Suppression of aggregation caused quenching in U-shaped thermally activated delayed fluorescence molecules: Tert-butyl effect

Journal of Luminescence xxx (xxxx) xxx

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Journal of Luminescence journal homepage: http://www.elsevier.com/locate/jlumin

Suppression of aggregation caused quenching in U-shaped thermally activated delayed fluorescence molecules: Tert-butyl effect Guanyu Jiang 1, Feiyan Li 1, Xiangpeng Kong, Jianzhong Fan, Yuzhi Song, Chuan-Kui Wang **, Lili Lin * Shandong Province Key Laboratory of Medical Physics and Image Processing Technology, School of Physics and Electronics, Shandong Normal University, 250014, Jinan, China

A B S T R A C T

Thermally activated delayed fluorescence (TADF) molecules which could realize full exciton usage have attracted great attention recently, and new-type TADF molecules emerge constantly. U-shaped TADF molecules with significant intramolecular interaction were reported to have excellent performance as TADF emitters. In this paper, the light-emitting properties of two U-shaped TADF molecules (B-oCz and B-oTC) in both gas and solid phase are studied based on first-principles calculations and the combined quantum mechanics and molecular mechanics method. The introduction of tert-butyl in donor groups products weak influence on emission colors and fluorescent rates. Nevertheless, the tert-butyl groups significantly change the stacking structure of the U-shaped molecules in crystal and the electron-vibration interaction, thus different light-emitting properties were found for two molecules in solid phase. B-oCz is confirmed to have aggregation caused quenching (ACQ) property, while effective suppression of ACQ is expected for B-oTC. Our theoretical results not only reproduce experimental results well, but also give deep insights on the influence of the tert-butyl on the light-emitting properties.

1. Introduction Thermally activated delayed fluorescence (TADF) molecules, which are thought as the third-generation light-emitting material in organic light-emitting diodes (OLED) have achieved great progress in recent years [1]. More than four hundreds of organic TADF molecules have been synthesized and reported until now [2–7]. Most of the TADF molecules are composed of donor groups (D) and acceptor groups (A), and several strategies are used to separate the electron distribution in the highest occupied molecular orbital (HOMO) and the lowest unoc­ cupied molecular orbital (LUMO), such as introduction of steric hin­ drance, using spiro linkers or X-shaped structures and multiple resonance effect [8–11]. Nevertheless, these strategies often lead to decreased transition dipole moment and thus low radiative efficiency. U-shaped molecules that geometries reveal a U shape with cofacial intramolecular alignment of a donor and an acceptor are thought as a unique strategy to obtain high efficient TADF molecules. The combined charge transfer path not only allows very small energy gap between the first singlet excited state (S1) and the first triplet excited state (T1), but also enough large transition dipole moment. Actually, TADF molecules with significant intramolecular interaction have been reported in some

references, [12–15] all of which have indicated that the intramolecular interaction is beneficial for obtaining smaller S1-T1 energy gap and TADF properties. Recently, Lu’s group reported two U-shaped molecules (B-oCz and B-oTC) including both through-bond and through-space charge transfer properties and found excellent performance in OLED [16]. Nevertheless, we noticed that the quantum yield (QY) of B-oTC is much higher than that of B-oCz in neat film due to the introduction of tert-butyl groups in the donor groups and the aggregation caused quenching (ACQ) phenomenon can be effectively suppressed for B-oTC. Although tert-butyl groups have been widely used to enhance the QY, its influence mechanism is rarely studied theoretically [17–19]. Here, two U-shaped molecules, B-oCz and B-oTC, with intra­ molecular interaction are studied theoretically (as shown in Fig. 1(a) and (b)). The light-emitting properties and mechanisms of two mole­ cules in both solid phase and gas phases are investigated, which could reveal the influence of tert-butyl groups on both the intrinsic properties of molecules and intermolecular interaction. Our theoretical study could provide more insights into the effect of tert-butyl groups in enhancing the QY of TADF molecules and may help the design of TADF molecule with high efficiency.

* Corresponding author. ** Corresponding author. E-mail addresses: [email protected] (C.-K. Wang), [email protected] (L. Lin). 1 Authors who contribute equally to the work. https://doi.org/10.1016/j.jlumin.2019.116899 Received 10 August 2019; Received in revised form 27 October 2019; Accepted 14 November 2019 0022-2313/© 2019 Elsevier B.V. All rights reserved.

Please cite this article as: Guanyu Jiang, Journal of Luminescence, https://doi.org/10.1016/j.jlumin.2019.116899

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Fig. 1. Chemical structure of B-oCz (a) and B-oTC (b). The acceptor group and the donor group are marked with red and green respectively. Some atoms are labeled with numbers. The three ary rings are marked with R1, R2 and R3 respectively. (c) and (d) the ONIOM model for B-oCz and B-oTC respectively. The molecule in the red circle is thought as the higher layer (HL) and calculated with quantum mechanics (QM) method. Other molecules left are treated as the lower layer (LL) and calculated with molecular me­ chanics (MM).

