Prediction of Intramolecular Charge-Transfer Excitation for Thermally

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Prediction of Intramolecular Charge-Transfer Excitation for Thermally Activated Delayed Fluorescence Molecules From a Descriptor-Tuned Density Functional Chao Wang, Chao Deng, Dan Wang, and Qisheng Zhang J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.7b10560 • Publication Date (Web): 17 Jan 2018 Downloaded from http://pubs.acs.org on January 17, 2018

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The Journal of Physical Chemistry

Prediction of Intramolecular Charge-Transfer Excitation for Thermally Activated Delayed Fluorescence Molecules from a Descriptor-tuned Density Functional Chao Wang, Chao Deng, Dan Wang and Qisheng Zhang*

MOE Key Laboratory of Macromolecular Synthesis and Functionalization, Department of Polymer Science and Engineering, Zhejiang University, Hangzhou, China, 310027

Abstract: The reliability of time-dependent density functional theory (TDDFT) for the calculation of the charge-transfer (CT) excitation energy depends on the proportion of the Hartree-Fock (HF) exchange (α) in a hybrid functional. Here, we develop a new descriptor-tuning methodology to determine the optimal α (OHF) in a hybrid PBE functional (PBEα). The conventional transition-density-based descriptors are shown to be inappropriate to measure the degree of CT for our approach because of the functional-dependence. A new functional-independent descriptor K, defined as the negative growth rate of the exciton binding energy upon α, is then developed and found to be highly correlated with the OHF in the PBEα. Applying the so-called K-OHF method, the lowest singlet excitation energy and singlet-triplet energy splitting of various reported thermally activated delayed fluorescence (TADF) 1

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materials are successfully reproduced with mean absolute deviations of 0.07 and 0.09 eV, respectively, compared to the carefully measured experimental data. The K-OHF method provides an easy-using way of choosing reliable density functional for the large CT systems.

1 INTRODUCTION Metal-free, thermally activated delayed fluorescence (TADF) molecules are characterized by their small energy gap between the lowest singlet (S1) and triplet (T1) excited states (∆EST).1 They can upconvert from the T1 to the S1 state by absorbing environmental thermal energy and can then radiatively decay from the S1 state. In 2012, the Adachi group developed highly efficient (nearly 100% internal quantum efficiency) green, blue and red TADF-based organic light-emitting diodes (OLEDs).2-5 Since then, many studies have been performed to understand the structure-property relationship of TADF molecules.6-8 TADF materials are now widely recognized as third generation organic electroluminescent materials because of their increased efficiency and lower costs in comparison with traditional florescent and phosphorescent materials. Computer-assisted molecular design on the basis of linear-response (LR) time-dependent density functional theory (TDDFT) plays an important role in the further development of novel TADF molecules.9-11 However, so far none of the known functionals with default parameters can accurately predict the excitation energies for all TADF molecules.

2


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The TADF molecules applied in efficient OLEDs are mainly intramolecular charge-transfer (ICT) molecules.12-13 Global gradient approximation functionals (GGA, e.g., PBE) and the frequently used hybrid GGA functionals (hGGA, e.g., B3LYP) always underestimate the charge-transfer (CT) excitation energies.14-16 It is possible to cancel out the error by tuning the proportion of the exact exchange term in a hybrid functional, but the proportion required for tuning each functional is not universal. The functionals suitable for the prediction of a CT S1 state may be unsuitable for the T1 state, particularly when T1 is a locally excited state (LE).17 Going beyond the GGA and hybrid GGA, range-separation exchange (RSE) functionals have proven capability for dealing with the CT excitations.18-21 Recently, it has been demonstrated that the IP-tuned methodology for RSE functionals can reliably predict the lowest vertical excitation energies (EVA(S1)) as well as the ∆EST for TADF molecules.22-24 Climbing up the Jacob’s ladder of DFT, doubly hybrid functionals with the Tamm-Dancoff approximation (TDA) can also accurately calculate excitation energies.25 However, the more complex the functional is, the more computational effort is needed, especially for large ICT molecules. Previous studies have revealed that the error in a vertical excitation energy calculated by a given hybrid functional greatly depends on the degree of CT of the excitation,26-27 which can be qualitatively described using some descriptors having similar or identical mathematical expressions to typical diagonal indexes, such as the norm of the highest occupied molecular orbital (HOMO) lowest unoccupied 3



molecular orbital (LUMO) overlap integral28, the electron-hole distance,28 and the amount of charge-transfer.26 By using previous descriptor-tuning methodology, even hGGA functionals can achieve high accuracy at relatively low computational costs.21, 26, 29-31

