Accurate Prediction for Dynamic Hybrid Local and Charge Transfer

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C: Plasmonics; Optical, Magnetic, and Hybrid Materials

Accurate Prediction for Dynamic Hybrid Local and Charge Transfer Excited States From Optimally-Tuned Range-Separated Density Functionals Yanrong Jiang, Zhubin Hu, Bin Zhou, Cheng Zhong, Zhenrong Sun, and Haitao Sun J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.9b00027 • Publication Date (Web): 12 Feb 2019 Downloaded from http://pubs.acs.org on February 14, 2019

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The Journal of Physical Chemistry

Accurate Prediction for Dynamic Hybrid Local and Charge Transfer Excited States from Optimally-Tuned Range-Separated Density Functionals Yanrong Jiang1#, Zhubin Hu1#, Bin Zhou1, Cheng Zhong3*, Zhenrong Sun1,2, Haitao Sun1,2*

1State

Key Laboratory of Precision Spectroscopy School of Physics and Materials Science, East China Normal University Shanghai 200062, People’s Republic of China 2Collaborative Innovation Center of Extreme Optics Shanxi University, Taiyuan, Shanxi 030006 3Department of Chemistry, Wuhan University, Hubei 430072, People's Republic of China

* Corresponding authors: [email protected]；[email protected] # These

authors contributed equally in this work.

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Abstract Fine regulation of excited-state characteristics of organic molecules plays a vital role in the rational design of novel optoelectronic materials. Recently the fluorescent emitters with a hybridized local and charge transfer (HLCT) excited state have attracted significant interest in developing high-efficiency organic light-emitting diodes. The HLCT state generally consists of a mixture of local excitation (LE) and charge transfer (CT) characters that are known to be sensitive to molecular configuration and surrounding environment. Thus both qualitative and quantitative characterizations of “dynamic” HLCT states remain challenging from a theoretical perspective. In this work, a series of donor-acceptor (D-A) molecules with HLCT excited-state characters were theoretically studied using density functional theory (DFT) and time-dependent DFT (TDDFT). Successful prediction of both vertical absorption and emission excitation energies (EVA and EVE) of the lowest singlet excited state (S1) is demonstrated when using the optimally-tuned range-separated (RS) density functionals with the smallest average mean absolute deviations (MADs) of 0.07 eV for LC-ωPBE* and 0.09 eV for ωB97XD* compared to the available experimental data. The percentages of CT character (CT%), nature transition orbitals (NTOs), hole-electron distribution and transition density matrix maps are further analyzed qualitatively and quantitatively, highlighting the importance of right balance between localization and delocalization effects of electronic structures. The results indicate that moderate amount of exact exchange (eX%) included in density functionals is key in reasonably predicting HLCT states. Thanks to the accuracy of optimally-tuned RS method, quantitative characterization of energy gaps and spin-orbit couplings between singlet and triplet excited states is performed to assess the possible “hot-exciton” paths. The present work provides a reliable and efficient theoretical tool for further developing novel HLCTbased optoelectronic materials.


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1. INTRODUCTION Organic semiconductor materials are highly promising for a variety of applications such as organic light emitting diodes (OLEDs), organic field effect transistors, organic photovoltaics, organic photodetectors, and organic bioelectronics.1-9 It is clear that the efficiency of these optoelectronic devices depends to a large extent on the control of nature of relevant electronic excited states and the rationalization of related photophysical phenomena.10-14 Typically in organic molecular semiconductors, when a photon is absorbed on an organic molecule, it is excited to form a singlet or triplet exciton according to spin multiplicity.15 Such an exciton generally consists of a hole and an electron which are bound to each other by the electrostatic Coulomb interaction, i.e., the strongly-bound locally excited (LE) exciton and the weakly-bound chargetransfer (CT) exciton. For instance, the thermally activated delayed fluorescence (TADF) mechanism put forward by Adachi et al. has opened a new paradigm through converting the lowest triplet (T1) excitons to singlet (S1) excitons for developing newgeneration, low-cost, and high-efficiency fluorescent OLEDs.16-20 Further, it has been demonstrated that a mixture of LE and CT contributions for S1 and T1 excitons is in favor of efficient TADF materials: a large CT component to minimize the S1-T1 energy difference (ΔEST) and a significant localized component to prompt spin-orbit coupling (SOC) that enhances T1 → S1 reverse intersystem crossing (RISC).21-23 Ma, Yang, and co-workers recently proposed a “hot-exciton” process from higher triplet excited states (Tn, n > 1) to S1 states that possess a hybridized local and charge transfer (HLCT) character.24-26 Construction of such a HLCT excited state in OLEDs can simultaneously benefit from the high-efficiency fluorescence emission of the LE part and full utilization of triplet excitons due to the weak binding energy and easy spin flip of CT part.11, 27 To this end, either the TADF or the “hot-exciton” materials generally consist of donor-acceptor (D-A) type of molecules where the state-mixing of LE and CT states are required to further contribute to tune the energy levels of excited states and to enhance triplet-singlet RISC. Considerable efforts have been taken in mixing moderate percentages of CT and LE species and constructing such a HLCT state to realize highly



