their reliability on reproducing the ΔEST of TADF emitters,16-17, 69 the geometry factor, has not been evaluated. Table S15 compares the relaxation energies of S1 and T1 and the difference between them (Δλ). In S group, the main difference occurs in DPA-DPS and DTPA-DPS where negative Δλ is obtained using CAM-B3LYP-optimized geometries and positive Δλ is obtained using PBEα and B3LYP. The CAM-B3LYP-optimized geometries provide substantially larger λT than PBEα and B3LYP. Here we also recall that λT is usually much larger than λS in conjugated oligomers, leading to a substantial large ΔEST for them.70 Comparing the experimental fluorescence and phosphorescence spectra of them, we can learn that their ΔEST is large (0.47 eV and 0.43 eV for DPA-DPS and DTPA-DPS, respectively) due to the large relaxation energies of T1 (or large overlap between the HOMO and LUMO17). Therefore, we believe CAM-B3LYP may predict more reasonable S1 and T1 geometries than B3LYP. Similarly in M and L groups, CAM-B3LYP provides better results especially when T1 is dominated by a LE nature like Cz-TRZ2. Additionally, we also notice that PBEα and B3LYP may provide poor S1 or T1 geometries in some cases with negative relaxation energies. These functionals result in an excited state geometry too far away from the ground state due to the very flat energy potential surfaces. The problem is severe in B3LYP results, especially when T1 should be dominated by a LE nature. Our results suggest that a large proportion of exact exchange is necessary for optimizing both S1 and T1 geometries of TADF emitters.


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Conclusions In this work, we evaluate both geometric and electronic factors for benchmarking the performance of different density functionals on the calculation of vertical emission energies (EVE(S1)) and the singlet-triplet splitting (ΔEST) of 28 typical TADF emitters. Our results suggest that a large fraction of exact exchange in functionals, like CAM-B3LYP, is necessary to avoid the redundant stretching of bond length and the twisting of dihedral angles between donor and acceptor fragments. Moreover, the flat potential energy surface suggests the importance of building a rigid molecular structure for avoiding the solid-state solvation effect and energy loss in OLEDs. Global hybrid functionals like B3LYP significantly underestimates EVE(S1) and ΔEST, while the RS functionals like LC-ωPBE overestimates them. Significant improvement is shown when the optimal tuning scheme of density functionals are used, i.e. descriptor- and IP-tuning. Interestingly, the impact of excited state geometries on EVE(S1) is unobvious when descriptor and IP tuning (MAD ~ 0.2 eV) is used due to the flexible tuning of HF exchange. On the other hand, obtaining reasonable S1 and T1 geometries is a precondition for reproducing correct ΔEST. Functionals of insufficient HF exchange will result in the substantial underestimation of the relaxation energy of T1, indicating that functionals like B3LYP should not be used. Overall, the best approach for calculating EVE(S1) and ΔEST is the descriptor-tuned LC-ωPBELOL functional combing the CAMB3LYP-optimized excited state geometries showing mean absolute deviations of 0.21 and 0.10 eV, respectively.

ASSOCIATED CONTENT Supporting Information. The geometric change upon excitation, vertical emission and singlettriplet splitting energies calculated using different functionals at S1 and T1 geometries optimized


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by CAM-B3LYP, PBEαo and B3LYP functionals combined with 6-311G(d) basis set in PCM toluene solvation, relaxation energies of S1 and T1. This material is available free of charge via the Internet at http://pubs.acs.org. AUTHOR INFORMATION Corresponding Author Qisheng Zhang (E-mail: [email protected]) Author Contributions ‡These authors contributed equally. ACKNOWLEDGMENT This work is supported by the Natural Science Foundation of China (Grant No. 51673164, 51873183) and National Key R&D Program of China (Grant No. 2016YFB0401004). REFERENCES 1. Endo, A.; Sato, K.; Yoshimura, K.; Kai, T.; Kawada, A.; Miyazaki, H.; Adachi, C., Efficient up-Conversion of Triplet Excitons into a Singlet State and Its Application for Organic Light Emitting Diodes. Appl. Phys. Lett. 2011, 98, 083302. 2. Goushi, K.; Adachi, C., Efficient Organic Light-Emitting Diodes through up-Conversion from Triplet to Singlet Excited States of Exciplexes. Appl. Phys. Lett. 2012, 101, 023306. 3. Goushi, K.; Yoshida, K.; Sato, K.; Adachi, C., Organic Light-Emitting Diodes Employing Efficient Reverse Intersystem Crossing for Triplet-to-Singlet State Conversion. Nat. Photonics 2012, 6, 253-258. 4. Mehes, G.; Nomura, H.; Zhang, Q.; Nakagawa, T.; Adachi, C., Enhanced Electroluminescence Efficiency in a Spiro-Acridine Derivative through Thermally Activated Delayed Fluorescence. Angew. Chem., Int. Ed. 2012, 51, 11311-11315. 5. Uoyama, H.; Goushi, K.; Shizu, K.; Nomura, H.; Adachi, C., Highly Efficient Organic Light-Emitting Diodes from Delayed Fluorescence. Nature 2012, 492, 234-238. 6. Samanta, P. K.; Kim, D.; Coropceanu, V.; Bredas, J. L., Up-Conversion Intersystem Crossing Rates in Organic Emitters for Thermally Activated Delayed Fluorescence: Impact of the Nature of Singlet Vs Triplet Excited States. J. Am. Chem. Soc. 2017, 139, 4042-4051. 7. Lee, K.; Kim, D., Local-Excitation Versus Charge-Transfer Characters in the Triplet State: Theoretical Insight into the Singlet–Triplet Energy Differences of Carbazolyl-


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For Table of Contents Only

TOC Graphic


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Figure 1 471x480mm (300 x 300 DPI)


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Figure 2



Figure 3


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Figure 4



Figure 5


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Scheme 1



TOC Graphic 192x135mm (120 x 120 DPI)


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Toward an Accurate Description of Thermally Activated Delayed

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