However, to date, almost all of the created CT diagonal indexes are based on

the excited state (ES) densities, requiring one more step and the use of additional software to calculate the descriptor. Additionally, the ES densities can vary significantly when the Hartree-Fock proportion (α) is adjusted, which consequently results in a significant change in the diagonal index in some cases (see Section 3.2). As a result, the functional chosen for the calculation of the ES density is not guaranteed to be correct because of the unknown optimal proportion of Hartree-Fock exchange (OHF, αo). We believe that αo should be pre-determined before the final calculation. An ideal descriptor is expected to be not only easy to use for both beginners and experimental chemists but also remain constant regardless of any change in α. In view of this correlation between the energy and the density, we believe that an elaborately constructed energy product may be able to numerically distinguish the CT and LE nature of the ES. In TDDFT, the excitation energy equals the difference between the molecular orbital gaps (between occupied and unoccupied orbitals) and the corresponding exciton binding energy (Eb).17 The descriptor K, defined as the negative growth rate of Eb to α, is mainly determined by the Coulomb interaction between the HOMO and the LUMO, and therefore reflects the degree of CT degree in 4


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the S1 excitation (Section 3.2). K can be easily accessed without any additional software. A linear relationship is observed between K and αo (using the K-OHF method) by employing the experimental data collected from 30 ICT (25 TADF) molecules. In comparison with the previous q-OHF method and IP-tuning methodology, the K-OHF method shows similar accuracy as well as more convenience of operation and a higher efficiency.

2 THEORETICAL BACKGROUND AND COMPUTATIONAL DETAILS 2.1 LR-TDDFT. In the matrix formulism, the LR-TDDFT excitation energies (ω) and transition vectors (|XY>) can be solved through a non-Hermitian eigenvalue equation32-33:

 A  * B

B  X  1 0  X   =ω   *  A  Y   0 −1  Y 

(1)

where the matrix elements A and B can be given in Mulliken notation for a hGGA functional as follows:

Aia , jb = δ ijδ ab (ε a − ε i ) + (ia | jb) − α (ij | ab) + (1 − α )(ia | f xc | jb)

(2)

Bia , jb = (ia | bj ) − α (ib | aj ) + (1 − α )(ia | f xc | bj )

(3)

where i, j and a, b denote the ground state (GS) occupied orbitals and virtual orbitals, respectively; δ is the Kronecker delta; ε denotes the molecular orbital energy differences between the virtual and occupied orbitals; α represents the fraction of HF exchange; and fxc is the exchange-correlation kernel. To avoid triplet instability issues34-37

and

improve

the

computational

efficiency,

5


the

Tamm-Dancoff


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Approximation (TDA)38 was imposed for all the ES calculations in this work. It simplifies (1) by neglecting B (B = 0) as expressed in (4):

AX = ωTDA X

(4)

2.2 Computational details. All the calculations were performed with Gaussian 09 D.0139 using an ultrafine grid. The GS molecular geometries were adapted from our previous works26, 40-42 and then re-optimized at the B3LYP/6-31G(d) level. Frequency analysis was used to confirm that the GS structures are at the local minima of the potential surfaces. The determination of the growth rate of the HOMO-LUMO energy gap with respect to α and the growth rate of the EVA(S1) with respect to α was carried out at the PBEα/6-31G(d) and the TDA-PBE/6-31G(d) levels in the gas phase. The optimal hybrid PBE functional is referred as PBEαo. The vertical excitation energy was calculated at the TDA-PBEαo/6-31+G(d) level (using the K-OHF method) using the PCM with cyclohexane solvation. Linear fitting of the data was carried out using a homemade program coded in Python. The density difference (∆ρ) between the GS and S1 and the CT distance (d) 43were calculated using Multiwfn 3.3.8.44 2.3 Experimental data. The UV-Vis absorption spectra in solution were recorded using a Shimadzu, UV-2600 spectrophotometer. The time-resolved spectroscopic studies were carried out using a PTI TimeMaster fluorimeter equipped with a PTI nitrogen laser (GL-3300, λ = 266 nm, pulse width ≈ 1 ns, pulse energy = 1.45 mJ). The time-resolved fluorescence (3−4 ns) and phosphorescence (200-2000 µs) spectra