efficient OLED materials.28-31

More importantly, the knowledge and understanding of behavior of these D-A molecules in HLCT excited states is intriguing and still challenging for both experimentalists and theoreticians.12, 13, 32 Recently, Yang et al. demonstrated that the hybridization and de-hybridization processes of HLCT states can be realized by functional group modification with increasing number of phenyls and transformation of an excited state character from the LE state to the CT state can be achieved through increasing solvent polarity.33 Our previous study confirmed that such a dominant contribution of excited state switching from LE-like to CT-like with increasing dielectric constant also exist in solid TADF materials.34 In other words, the balance between exciton localization (related to LE) and exciton delocalization (related to CT) plays a key role in designing novel OLED materials. Quantum chemical calculations can provide important and deep insights into the electronic and optical properties of organic materials, rationalize experimental results, and assist in the design of novel materials.13, 14 It is thus intensely desired to look for more precise theoretical methods to quantify HLCT state which is considered as a superposition of LE and CT states.

Time-dependent density functional theory (TDDFT)35, 36 with standard approximations (e.g., global hybrid B3LYP37 functional) is known to provide efficient and accurate predictions for the locally excitations or valence excitations of molecules.38-40 However, TDDFT calculations based on those standard functionals fail in describing the CT excitations that commonly exist in D-A molecular system.41-43 Particularly in the socalled (de-)hybridization process where the percentages of LE/CT change dynamically, fine modulation of LE/CT components and accurate prediction of the HLCT states post a more challenged task from a theoretical perspective. In addition, it has to be pointed out that the relatively large size of D-A molecules limits routine application of highlevel methods such as couple cluster (CC) theory, complete active space with secondorder perturbation theory (CASPT244) and etc. due to their expensive computational cost.12, 45, 46 Furthermore, the introduction of an “optimal” amount of nonlocal Hartree-


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Fock exact-exchange (eX%) and choice of a reliable approximation for the exchangecorrelation (XC) potential for TDDFT have been demonstrated to provide an improved description of various properties of molecules and solids such as fundamental gaps,4749

excitation energies,46,

50-52

polarization energies,53 (de-)protonation energies,54

spin‐state energetics55 and intermolecular electronic couplings.56,

57

Note that the

quantitative characterization of HLCT states and the behavior of LE/CT contribution as a function of various density functionals (i.e. eX%) are rarely reported. So far, the great challenge comes from looking for the appropriate level of theory capable of providing both qualitative and quantitative predictions for HLCT excited states of molecules and further efficiently designing novel optoelectronic materials. In this work, a series of D-A type molecules as shown in Figure 1 were theoretically studied and they are typically employed as non-doped emitting layers in fluorescent OLEDs that significantly break through the 25% upper limit of exciton utilizing efficiency. The good performance of optimally-tuned range-separated (RS) density functional approach is demonstrated compared to the experimental data. The relationship between LE/CT components and eX% is explored. The HLCT characters of excited states are quantitatively and qualitatively characterized by the percentages of CT character (CT%)23, nature transition orbitals (NTOs)58, hole-electron distribution59 and transition density matrix maps60. The resulting “hot-exciton” paths of T → S conversion are proposed based on results of optimally-tuned RS method.



Figure 1. Chemical structures of D-A molecules studied in this work.

