High-Lying Triplet Excitons of Thermally Activated Delayed

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High-Lying Triplet Excitons of Thermally Activated Delayed Fluorescence Molecules Yoshifumi Noguchi, and Osamu Sugino J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.7b06913 • Publication Date (Web): 06 Sep 2017 Downloaded from http://pubs.acs.org on September 12, 2017

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The Journal of Physical Chemistry

High-Lying Triplet Excitons of Thermally Activated Delayed Fluorescence Molecules Yoshifumi Noguchi∗ and Osamu Sugino Institute for Solid State Physics, The University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa, Chiba 277-8581, Japan E-mail: [email protected] Phone: +81 (4)7136 3291. Fax: +81 (4)7136 3443 Abstract We investigate high-lying triplet excitons involving a transition from the highestoccupied molecular orbital (HOMO) to the lowest-unoccupied molecular orbital (LUMO) for eighteen thermally activated delayed fluorescence (TADF) molecules, within the first-principles one-shot GW +Bethe–Salpeter method. Based on our exciton analysis using the exciton wave functions, detailed exciton features are discussed in terms of exciton size, exciton binding energy, electron–hole separation distance, exciton map, and the overlap strength between the electron and hole wave functions. Contrary to our expectation, no exciton that could be purely classified as a charge-transfer exciton is found in our exciton map; moreover, the energy difference between the lowest singlet exciton and the high-lying triplet exciton is nearly zero for some TADF molecules. Our simulation strongly suggests that the hot-exciton process involving a high-lying triplet exciton is more likely to occur in the TADF mechanism than the conventionally considered process between the lowest singlet and triplet excitons, and our results support those of recent experiments. We propose a new method for calculating the energy difference between singlet and triplet excitons from the expectation value of

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the exchange bare Coulomb interaction and demonstrate that the combined use with exciton map is efficient and accurate for screening TADF molecules.

INTRODUCTION Organic light-emitting diodes (OLEDs) have recently drawn attention because of their high efficiency as light emitters. 1–7 OLEDs utilize thermally activated delayed fluorescence (TADF) 1,3 in which a triplet exciton (T) is converted into a singlet exciton (S) of higher energy via the reverse intersystem crossing (RISC) process, T→S. 2 The TADF mechanism, however, remains unclear, and the commonly accepted view has simply been that the key to achieving higher efficiency OLEDs lies in lowering the energy barrier associated with converting the triplet excitons to singlet excitons, which involves a highest-occupied molecular orbital (HOMO) to lowest-unoccupied molecular orbital (LUMO) transition (HOMO→LUMO). Accordingly, experimental efforts have attempted to reduce the energy barrier, or alternatively, the singlet-triplet splitting, which is defined as the difference in energy between the lowest singlet (S1 ) and the lowest triplet excitations (T1 ). 3,8–14 Correspondingly, simulations have been performed that focus on the splitting of S1 and T1 . 15–23 Recent experiments, however, have shown evidence that the “hot-exciton process” 24,25 involving the transition from higher triplet excitons (Tm → S1 , m > 1) is more important in the TADF mechanism, 5,26–34 because of spin-orbit coupling between the singlet and triplet excitations; 35,36 however, the details of such high-lying triplet excitons are unclear. In this context, the aim of this paper is to provide reliable information on the high-lying triplet exciton from first-principles simulations and thus, provide deeper insight into the “hot-exciton” of TADF molecules. Theoretically, however, it is not a trivial task to accurately compute the excited states of TADF molecules, because the standard computational methods are either too expensive or too approximate. Density functional theory (DFT) provides a method to calculate the total energy of a system of promoted electron occupancy, which is known as the delta self-