6


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were obtained from PTI's patented strobe technique and gated detection, respectively, in toluene at 77 K. The molecules studied in this paper are synthesized according to the synthetic routes reported by previous references.1, 5, 40-42, 45-48 The experimental data for the EVA(S1) were obtained from the UV-Vis absorption spectra in cyclohexane at room temperature. For some molecules studied in ref 26, the determination of EVA(S1) from their absorption spectra was applied to the emission spectra utilizing the mirror image rule.49 However, significant rotational ES relaxation has been demonstrated in many ICT molecules in solution and even in solid films,50-52 indicating asymmetry in the absorption and emission bands. Thus, herein we simply determined the EVA(S1) values from the peak maxima of the S1 bands in the absorption spectra. The S1 bands of 4CzIPN and Cz-TRZ show vibronic structure, in which the intensities of the 0-0 and 0-1 bands are almost the same. Therefore, an average of the 0-0 and 0-1 energies was used as the vertical energy. The experimental ∆EST of most of the molecules in Table 1 were estimated from the energy difference between the E0-0(S1) and E0-0(T1) in toluene at 77 K. If the spectrum of the S1 (fluorescence) or the T1 (phosphorescence) emission showed distinct vibronic peaks, the E0-0 was determined from the highest energy peak. In contrast, if the S1 or T1 emission spectrum was broad and lacked structure, the E0-0 was determined from the emission onset as suggested by our previous studies.46,

53

Due to the low phosphorescence yield for the eight

anthraquinone derivatives in toluene at 77 K, their experimental values of ∆EST (listed 7



in Table 1) were calculated from an approximate relationship among ∆EST, the fluorescence rate and the TADF rate in doped films.42

3 RESULTS AND DISCUSSION 3.1 The impact of Hartree-Fock exchange in the user-defined PBEα functional Here we employ the user-defined HF exchange hGGA PBEα54-57 instead of conventional hGGA, with a different proportion of HF exchange. As a result, any difference other than the HF exchange arising from different density functionals can be removed. Consequently, the change in the ES excitation energy with α becomes smooth, which will help with the construction and evaluation of the descriptor from the energy index. The dependence of the excitation energy of PhCz, DTC-DPS, and Spiro-CN (Figure 1a) on the HF exchange, employing different GGA and hGGA functionals, has been previously studied in Ref 26. For comparison, these three typical compounds with different degrees of CT were also used in this study to determine the influence of α on the EVA(S1) and EVA(T1), calculated at the TDA-PBEα/6-31G(d) level. As shown in Figure 1b, EVA(S1) monotonically increases with α, following a similar slope when calculated using multiple functionals.26 The T1 stability is strongly improved by the TDA and a small change in EVA(T1) can be seen at large values of α, which can be ascribed to the LE transition. In contrast, T1 must be characterized by a main CT transition when EVA(T1) is sensitive to changes in α. Since identical or similar orbitals 8