2. COMPUTATIONAL DETAILS The ground-state (S0) geometries of D-A molecules presented in Figure 1 taken from the work of Ma et al.26, 30 and Su et al.27 are optimized at the B3LYP/6-31G(d)61 level. Vertical absorption energies EVA(S1) and vertical emission energies EVE(S1) of the lowest singlet excited states are calculated using linear-response TDDFT approach with the TZVP62 basis set based on the S0 geometries and S1 geometries, respectively. The S1 geometries are optimized with the optimally-tuned ωB97XD* (vide infra) functional with the 6-31G(d) basis set. To allow a better comparison to experimental measurements, the polarizable continuum model (PCM)63 is employed to take into account the effects of dielectric medium of isopropyl ether. To test the performance of


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various density functionals and the influence of eX percentages (eX%), we perform TDDFT calculations with ten density functionals: one pure generalized-gradient approximation (GGA) functional (PBE64); one hybrid-GGA functional (B3LYP); three Minnesota functionals (MN1565, M062X66 and M06HF67); and three RS functionals (CAM-B3LYP68, LC-ωPBE69 and ωB97XD70) and two optimally-tuned RS functionals (LC-ωPBE* and ωB97XD*). Compared to the default version of LC-ωPBE and ωB97XD functionals, the symbol of asterisk in LC-ωPBE* and ωB97XD* functionals represents that the range-separation parameters ω values were nonempirically and optimally tuned according to the "tuning" procedure proposed by Baer and Kronik.51, 52, 71, 72

In exact Kohn−Sham (KS) and generalized KS (GKS) theory,73 the energy of

highest occupied molecular orbital (HOMO) for an N-electron system εHOMO (N) should exactly equal to the corresponding negative ionization potential IP(N). An optimal ω value based on the RS functional is obtained by minimizing the following equation: 1

𝐽2 = ∑𝑖 = 0[𝜀𝐻𝑂𝑀𝑂(𝑁 + 𝑖) + 𝐼𝑃(𝑁 + 𝑖)]2

(1)

which not only tunes HOMO (N) vs. IP (N) but also HOMO (N+1) vs. IP (N+1). The HOMO (N+1) and IP (N+1) approximately corresponds to LUMO (N) and EA (N) if ignoring relaxation effects of orbitals. All the optimal ω values are listed in Table S1 in Supporting Information (SI). In order to deeply examine the nature of the lowest electronic transitions, natural transition orbital (NTO) analysis and hole-electron distribution analysis for the S0 → S1 excitations were performed by Multiwfn 3.6(dev) program.74 The NTOs were further exploited to quantitatively evaluate their LE and CT contributions. The weights of CT (CT%) were quantitatively evaluated by calculating the donor fragment (TPA) contributions to hole/particle wave functions obtained from the dominant NTO pairs. Moreover, transition density matrix color-filled maps of S1 states were also performed to get a more intuitive insight to the hybrid character of HLCT excited states.33 The energy difference between singlet and triplet states (ΔEST) and the corresponding spin−orbit coupling (SOC) values were evaluated for the selected molecules to rationalize the progress of intramolecular RISC in the “hotexciton” channel using PySOC program.75 Due to the lack of reliable experimental data



for other closely-related excited states, the high-level second-order approximate coupled cluster singles and doubles (CC2)76 method was employed as a reference. The three lowest lying singlet and triplet excited energies of selected molecules were obtained at the CC2/TZVP level in gas phase using Turbomole77 program. All the CC2 calculations employed the resolution-of-the-identity (RI) approximation for the electron repulsion integrals used in the correlation treatment and the description of excitation processes with the TZVP/C auxiliary basis set. All the DFT calculations were carried out by the Gaussian 0978 and Gaussian 1679 codes. The distributions of NTOs were rendered using VMD 1.9.3 program.80