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consistent field (∆SCF). The ∆SCF-DFT is favored because of the low computational cost. Though it was shown to provide reasonable results for the singlet-triplet splitting of low-lying excited states, 37 higher excited states are more difficult to access variationally; thus, ∆SCFDFT is unsuitable for our purpose of studying the hot-exciton process. ∆SCF-DFT has been introduced in the past as an ad hoc process, but its theoretical justification is in progress (see, for example, Ref. 38 ). Time-dependent DFT (TDDFT) is a legitimate density functional theory for excited states, and it can provide information not only on singlet-triplet splitting but also on the electron density. The results calculated with the standard (semi-) local and range-separation functionals are, however, usually inferior to those of ∆SCF. 17–23 Because of strong functional dependence, some recently proposed functionals beyond the standard functionals might overcom the problem if the most suitable functional for the purpose is employed. Green’s function method, based on many-body perturbation theory, is another firstprinciples theory for calculating excited states. Green’s function methods were initially developed for extended systems, but they have attracted attention as powerful tools for studying molecular systems. In particular, the Bethe–Salpeter equation (BSE) 39–41 within the GW approximation (GWA), 39,42 or the so-called GW +BSE, 43,44 is a well-established method capable of simulating the optical properties not only of local excitons but also of Rydberg and CT excitons of molecules. 45–49 Moreover, this method can simulate whole excitons, not only the lowest singlet and triplet excitons but also high-lying excitons. In fact, the GW +BSE method has been applied to molecular systems containing approximately 160 atoms without requiring additional approximations. 50 The accuracy of the GW +BSE method depends on the appropriateness of the GWA in describing the target molecule, and the accuracy was shown to deteriorate for very small molecules. 51 In this context, our study begins by examining the theoretical accuracy of the GW +BSE method in providing excitation spectra of TADF molecules; this is performed by comparing the calculated results with experimental ultraviolet-visible (UV-vis) absorption

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spectra of eighteen TADF molecules. After verifying the accuracy of the method, we study the high-lying triplet (Tm ) excitons involving the HOMO→LUMO transition and the energy difference from the corresponding singlet exciton (Sn ), where n, m ≥ 1. In analyzing the calculated results, we utilize a recently developed method for classifying excitons, 52 and discuss the character of the singlet and triplet excitons in detail. The classification method also provides a way to evaluate the expectation value of the bare exchange Coulomb interaction (v ex ) from the computed exciton wave function, thereby yielding a method for evaluating the energy difference between singlet and triplet excitons (Tm − Sn ) without calculating the singlet and triplet states separately. We compare the Tm − Sn value obtained by the original and alternative methods to see if it is possible to reduce the computational cost by using the alternative methods, which will make it easier to design a TADF molecule by performing capacity computing.

METHOD Bethe-Salpeter equation We employ a standard one-shot GW +BSE method in which BSE is solved within GWA to simulate the optical properties of TADF molecules from first-principles. The GW +BSE method has been implemented into our original program code employing an all-electron mixed-basis approach 51,53–58 (the detailed calculation condition is given in Supporting information S1). We follow the conventional scheme of adopting the Tamm–Dancoff approximation 51 and convert BSE into an eigenvalue problem of the Hermitian BSE Hamiltonian (H BSE ), H BSE Ai = Ωi Ai .

(1)

The eigenvalue (Ωi ) corresponding to the ith excitation energy is denoted as Si for the singlet excitation energy without spin flip and Ti for the triplet excitation energy with spin flip.

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The Hamiltonian H BSE is given as

H BSE = EgGW − W d + 2v ex

(2)

H BSE = EgGW − W d

(3)

for singlet excitation and

for triplet excitation, where EgGW is the diagonal matrix representing the GW quasiparticle gap, W d is the dynamically screened Coulomb interaction (called the direct term), and v ex is the bare Coulomb interaction (called the exchange term). To obtain singlet-triplet splitting from the original definition, we need to solve Eq. (1) twice, i.e., for single and triplet excitations, and calculate the difference. The need for this double calculation is unfavorable from the standpoint of computational cost because the BSE calculation is quite time-consuming.

Exciton wave function To reduce the computational cost, we could consider a simple and often-used strategy based on the one-particle picture. That is, singlet-triplet splitting is obtained from the diagonal element of v ex ,

S1 − T1 ≃

ex 2ve,e ′ ;h,h′

X < e|e−iG·r |h >< h′ |e+iG·r ′ |e′ > , =2 |G| G

(4)

with e = e′ and h = h′ . Eq. (4) corresponds to the difference in the excitation energy between Eqs. (2) and (3) obtained by ignoring the off-diagonal elements, that is, by neglecting the many-body effects. Therefore, even though the computational cost is reduced by half, the applicability of Eq. (4) needs to be carefully verified by comparing with the result directly calculated from Eqs. (2) and (3). To avoid this problem, we propose a novel method for calculating an average of the bare 5



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exchange interaction by considering the many-body effects. The method utilizes the exciton wave function (Ψi ), Ψi (r1 , r2 ) =

X

Aie,h ψeLDA (r1 )ψh∗LDA (r2 ),

(5)

e,h

where r1 (r2 ) is the coordinate of the electron (hole). The expectation value of the bare exchange term is used to calculate th difference in energy between singlet and triplet excitons (∆ST ) as ∆ST = Sn − Tm = 2 ×

< Ψi |v ex |Ψi > . < Ψi |Ψi >

(6)

Hereafter, we denote the value of ∆ST estimated in Eq. (6) as < 2v ex > to distinguish it from the value obtained using the original definition in Eq. (4).