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are involved in the 1CT and 3CT transitions,17, 25-26 for instance, a dominant HOMO → LUMO excitation, the trend in EVA(3CT) and EVA(1CT) with respect to α should be similar. Thus, it may be possible to accurately predict EVA(S1), EVA(T1) and ∆EST using the same α value (αo), regardless of the CT or LE nature of the T1 state. Previous studies have shown that αo can be evaluated using a descriptor-tuning process.26 However, the conventional descriptors based on the transition densities are susceptible to changes in α (density functionals with different α). The transfer of charge between the GS and ES (∆ρ) and the CT distance (d) between the positive (∆ρ+) and negative (∆ρ-) increment barycenters have been used to measure the degree of CT.43 The values of ∆ρ and d as functions of the proportion of HF (α) for PhCz, DTC-DPS and Spiro-CN are compared in Figure 1c. These two descriptors share very similar trends with respect to α for each compound, so only ∆ρ will be discussed here. For Spiro-CN, ∆ρ gradually increases, reaching a maximum of ~1.4 at α = 0.7 and then rapidly decreases to ~0.6 at α > 0.7. For DTC-DPS, a small increase in ∆ρ is observed until α = 0.3 and then ∆ρ gradually decreases. For PhCz, ∆ρ significantly decreases at α < 0.1 and then slightly increases and remains constant at α > 0.2. Thus, based on the PBE (α = 0) results, PhCz has a stronger CT nature than DTC-DPS. In contrast, the weakest CT nature is shown when PBE0 (α = 0.25) is used. A more intuitive understanding of this contrast can be obtained from the strong fluctuation in the transition density due to α, as shown in Figure 1d. For pure PBE (α = 0), self-interaction leads to too much delocalization in the ES density and results in 9



a spuriously strong CT excitation from carbazole (Cz) to phenyl (Ph). Although the transition is mainly localized at the Cz fragment when α = 0.041 (from the previous q-OHF result), 0.1 and 0.25 (PBE0), a small amount of CT is found from Cz to Ph at α = 0.041, but from Ph to Cz at the PBE0 level. In short, S1 state becomes more and more tightly bound with increasing α because the Coulomb self-interaction is cancelled by the exact exchange. This means that due to the increased spatial overlap between the hole and electron wavefunctions, an increased proportion of LE nature results. Thus, it is not easy to obtain the correct descriptors and transition density when αo is unknown. To avoid the influence of α on the transition densities, a new descriptor is required that can remain constant despite changes in α.

Figure 1. a) Chemical structures of PhCz, DTC-DPS41, and Spiro-CN.4 b) EVA(S1) and EVA(T1) as functions of α. c) The density difference between GS and S1 (∆ρ) and CT distance (d) as functions of α. d) NTOs of the S1 transitions of PhCz. The GS and ES 10


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are calculated at the PBEα/6-31G(d) and TDA-PBEα/6-31G(d) levels, respectively. Only the main excitations with coefficients > 0.05 are included. The e and h denote electron and hole, respectively.

3.2 The construction of the descriptor K. We suggest the use of an energy product to construct the descriptor instead of the transition density. To clarify this idea, a two-level model is applied,58-59 assuming that the S1 is solely described by a HOMO → LUMO excitation:

EVA (S1 ) = ∆ε + 2( HL | HL) − 2α ( HH | LL) + (1 − α )( HL | f xc | HL)

(5)

where the first term ∆ε on the right is the energy gap between the HOMO and the LUMO, the second to forth terms are called the exciton binding energy (Eb, Eb = EVA(S1) –∆ε), and H and L denote the HOMO and LUMO, respectively. When a small change, ∆α, is applied, (5) can be rewritten as:

EVA (S1 ) ' = ∆ε '+ 2( HL | HL) − 2α '( HH | LL) + (1 − α ')( HL | f xc | HL)

(6)

Subtracting (5) from (6), we have:

∆EVA (S1 ) = ∆(∆ε ) − 2∆α ( HH | LL) − ∆α ( HL | f xc | HL)

(7)

(7) can be rewritten to obtain: ∆ (∆ε ) − ∆EVA (S1 ) = 2( HH | LL) + ( HL | f xc | HL) ∆α

(8)

The term on the left is the negative growth rate of Eb with respect to α, which is defined as our descriptor K:

K = 2( HH | LL) + ( HL | f xc | HL)

11


(9)