3. RESULTS AND DISCUSSION 3.1 TDDFT Benchmark of vertical absorption and emission energies The results of statistical analyses including the signed errors (Figure 2a and 2b) and mean absolute deviations (MADs, Figure 2c) between the theoretical and experimental data for the vertical absorption energies EVA(S1) and emission energies EVE(S1) are displayed in Figure 2. The numeric values of MADs using various functionals were listed in Table S2. The experimental values were collected by the maximum wavelength of absorption spectrum in solvents taken from references26, 27, 30. First, for the absorption energies EVA(S1), the optimally-tuned density functional approach reproduces the EVA(S1) that are in excellent agreement with experimental values. The tuned LCωPBE* and ωB97XD* functionals yield the MADs of 0.03 eV and 0.10 eV for EVA(S1), respectively. Interestingly, the MN15 functional performs well with a small MAD of 0.08 eV. The M062X, CAM-B3LYP and non-tuned ωB97XD functionals produce the moderate MADs of 0.20 eV, 0.20 eV and 0.28 eV, respectively. As expected, the PBE (MAD = 1.20 eV) and B3LYP (MAD = 0.50 eV) functionals strongly underestimate the experimental EVA(S1) data. Conversely, the M06HF (MAD = 0.62 eV) and nontuned LC-ωPBE (MAD = 0.54 eV) functionals significantly overestimate the experimental EVA(S1) values. For the emission energies EVE(S1), it can be seen that six density functionals including M062X (MAD = 0.06 eV), CAM-B3LYP (MAD = 0.07


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eV), ωB97XD* (MAD = 0.08 eV), LC-ωPBE* (MAD = 0.11 eV), ωB97XD (MAD = 0.12 eV) and MN15 (MAD = 0.13 eV) can give reasonable prediction compared to the corresponding experimental data. Similarly, the PBE (MAD = 0.79 eV) and B3LYP (MAD = 0.39 eV) functionals still fail to reproduce the experimental EVE(S1). And the M06HF (MAD = 0.37 eV) and non-tuned LC-ωPBE (MAD = 0.31 eV) functionals tend to overestimate the experimental EVE(S1) values. Overall, it is worth noting that the optimally-tuned functionals can produce the best performance for prediction of both EVA(S1) and EVE(S1) as a whole with an average MAD of 0.07 eV for LC-ωPBE* and 0.09 eV for ωB97XD* compared to the experimental data. Notably, the MN15, M062X and CAM-B3LYP functionals can also give reasonable prediction and yield an acceptable average MAD of 0.11 eV, 0.13 eV, 0.13 eV, respectively. This observation is also confirmed by Yang and co-workers.26, 30

Figure 2. Signed error (Ecal.-Eexp.) bar of calculated (a) vertical absorption energy EVA(S1) (eV), (b) vertical emission energy EVE(S1) (eV), (c) calculated mean absolute deviation (MAD, eV) of vertical absorption and emission energy using various DFT



methods compared to the corresponding experimental data.

It is found that the performance of various density functionals or size of errors seems to be closely related to their percentages of exact-exchange (eX%) included in the functionals. Generally, the density functional with low (high) eX% tend to describe the π-conjugated electronic structures with more delocalized (localized) character and accordingly underestimate (overestimate) the excitation energies. As seen in Figure S1, at an interelectronic distance r12 of 2.75 Bohr (roughly 1.455 Å), which is the average distance of carbon-carbon single and double bonds in π-conjugated system, the LCωPBE* functional affords roughly 52% eX whereas the non-tuned LC-ωPBE with the default ω of 0.4 gives almost 88% eX. The CAM-B3LYP and ωB97XD functionals possess 56% and 66% eX, respectively, at this r12 distance. The MN15, M062X and M06HF functionals always have 44%, 54% and 100% eX at any r12 distance. The PBE and B3LYP functionals include relatively low 0% and 20% eX, respectively. As a result, the significantly large errors arise from too low eX% (such as PBE and B3LYP) or too high eX% (such as non-tuned LC-ωPBE and M06HF). The good performance of LCωPBE* functional and other functionals such as MN15, M062X and CAM-B3LYP can be attributed to their suitable amount of eX in the range of 44%~56%. Such a reasonable eX% is in favor of producing neither too delocalized nor too localized electronic structures.