RESULTS AND DISCUSSION Figure 1 shows the top and side views of the molecular geometries optimized for eighteen TADF molecules using Gaussian09 59 with B3LYP/cc-pVTZ including dispersion correction 60–62 (note tat the dispersion correction is significant effect for 4CzPN, 4CzlPN, 4CzTPN, PIC-TRZ, PIC-TRZ2, ACRFLCN, and Spiro-CN). The largest molecule in this study is PIC-TRZ (or N7 C63 H39 ) and the smallest molecule is PhCz (or NC18 H13 ). These TADF molecules have been designed as candidates for an OLED molecular device, where RISC obeys the TADF mechanism. Therefore, the singlet-triplet splitting should be nearly zero, which also means that the overlap of the hole (in particular, HOMO) and electron (in particular, LUMO) wave functions should be almost zero (see the matrix element of the bare exchange term in Eq. (4)). To satisfy this requirement, the TADF molecules are commonly composed of acceptor and donor fragments that are connected through a nitrogen atom with an arbitrary, but nonzero, angle, as shown in Fig. 1.

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Figure 1: Molecular geometries optimized using B3LYP/cc-pVTZ in vacuum. The dispersion correction (D3) is considered.

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UV-vis absorption spectra To check the theoretical accuracy of our simulations, we verify the theoretical accuracy of the GW +BSE method by comparing the calculated result with the available experimental UV-vis absorption spectra measured in cyclohexene and toluene solutions at 300 K. 9–12,14,18 For a reasonable comparison, we estimated the effect of the solution in the TDDFT level simulation using the polarizable continuum model (PCM) solution, 63,64 and we found that the solution has a negligibly small effect on the molecular geometry and electronic structure of the TADF molecules studied here (see Supporting Information S2). Figure 2 shows the UV-vis absorption spectra of the eighteen TADF molecules. Our BSE spectra (in vacuum) are generally in good agreement with the experimental spectra, especially at the peak positions and peak heights; however, the calculated spectra for CC2TA are blue shifted by about 0.5 eV relative to the experiment. The good agreement with experiment encourages using the GW +BSE method for examining the hot-exciton process, which involves high-lying excitons (note that the triplet excitations cannot be compared with experiment because they are forbidden in the photoabsorption process and are therefore invisible in the experiment). We also plotted the TDDFT spectra simulated with the semi-local exchange-correlation (PBE and B3LYP) functionals and the range-separation (CAM-B3LYP 65 and LC-ωPBE 66 ) functionals in the upper panels for comparison. The peak positions obtained using PBE, B3LYP, LC-ωPBE, and CAM-B3LYP are sensitive to the functionals and are generally located in correspondingly increasing order; however, the shapes of the peak are rather insensitive to the functionals. The TDDFT calculations are thus insufficiently accurate enough, which supports the previous report in which TDDFT fails to simulate the optical properties of TADF molecules and a more advanced method is required. 18 Because BSE shows reasonable values for the excitation energy for the singlet excitations, we can now analyze the excitons.

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Figure 2: Simulated and experimental UV-vis absorption spectra. In the lower panel, BSE spectra (red solid line) are compared with the available experimental spectra measured in cyclohexene (blue dot) and in toluene (purple square) at 300 K. 9–12,14,18 The TDDFT spectra simulated with PBE (blue dotted line), B3LYP (green dotted line), LC-ωPBE (red dotted line), and CAM-B3LYP (purple dotted line) are plotted in the upper panel for comparison.