The magnitude of K reflects the Coulomb repulsion and the exchange and correlation between the HOMO and the LUMO. Therefore, the CT nature can be evaluated from K: the more significant the CT is, the smaller the K will be. It is worth noting that K is related to the intrinsic physical properties at a certain level of theory and will only change by using a different level of theory. On the other hand, K measures how fast Eb grows with respect to α. The stronger the CT nature is, the more HF exchange is required because 2(HH|LL) originates from the HF exchange.15 As a result, the descriptor K is connected to αo by the CT nature. As a CT descriptor, K can be used to qualitatively compare the CT nature between different molecules. For instance, Spiro-CN (K = 2.87) has a much greater CT nature than PhCz (K = 5.20) and is also greater than DTC-DPS (K = 4.21). It is noteworthy that our assumption, that the CT excitation Eb grows faster than that of the LE excitations, does not hold rigorously for each molecule, especially for comparisons between two LE molecules. Our initial purpose is to construct an easily used numerical descriptor to access αo. The calculation of K is not difficult. For example, in the case of DTC-DPS, shown in Figure 2, ∆ε is linearly related to α. The GS density is stable and the change in ∆ε is linear because of the linear replacement of the exchange-correlation energy with exact exchange. In addition, the linearity between EVA(S1) and α is good (R2 = 0.97) for other TADF (or ICT) molecules. The growth rates of ∆ε and EVA(S1) with respect to α are defined as k0 and k1, respectively. Then K can be simply evaluated as: 12


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K = k0 − k1

(10)

To apply this, 4 calculations (2 GS single points plus 2 S1 TDA calculations) are sufficient to evaluate k1 and k0, due to their highly linear relationship. For this, we suggest the use of the values α = 0.1 and 0.9.

Figure 2. ∆ε and EVA(S1) as functions of α for DTC-DPS at the TDA-PBEα/6-31G(d) level. The two curves are not fitted.

3.3 The K-OHF method for the calculation of EVA(S1) and ∆EST. The analytic relationship between K and αo can be obtained by fitting the experimental data. Reference 26 and 42 provide the absorption spectra of many reported TADF molecules in the nonpolar solvent cyclohexane. These molecules were chosen for this 13



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study to determine the relationship between K and αo (Table S1 and Scheme 1). Spiro-CN and ACRFLCN were omitted, since they have oscillator strengths (f) near zero for the S1 transition. The value of αo can be obtained by substitution of the experimental absorption data into the linear equation for the dependence of calculated EVA(S1) on α. As shown for DTC-DPS in Figure 2 (red line), the fitted equation is EVA(S1) = 2.67α + 2.78. Substituting the experimental EVA(S1) value of 3.62 (eV) into the equation, we can have αo = (3.62 - 2.78) / 2.67 = 0.31 for DTC-DPS. This determination process for EVA(S1) from the absorption spectrum has changed somewhat compared with the previous q-OHF method. Therefore, we should bear in mind the respective correspondence between the calculated EVA(S1) and the spectroscopic analysis as we apply these two OHF methods. By studying 14 ICT molecules (Table S2), the relationship between K and αo is illustrated in Figure 3 and a linear equation is obtained (11):

α 0 = −0.1K + 0.73

(11)

The two sets of data show good linearity, with R2 = 0.96. To apply these results, after the determination of k1 and k0 (employing the method mentioned above), the descriptor K and αo can be obtained using (10) and (11), respectively. Then the EVA(S1) can be directly calculated at the PBEαo/6-31+G(d) level of theory. The general process for this K-OHF method is shown in Scheme S1.

14


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Scheme 1. The chemical structures of the molecules studied in this work. The molecular geometries at the ground state are optimized using B3LYP/6-31G(d).

15



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Figure 3. αo as a function of K. The 14 molecules in Table S2 are used.

To verify the K-OHF method, the EVA(S1) of another 17 available TADF compounds (the remaining molecules in Scheme 1)40-42,

45

were calculated and

compared to the experimental values estimated from the absorption spectra in cyclohexane (Figure S1-S4). The influence of the cyclohexane solvation on the excitation energies is little (Table S3). As listed in Table 1, the mean absolute deviation (MAD) of the calculated EVA(S1) for the 16 test molecules is 0.07 eV. If the 14 molecules selected for the K-αo fit are also included, the MAD for all the molecules is still 0.07 eV. The high accuracy of the K-OHF method used in the prediction of EVA(S1) confirms the validity of our K-αo fitting. It can be seen that the αo values listed in Table 1 are within a range of 0.24-0.44. Although there are a few 16


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default density functionals, such as PBE0 (0.25) and PBE0-1/3 (0.33), have this proportion of HF, a descriptor-tuned density-functional (e.g., PBEαo) of combining the K-OHF method performs better than them (Table S4).