3.2 Quantitative analysis of HLCT states 3.2.1 Analysis of contribution of CT character The percentages of CT character and LE character of S1 states for seven molecules are quantitatively analyzed based on the combination of NTO analysis and orbital composition analysis23, 81 as shown in Figure 3. The CT% are calculated in the range from 1% to 94% listed in Table S3, indicating that the CT% and excited-state characters strongly depend on the employed density functionals. In theory, the seven D-A molecules consist of TPA donor and acceptors with various strength and should possess different CT% or LE%. For example, the excited-state (S1) character of TPA-AN


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molecule that is composed of TPA and anthracene (AN) groups should be assigned as more LE type. The TPA-BZP molecule consisting of TPA donor and relatively strong benzothiadiazole (BZP) acceptor should possess more CT character. However, due to the low eX% and over-delocalization effect of electronic structure, the PBE and B3LYP functionals incorrectly predict the S1 states of seven molecules as “pure” CT states or HLCT states with relatively large CT% (72%~94% for PBE and 54%~87% for B3LYP). The M06HF and non-tuned LC-ωPBE functionals suffering from too high eX% yield the CT% as low as 1%~22% and unreasonably describe these S1 states as “pure” LE states. To this point, the above four functionals even fail to qualitatively describe the excited-state characters of seven molecules. Thanks to the suitable amount of eX, the MN15, M062X and CAM-B3LYP functionals successfully recognize these molecules with HLCT characters. This is in line with the observation in Section 3.1. Particularly, the optimally-tuned LC-ωPBE* functional yields the CT% of 28% for TPA-AC, 6% for TPA-AN, 44% for TPA-BZP, 21% for TPA-NZP, 21% for TPA-BPI, 19% for TPAPPI and 19% for TPA-PBPI and can provide quantitative description of these HLCT states.

Figure 3. Percentages of charge transfer character (CT%) of S1 states for seven molecules calculated with various density functionals (LE% = 100% - CT%).



The relationship between CT% and eX% included in the functional is also explored as shown in Figure S2. The CT% is found to be inversely correlated with increasing eX%. It is known that the energy of S1 state is composed of energy difference between oneelectron energy of the HOMO and LUMO orbitals, the Coulomb repulsion energy and the corresponding electron exchange energy in a simple two-level model.14 Thus the greater eX% results in the larger energy of S1 state and thus more LE character. Interestingly, the TPA-BZP molecule with significant CT character (44% CT, 56% LE) shows an almost linear correlation with respect to the increasing eX%. The TPA-AN molecule (6% CT, 94% LE) and TPA-BPI molecule (21% CT, 79% LE) with less CT and more LE characters firstly show a sharp and then smooth decrease of CT% as a function of the increasing eX%. As comparison, the TPA-TPA molecule is constructed showing 100% LE character that does not depend on the type of density functionals. The result highlights that the molecules with HLCT excited-state characters are very sensitive to the employed density functionals. Particularly, the HLCT molecules with more LE character seem to be more sensitive to the functionals with low eX% and less sensitive to the functionals with high eX%.

3.2.2 Analysis of natural transition orbital To intuitively understand these HLCT states and provide further direct evidence for the performance of various density functionals, the natural transition orbitals (NTOs) are plotted and displayed for S1 states of seven molecules using optimally-tuned LCωPBE*, non-tuned LC-ωPBE and B3LYP as shown in Figure 4. The NTOs are found to be in line with the analysis of CT% as shown in Figure 3. For instance, the mixture of CT and LE characters, except for TPA-AN, is successfully captured by the LCωPBE* functional. For a NTO pair predicted by the B3LYP functional, the particle mainly locates on the acceptor fragment and the hole dominantly distributes on the TPA donor, indicating more CT characters. The hole and particle from the LC-ωPBE functional tends to populate on various acceptors and the resulting NTOs show more LE characters. Notably, for TPA-BPI, TPA-PPI and TPA-PBPI, their NTOs by the


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three functionals seem not able to provide a visually intuitive difference to distinguish each other. Thus the two-dimension color-filled maps of transition density matrix of S1 states are plotted in Figure 5 and Figure S3. The color-filled map reflects the coherence of electron and hole between non-hydrogen atom A and atom B upon electronic transition.30 The B3LYP functional produces larger coherence of electron and hole at off-diagonal region while smaller coherence at diagonal region, indicating the greater probability of finding the electron and hole between two distant atoms and indirectly reflecting the CT character. The LC-ωPBE functional shows strong coherence between hole and electron at diagonal and suggests significant LE character. The calculated results are basically consistent with the qualitative description from NTOs. To conclude, the above results emphasize again the importance of using optimally-tuned rangeseparated density functional approach as a reliable tool to describe HLCT excited states.