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Exciton classification In the following study, we focus on the singlet and triplet excitons of the lowest energy among all excitons involving the HOMO→LUMO transition. Note that the HOMO and LUMO excitations do not necessarily correspond to the excitons of the lowest energy; therefore, the excitons are denoted for the singlet as Sn and for the triplet as Tm when they are in the n-th and m-th excited state, respectively. This notation is used to define ∆ST ≡ Sn − Tm in the following. We begin our study by finding the excitons with the lowest energy among those involving the HOMO→LUMO transition. Table 1 lists the exciton profile of the eighteen TADF molecules simulated by BSE for Sn and Tm . Among those molecules, the HOMO→LUMO transition is primarily involved with S1 for eleven molecules (PhCz, 2CzPN, 4CzlPN, SpiroCN, ACRFLN, PXZ-TRZ, NPh3, α-NPD, 4CzPN, 4CzTPN, and PIC-TRZ2), in S2 for four molecules (PIC-TRZ, PPZ-DPO, PPZ-3TPT, and Spiro-AN), in S3 for two molecules (CBP and PPZ-4TPT), and in S8 for CC2TA. The state hybridization occurs most strongly for α-NPD, CC2TA, and PPZ-3TPT, but it occurs quite weakly for other molecules where more than 62% of the primary excitation is composed of the HOMO→LUMO transition. In triplet excitation, the exchange bare Coulomb interaction (v ex ) is zero by definition (see Eq. (3)). This makes the exciton binding energy stronger, in which case state hybridization is usually more strongly affected by the Coulomb interaction. In fact, for most TADF molecules, the HOMO→LUMO transition involved in Tm with m > 1 because of the state hybridization, and therefore m > n, is consistent with recent experiments, suggesting the importance of the hot-exciton process in the TADF mechanism. 5,26–31 In other words, the energy of the first excited state (T1 ) is too low to be aligned to S1 , whereas the alignment occurs more closely for a high-lying triplet exciton (Tm , m > 1) involving the HOMO→LUMO transition, as required for the TADF mechanism (see also Supporting Information S5-40). As shown in Table 1, our simulation suggests that seven molecules (Spiro-CN, PXZ-TRZ, PPZ-DPO, PPZ-3TPT, Spiro-AN, PPZ-4TPT, and PIC-TRZ2) with almost zero energy barrier between 10


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Table 1: First singlet (Sn ) and triplet (Tm ) excitons involving the transition of HOMO→LUMO. The optical gaps (eV) and the contribution (%) of the transition of HOMO→LUMO are listed here.

PhCz

S1 T2 S1 − T2 2CzPN S1 T1 S1 − T1 CBP S3 T3 S3 − T3 PIC-TRZ S2 T5 S2 − T5 4CzlPN S1 T1 S1 − T1 Spiro-CN S1 T7 S1 − T7 ACRFLN S1 T6 S1 − T6 PXZ-TRZ S1 T4 S1 − T4 PPZ-DPO S2 T5 S2 − T5

energy ratio (eV) (%) 3.719 73.9 2.632 75.7 1.087 — 3.227 77.8 2.427 39.3 0.800 — 3.744 75.7 2.639 28.9 1.105 — 3.357 89.4 2.836 14.0 0.521 — 2.630 93.8 2.329 48.8 0.301 — 2.759 97.6 2.761 94.7 −0.002 — 3.202 95.5 3.073 55.4 0.129 — 2.761 87.2 2.749 86.4 0.012 — 2.537 76.9 2.506 66.7 0.031 —

NPh3

S1 T3 S1 − T3 α-NPD S1 T9 S1 − T9 CC2TA S9 T41 S9 − T41 4CzPN S1 T2 S1 − T2 4CzTPN S1 T1 S1 − T1 PPZ-3TPT S2 T7 S2 − T7 Spiro-AN S2 T12 S2 − T12 PPZ-4TPT S3 T6 S3 − T6 PIC-TRZ2 S1 T15 S1 − T15

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energy ratio (eV) (%) 3.408 87.6 2.754 80.5 0.654 — 3.190 62.1 3.080 12.9 0.110 — 4.260 45.5 4.808 12.2 −0.548 — 2.677 81.3 2.408 68.9 0.269 — 2.451 96.5 2.175 92.1 0.276 — 2.902 54.2 2.884 52.8 0.018 — 3.338 91.8 3.312 92.9 0.026 — 2.768 78.4 2.749 51.0 0.019 — 3.423 92.1 3.437 37.9 −0.014 —