Table 1. Comparison of the calculated EVA(S1) and ∆EST with experimental data Calc.a Compound

K

Expt.

αo EVA(S1)

∆EST

EVA(S1)

∆EST

CBP

4.57

0.27

3.76

0.59

3.80

0.71

NPD

4.38

0.29

3.29

0.57

3.31

0.62

PIC-TRZ

3.73

0.36

3.47

0.40

3.35

0.17

CC2TA

3.48

0.38

3.79

0.46

3.64

0.30

PXZ-TRZ

3.25

0.41

2.98

0.02

2.93

0.03

DPAC-TRZ

3.24

0.41

3.42

0.13

3.26

0.16

Cz-TRZ

3.98

0.33

3.47

0.45

3.43

0.40

Cz-TRZ2

3.20

0.41

3.38

0.10

3.22

0.31

3Cz-TRZ

3.43

0.39

3.58

0.45

3.59

0.37

BCz-TRZ

3.45

0.38

3.46

0.42

3.34

0.39

2CzPN

3.99

0.32

3.16

0.39

3.33

0.40

4CzPN

3.69

0.36

2.92

0.27

2.94

0.25

4CzIPN

3.88

0.34

2.86

0.16

2.85

0.12

4CzTPN

3.77

0.35

2.64

0.16

2.70

0.01

4CzTPNMe

3.58

0.37

2.67

0.15

2.67

0.01

DPA-DPS

4.84

0.24

3.51

0.55

3.61

0.47

DTPA-DPS

4.77

0.25

3.47

0.54

3.58

0.43

17



Page 18 of 34

DTC-DPS

4.21

0.31

3.57

0.37

3.62

0.37

DMOC-DPS

4.16

0.31

3.37

0.37

3.38

0.31

PXZ-DPS

3.74

0.36

3.03

0.05

3.15

0.03

DMAC-DPS

3.67

0.36

3.29

0.02

3.39

0.14

PPZ-DPS

3.61

0.37

2.66

0.01

2.76

0.01

DPA-AQ

4.18

0.31

2.75

0.52

2.81

0.29

DBPA-AQ

3.88

0.34

2.68

0.49

2.72

0.27

DTC-AQ

3.54

0.38

2.69

0.32

2.68

0.17

DMAC-AQ

3.05

0.43

2.39

0.02

2.37

0.08

DPA-Ph-AQ

3.30

0.40

2.80

0.36

2.78

0.24

DBPA-Ph-AQ

3.05

0.42

2.82

0.35

2.73

0.22

DTC-Ph-AQ

3.22

0.41

2.97

0.31

2.96

-

DMAC-Ph-AQ

2.88

0.44

2.90

0.03

2.91

0.07

a

Calculated at the TDA-PBEαo/6-31+G(d) level in a PCM with cyclohexane solvation.

The ∆EST of the 30 ICT compounds, another important parameter, was also reproduced at the same level of theory as EVA(S1). As listed in Table 1, the calculated values of ∆EST agree well with the experimental values estimated from the fluorescence and phosphorescence spectra (Figure S5-S26) with the MAD of 0.09 eV. Note that herein the ∆EST are calculated as the vertical absorption energy difference, while the experimental ∆EST is the zero-zero energy difference between the S1 and T1, or the adiabatic energy difference if we neglect the small zero-point vibrational energies of the GS and ES (~0.02 eV) in the cancellation (Scheme 2).60 From the perspective of calculation, it has been reported that the geometry relaxation energies of the 1CT are higher than those of the 3LE by 0.1 eV on average for TADF emitters.23 18


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Herein, the calculated vertical ∆EST is averagely 0.05 eV higher than the experimental one. The comparable relaxation energies of the S1 and T1 can be attributed to the suppression of the large-amplitude geometry relaxation of the CT state in the rigid solvent glass. Meanwhile, we should also keep in mind that the ∆EST of an ICT molecule can be smaller in fluid toluene or amorphous organic semiconductors than in 77K toluene by 0.1-0.2 eV,1,5,40-42,45-48 because the energy of the 1CT state can be considerably lowered in the former by the solvation.46 Overall, taking the computational costs of the calculation into account, evaluating the vertical singlet-triplet splitting at the GS molecular geometry by the K-OHF method is an efficient way to predict the TADF character.