Figure 4. The NTO distributions of S1 states for all molecules studied in this work using LC-ωPBE*, LC-ωPBE and B3LYP functionals (isovalue = 0.02). The contribution of each NTO pair is also listed.


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Figure 5. Color-filled maps of transition density matrix of S1 states of TPA-PPI using the (a) LC-ωPBE, (b) LC-ωPBE*, and (c) B3LYP functionals. d) The non-hydrogen atom numbers are consistent with the numbers in x axis of transition density matrix maps. 3.2.3 Analysis of hole-electron distribution

Figure 6. The heat maps of a) D index (in Å) and b) Sr index (in a.u.) for S1 states of seven molecules using various density functionals.

It is known that the analysis of hole and electron distribution has advantages over the NTO analysis, especially for some molecules whose singlet excited states cannot be described by one single dominant NTO pair. Thus the analysis of hole-electron distribution is also performed to further reveal the characters of LE/CT states. The D index measured by distance between centroids of holes and electrons, and the overlap



Sr index between hole and electron distribution were quantitatively calculated as shown in Figure 6 and Table S4. Apparently the optimally-tuned RS functionals show the moderate D index and Sr index simultaneously. The calculated D values are ranged from 1.36 to 2.69 (in Å) and Sr values are ranged from 0.68 to 0.80 (in a.u.) using LC-ωPBE*, which clearly suggest the nature of HLCT character of S1 states for all the molecules except TPA-AN. However, the B3LYP functional generates significantly large D index (5.46 ~ 7.96 Å) and small Sr index (0.30 ~ 0.57 a.u.), indicating much more CT characters. The default LC-ωPBE functional produces relatively small D index (0.11 ~ 1.27 Å) and large Sr index (0.79 ~ 0.90 a.u.), indicating more LE characters. In addition, the maps of D index and Sr index are consistent with the magnitude of CT% as shown in Figure 3.

Figure 7. Calculated (a) energy gaps, (b) SOC values, and (c) energy levels of five lowest excited states and the corresponding SOC values of TPA-BZP using LC-ωPBE*, LC-ωPBE and B3LYP functionals.


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3.3 Quantitative analysis of “hot-Exciton” Path. The “hot-exciton” path arises from a higher-energy triplet state (Tn, n > 1), so-called hot exciton, to the S1 state by RISC process, which robustly improves the internal quantum efficiency in high-efficiency fluorescence OLEDs.26 Meanwhile, different “hot-exciton” paths determining the efficiency of exciton utilization are closely related to the energy gap and strength of spin-orbit coupling (SOC) between Tn and S1 states that strongly depend on the characters of excited-states. However, it is known that the energy-levels or energy gaps are very sensitive to the employed density functionals that further bring great challenges to assign the “hot-exciton” path.

The energy gaps ΔES-T between singlet and triplet states are listed in Figure 7a and Table S5. It is clear that the ΔES-T values of optimally-tuned LC-ωPBE* functional are comparable to those of CC2 method and are significantly superior to the non-tuned LCωPBE functional. Interestingly, the B3LYP functional also shows a “fortuitously” good performance compared to the CC2 results. This is mainly due to an error cancellation resulting from the simultaneous underestimation of singlet and triplet excitation energies.46 As shown in Figure 7b, the calculated SOC values are basically sensitive to the density functional methods, highlighting the great necessity to use a reliable theoretical tool. According to the El-Sayed rule,82 the rate of intersystem crossing (ISC) is relatively large if the non-radiative transition involves a change of orbital type. As a result, reliable prediction of excited-state characters is a first condition to produce the reasonable SOC values.

Thus we take the TPA-BZP molecule as an example, that is known as a typical “hotexciton” molecule. The calculated energy levels of five lowest excited states and the corresponding SOC values of TPA-BZP are shown in Figure 7c and Table S6. Clearly, the TPA-BZP molecule is not TADF type due to the fairly larger ΔET1-S1 value of -0.90 eV and the negligible SOC of 0.09 cm-1. For the perspective of energy levels, the “hotexciton” path from T2 to S1 becomes possible due to the small ΔET2-S1 of 0.07 eV and



the much larger ΔET2-T1 of 0.97 eV severely prevent the internal conversion from T2 to T1. The another possible path for TPA-BZP is from T3 to S1 due to the low ΔET3-S1 of 0.34 eV and large SOC of 2.98 cm-1. The large SOC value is due to the different state character between T3 (LE) and S1 (HLCT) as shown in Figure S4, indicating that a RISC process may take place through the higher excited states channel T3 → S1. It is worth noting that the default LC-ωPBE functional completely fails to describe the “hotexciton” path accompanying with incorrect energy levels and too small SOC values. The B3LYP functional seems to distinguish the “hot-exciton” path but with relatively low excited-state energy levels and small SOC values.