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singlet and triplet excitons (Sn − Tm < 0.1 eV) are strong TADF candidates where RISC can easily occur (note that other molecules have somewhat large energy barriers). These findings in Table 1 show that (1) the first triplet exciton (Tm ) involving HOMO→LUMO transition can occur at m > 1 levels even in vacuum at the zero-temperature condition, and (2) Tm is located very closely to the corresponding first singlet exciton (Sn , where n = 1 for most of molecules). As already discussed in Refs., 5,26–31 since the excitons in actual TADF process are affected by the external experimental environment such as temperature, solution, or surrounding host molecules, m (or also n) is the environmental dependence. Nevertheless, we emhasize that our simulation supports the experimental evidence that, in the RISC process, the hot-exciton process (Tm → S1 , m ≥ 1) is more significant than the conventional T1 → S1 process. We also emphasize that the alignment of the high-lying triplet exciton, Tm (m ≥ 1), with S1 , is intrinsic to the TADF molecule rather than the property realized by external environmental conditions. To see the exciton features more in detail, we classify the excitons into types for both Sn and Tm . This classification is performed using two dimensionless parameters, Λ 67 and deh /dexc , where Λ is the e-h overlap strength defined as,

Λ≡

i 2 e,h |Ae,h |

P

R

dr|ψeLDA (r)||ψhLDA (r)| P , i 2 e,h |Ae,h |

(7)

and the electron-hole separation distance deh and exciton size dexc 68,69 are, respectively, defined as deh and

< Ψi |r2 |Ψi > − < Ψi |r1 |Ψi > ≡ < Ψi |Ψi > dexc ≡

s

< Ψi ||r 2 − r 1 |2 |Ψi > < Ψi |Ψi >

(8)

(9)

following Ref. 52 The Λ vs deh /dexc map, or the exciton map, is shown in Fig. 3 for singlet (Sn ) and triplet (Tm ) excitons. Note that the CBP and 4CzTPN molecules have centroid symmetry in which deh is always zero by symmetrical restrictions, and thus, these molecules 12


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cannot be properly analyzed with our approach. 68–70 Unexpectedly, a pure CT exciton is not observed in the eighteen TADF molecules; eight of the TADF molecules are classified to have local excitons, and the other excitons are either Rydberg or CT-like. Interestingly, the distribution in the map is very similar for the singlet and the triplet. Our exciton map (Fig. 3) seems consistent with Table 1: (1) Six molecules classified as CT-like (ACRFLCN, PXZ-TRZ, Spiro-AN, PPZ-4TPT, PPZ-DPO, and PIC-TRZ2) have almost zero energy difference (Sn − Tm ≤ 0.1 eV) in Table 1, (2) Excitons classified as local for eight molecules (PhCz, NPh3, 4CzPN, 4CzlPN, 4CzTPN, α-NPD, 2CzPN, and CBP) tend to have larger energy difference (> 0.1 eV), (3) Excitons classified as Rydberg for other molecules (PXZ-TRZ, PPZ-DPO, PPZ-3TPT, Spiro-AN, PPZ-4TPT, Spiro-CN, and PICTRZ2) have smaller energy difference than that of local and larger energy difference than that of CT-like. Our simulations suggest that, in order to have a small enough Sn − Tm value to make the TADF process active, the corresponding excitons should be Rydberg or CT-like.

Efficient screening of TADF molecules In this section, by using a reasonable correlation between our exciton map (Fig. 3) and the Sn − Tm (shown in Table 1), we propose a new method, which is capable of simulating accurate Sn − Tm values and efficiently finding good TADF molecules from a number of candidates with reduced computational costs. As shown in Table 1 and S6-S41 in Supporting Information, if the energy of the lowest triplet exciton (T1 ) is too low, the more likely triplet exciton for the TADF mechanism is Tm and has similar transition states with Sn . Therefore, we simulate ∆ST for Sn and Tm and compare the value calculated using (1) the original definition (Sn − Tm ) and that calculated using (2) twice the expectation value of the bare exchange term (< 2v ex >n ). From Fig. 4, the results are similar for the Rydberg and CT-like excitons, but the difference is remarkably larger for PhCz, NPh3, 2CzPN, PIC-TRZ, and CBP, whose excitons are local 13



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Figure 3: Classification of Sn (upper panel) and Tm (lower panel) excitons according to our method with Λ and deh /dexc .