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Scheme 2. The potential energy surface for TADF molecules. The subscripts ST denotes the singlet-triplet splitting. Note that 3CT may not be the T1 state for a large nuclear distance away from its potential surface minimum.

The α/ω-tuned methods, i.e., LC-ωPBE*, K-OHF and q-OHF, all provide good accuracy in the calculation of EVA(S1) and ∆EST (Table S4), indicating the necessity of tuning the HF exchange. Saving computational time and providing an easily used method were also among our initial requirements. For the previous q-OHF method, manual partition of the molecule into donor and accepter fragments and the later calculation of q using other software are required.26 Comparing our current K-OHF with the q-OHF method shows an improvement in the ease-of-use at the cost of an acceptable loss of accuracy. Meanwhile, the K-OHF method also takes advantage of the fast determination process in comparison to the IP-tuned LC-ωPBE functional, especially for large molecules like the DBPA-Ph-AQ (see Figure S27). Computer-aided high-throughput virtual screening (HTVS) has been reported to be a powerful computational chemistry tool for molecular design.61-62 The manual partition step in the q-OHF method and the determination of the optimal ω in a self-consistent manner limit the efficiency of HTVS for TADF materials.9,

62-63

In contrast, the

K-OHF method has very good accuracy and efficiency at relative low computational costs. It is suitable for use in a future HTVS study.

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4 CONCLUSION Descriptors that depict the characteristics of various ICT transitions have been used to estimate the system-dependent OHF (αo) in hGGA functionals to calculate the vertical energies. This is the so-called descriptor-tuning methodology. However, we show in this work that the conventional descriptors based on the transition density provide less benefit than expected for the screening of CT (LE) transitions because the descriptor itself is highly dependent on α and may not be correctly calculated when αo is unknown. On the basis of a user-defined HF (α) PBEα density functional, we constructed a new descriptor, K, which is defined as the negative growth rate of the exciton binding energy Eb with respect to α (K = -dEb/dα). The descriptor K does not suffer from a strong fluctuation in the transition density with changes in α and has the advantage of being easily used without requiring additional software. The EVA(S1) and ∆EST of 30 ICT molecules (25 TADF) were calculated using this K-OHF method and are in good agreement with the experimental data. In summary, the descriptor K provides a new way to qualitatively determine the degree of CT. The K-OHF method can be used as an efficient computational tool for HTVS studies to accelerate the development of new TADF molecules.

ASSOCIATED CONTENT

Supporting Information

21



The comparison between the 4-points estimation and linear fitting method on the calculation of K and αo. Parameters k0, k1, K and αo for 14 ICT molecules and the flowchart of the K-OHF method. The absorption and emission spectra of the TADF emitters. The influence of the dielectric medium on the calculation of the EVA(S1) and ∆EST. The comparison between different functionals on the EVA(S1) and ∆EST. The absorption spectra in cyclohexane at room temperature and the fluorescence and phosphorescence spectra in cyclohexane at 77 K. The flowchart for the K-OHF method.

AUTHOR INFORMATION Corresponding Author *Email: [email protected]

Notes The authors declare no competing financial interest.

ACKNOWLEDGMENT This work is supported by the Natural Science Foundation of China (Grant No. 51673164）and National Key R&D Program (Grant No. 2016YFB0401004).

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For Table of Contents use only

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Figure 1 489x292mm (150 x 150 DPI)



Figure 2 241x177mm (150 x 150 DPI)


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Figure 3 146x103mm (220 x 220 DPI)



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Scheme 2 157x158mm (120 x 120 DPI)



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Prediction of Intramolecular Charge-Transfer Excitation for Thermally

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