4. CONCLUSION AND OUTLOOK In summary, we have evaluated the vertical absorption (EVA) and emission (EVE) energies of the lowest singlet excited state (S1) for a series of D-A molecules with various degrees of HLCT characters. The optimally-tuned LC-ωPBE* and ωB97XD* functionals yield the MADs of 0.03 eV and 0.10 eV for EVA(S1), respectively, and 0.11 eV and 0.08 eV for EVE(S1), respectively, that are significantly superior to the nontuned RS functionals. Notably, the MN15, M062X and CAM-B3LYP functionals can also give reasonable predictions and yield acceptable MADs that benefit from their moderate eX%. The PBE and B3LYP functionals significantly underestimate the EVA(S1) with considerable MADs. The M06HF functional significantly overestimates the EVA(S1) and EVE(S1) with the unignored MADs. The performance of various density functionals can be attributed to a suitable amount of eX that can produce neither too localized nor too delocalized electronic structures. The relationship between the percentages of charge-transfer character (CT%) and eX% included in the functionals is quantitatively explored, suggesting molecules with various CT% have different sensitivity as a function of eX%.

The natural transition orbitals (NTOs) and two-dimension color-filled maps of transition density matrix of S1 states for the molecules are further plotted to intuitively


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understand the HLCT characters of excited states. And the results show that the mixture of CT and LE characters is successfully captured by the LC-ωPBE* functional. The energy gap and strength of spin-orbit coupling between Tn and S1 states are assessed to assign the “hot-exciton” paths that determine the efficiency of exciton utilization in high-efficiency OLEDs. Unfortunately, the “dynamic” change of HLCT characters cannot be captured by other conventional density functionals. Thus great attention should be paid to select suitable density functional methods for accurate description of HLCT states. Because of its reliability in predicting both localized and charge transfer excitations, such an optimally-tuned method can be explored for further efficient design of novel HLCT-based high-efficiency optoelectronic materials. Meanwhile, current work in our group is exploring the environmental electrostatics or solid-state polarization effects34,53,69 and molecular conformational effects83 in determining the nature of HLCT states because these HLCT molecules are typically doped into various host matrix in practical applications.

ASSOCIATED CONTENT *Supporting Information The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcc.XXX. Full names of seven molecules studied in this work; percentages of exact-exchange (eX) included as a function of intereletronic distance (r12, Bohr) for various functionals; relationship between the CT% and eX% for lowest singlet excited states for selected molecules using various functionals; color-filled maps of transition density matrix of S1 states of other six molecules; NTOs of Tn states based on S0-geometries for selected molecules; optimal range-separation parameter ω*; quantum chemical calculations of vertical absorption energy and vertical emission energy; calculated CT% and LE% for the S1 states using various DFT methods; calculated D index and Sr index by holeelectron analysis; energy difference between singlet and triplet excited states (ΔE, eV) and corresponding spin orbital coupling (SOC, cm-1); energy level of excited states in



gas phase using DFT functionals and CC2 method.

ACKNOWLEDGMENTS This work has been supported by National Natural Science Foundation of China (Nos. 21603074, 11727810 and 61720106009), “Chenguang Program” by Shanghai Education Development Foundation and Shanghai Municipal Education Commission (16CG25), Shanghai-International Scientific Cooperation Fund (17ZR146900 and 16520721200) and Program of Introducing Talents of Discipline to Universities 111 project (B12024). C.Z. thanks National Natural Science Foundation of China (Nos. 51873160) for financial support. We acknowledge the ECNU HPC Research Computing Team for providing computational and storage resources.

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Accurate Prediction for Dynamic Hybrid Local and Charge Transfer

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