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Figure 4: ∆ST simulated by Sn − Tm (blue circle) and < v ex > (red square) given in eV. Here, capital letters on the upper axis represent the results of our exciton classification in Fig. 3, where (L) means local exciton, (R) means Rydberg exciton, and (C) means CT excition classified for (Sn , Tm ).

or centrosymmetric (see Fig. 3). The differences between these two methods are, however, insignificant for finding Rydberg and CT-like excitons as a screening process, as shown in S42 in Supporting Information. The average mean absolute deviation (MAD) is 0.246 eV, but MAD is 0.152 eV for the Rydberg and CT excitons, which is much smaller than the value 0.363 eV obtained for the local exciton. Note that < 2v ex >n would be equal to ∆ST when the amount of the state hybridization was identical for Sn and Tm , but this case does not occur for the local exciton because of its strong state hybridization. Obviously, as shown in Supporting Information S6-41, the distribution the singlet (S1−30 ) and triplet (T1−30 ) excitons of PhCz, NPh3, 2CzPN, PIC-TRZ, and CBP, where relatively large differences are observed is denser in the area classified as local excitons (note that CBP is a centroid system in which deh is always zero). This distribution reflects the fact that the excitation level is denser and the state hybridization can occur more easily. Now that < 2v ex >n is found to approximate the value of ∆ST with an average error of 0.152 eV for the Rydberg and CT excitons, which are required for candidate TADF

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Figure 5: Flow chart of our method, which is capable of efficiently screening TADF molecules and accurately simulating ∆ST with an acceptable computational cost.

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molecules, we can effectively screen the candidate molecules using the exciton classification and the value of < 2v ex >n . With this technique, we can reduce the computational cost by one-half. The flow chart shown in Fig. 5 can be used to improve screening efficiency. In the first step, we solve the BSE (Eq. (1)) for the singlet excitation to obtain the BSE eigenvalues (corresponding to the optical gap) and eigenvectors (corresponding to oscillator strength or exciton wave function). In the second step, we find the first exciton involved in the HOMO→LUMO transition (Sn ). In the third step, we use the exciton wave function in Eq. (5) to make the exciton map and classify the excitons. If the exciton is local, we discard the candidate because ∆ST is expected to be large, and if the exciton is either Rydberg or CT, we retain the candidate. In the last step, we calculate ∆ST from < 2v ex >n .

SUMMARY We applied the first-principles GW +Bethe–Salpeter method to eighteen TADF molecules and discussed the high-lying exciton (or hot-exciton) in detail. The GW +Bethe–Salpeter method can reliably yield the optical properties of TADF molecules as found through comparisons with experimental UV-vis absorption spectra. In particular, the accuracy of the method is not deterioriated evern for the exciton type, such as local, Rydberg, or CT excitons. We found that the singlet and triplet excitons involved in the HOMO→LUMO transition are generally high in energy compared with the first excited states, which is consistent with recent experiments. Those experiments showed that Tm (m > 1) is relevant to the TADF mechanism owing to spin-orbit coupling with the corresponding singlet exciton. To these excitons (Sn and Tm ), we then applied the exciton analysis method and classified the type of excitons. Our exciton map showed that eight TADF molecules have only local excitons and others have either Rydberg or CT-like. We found a good correlation between the type of exciton and smallness of | Sn − Tm | and concluded that the excitons should be Rydberg

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or CT-like to activate the TADF process. We have also compared the energy difference of Sn and Tm (n, m ≥ 1) between (1) the original definition (Sn − Tm ) and (2) the expectation value of the bare exchange Coulomb interaction (< 2v ex >n ) by using the exciton wave functions. The latter method is found to be as reliable as the former method because the calculated values are different on average by 0.152 eV for the Rydberg and charge transfer excitons, which are relevant for the TADF mechanism. Note that the difference is somewhat larger (=0.363 eV) for local excitons, which are irrelevant for the TADF mechanism because of different extent of state hybridization. The agreement between the two methods is due to the fact that the state hybridization occurs similarly for the singlet and the triplet excitons.

Acknowledgement We used the supercomputers installed at the Institute for Solid State Physics and Information Technology Center, the University of Tokyo. Y. N. was supported by a Grant-in-Aid for Scientific Research (C) (nos. 26400383 and 17K05565) from the Japan Society for the Promotion of Science (JSPS).

Supporting Information Available The effect of the solution, Stokes shift, HOMO and LUMO wave functions, and all data from our exciton analysis is included in the Supporting Information.

This material is available

free of charge via the Internet at http://pubs.acs.org/.

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High-Lying Triplet Excitons of Thermally Activated Delayed

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