2. Theoretical methods

nonradiative rate for S1 can be calculated using the thermal vibration correlation function (TVCF) method [21–23]. In this method, the non­ radiative rate which is deduced from the Fermi’s golden rule and first-order perturbation theory can be written as Z ∞ X1 � � Knr ¼ R dt eiωif t Z i 1 ρIC ðt; TÞ : (2) 2 kl ћ ∞ kl

Based on the crystal structures of B-oCz and B-oTC obtained exper­ imentally [16], we optimized the geometry of the B-oCz and B-oTC in solid phase by using the combined quantum mechanics and molecular mechanics (QM/MM) method. The models we used are shown in Fig. 1 (c) and (d). The two-layer ONIOM method is adopted with one molecule in the center calculated with the QM method and the other molecules surrounded calculated using the MM method. For the QM calculation, the density functional theory (DFT) is used to investigate the properties of the ground state and the time-dependent density functional theory (TDDFT) is adopted to study the properties of excited states. All the QM calculations are performed at BMK/6-31G* levels. For the MM calcula­ tion, the universal force field (UFF) is applied, and the electronic embedding is adopted to describe the coupling of QM/MM interfaces. For comparison, the light-emitting properties of two molecules in vac­ uum are also studied based on DFT and TD-DFT calculations. The same calculation levels are used for the calculation in vacuum as that in solid phase. In all the QM calculations, the basis set superposition error (BSSE) is considered. All the calculations above are realized in Gaussian 16 program [20]. After obtaining the geometric and electronic structures as well as vibrational information, the excited-state dynamics are studied. The radiative rate for S1 can be calculated with the Einstein’s spontaneous emission equation, Kr ¼

f ΔE2fi 1:499 ​

b fk jФi Фi j P b fl jФf is the non-adiabatic electronic coupling. here, Rkl ¼ Фf j P b Hi b fl e iτi b b fk e iτf H f P ρIC ðt; TÞ ¼ Trð P Þ is the TVCF in non-adiabatic process and Zi is the partition function. The electronic coupling term at the equilibrium position can be written as: b fk jΦi ¼ Φf j P

iћΦf j

∂ ∂Qfk

jΦi ¼

iћ

Φ0f j ∂∂QUfk jΦ0i E0i

E0f

:

(3)

here, Φ0f j

∂U 0 jΦ ¼ ∂Qfk i

X Zδ e2 X pffiffiffiffiffiffi Ei→f ;δτ Lδτ;k : Mδ τ¼x;y;z δ

(4)

U is the electron-nuclear potential energy term in Hamilton. ​ Ei→f ;δτ is the transition electric field and it can be calculated by time-dependent density functional theory (TD-DFT). Фi and Фf are the wavefunctions of the initial state and the final state respectively. For more details, please refer to Ref 21–23. For the intersystem crossing rate KISC and reverse intersystem crossing rate KRISC , the Marcus rate equation is used,

(1)

where f is the oscillator strength and ΔEfi is the vertical energy between S1 and the ground state (S0) in units of wave numbers (cm 1). The 2

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Table 1 Geometry parameters of S0, S1 and T1 for B-oCz and B-oTC in gas and solid phase respectively. Δ represents the variation between S0 and S1 (ΔS0-S1) or S1 and T1 (ΔS1T1). All the parameters are defined as shown in Fig. 1. System B-oCz

Bond length(Å) Gas

Solid

B-oTC

Gas

Solid

Bond angle (� )

Dihedral angle(� )

B1

B2

B3

B4

B5

A1

A2

A3

A4

A5

D1

D2

S0 S1 T1 ΔS0-S1 ΔS1-T1 S0 S1 T1 ΔS0-S1 ΔS1-T1

1.38 1.40 1.40 0.02 0 1.39 1.39 1.39 0 0

1.39 1.38 1.39 0.01 0.01 1.39 1.39 1.39 0 0

1.43 1.43 1.43 0 0 1.43 1.44 1.44 0.01 0

1.58 1.54 1.57 0.04 0.03 1.60 1.54 1.56 0.06 0.02

1.56 1.58 1.53 0.02 0.05 1.57 1.59 1.57 0.02 0.02

126.1 123.5 127.1 2.6 3.6 124.5 122.9 122.1 1.6 0.8

121.3 120.2 121.9 1.1 1.7 123.1 122.4 122.1 0.7 0.3

122.3 121.6 121.9 0.7 0.3 123.1 124.3 122.5 1.2 1.8

120.1 115.3 120.1 4.8 4.8 119.5 117.5 116.7 2 0.8

119.6 122.0 123.2 2.4 1.2 120.2 121.7 122.7 1.5 1

79.73 57.55 55.09 21.88 2.46 84.91 76.43 73.82 8.48 2.61

52.18 56.19 41.43 4.01 14.76 63.14 67.02 62.59 3.88 4.43

S0 S1 T1 ΔS0-S1 ΔS1-T1 S0 S1 T1 ΔS0-S1 ΔS1-T1

1.39 1.39 1.39 0 0 1.39 1.38 1.39 0.01 0.01

1.39 1.38 1.39 0.01 0.01 1.39 1.38 1.38 0.01 0

1.43 1.42 1.43 0.01 0.01 1.43 1.43 1.42 0 0.01

1.58 1.54 1.57 0.04 0.03 1.60 1.55 1.55 0.05 0

1.56 1.58 1.53 0.02 0.05 1.57 1.59 1.57 0.02 0.02

126.3 124.1 125.2 2.2 1.1 128.3 125.8 126.1 2.5 0.3

121.4 120.2 120.4 1.2 0.2 122.6 121.2 121.3 1.4 0.1

122.5 122.2 120.5 0.3 1.7 123.0 123.3 122.1 0.3 1.2

119.0 117.1 117.1 1.9 0 119.0 117.8 118.2 1.2 0.4

120.2 121.9 121.2 1.7 0.7 120.0 122.1 122.3 2.1 0.2

76.35 58.60 58.97 17.75 0.37 68.91 61.60 57.39 7.31 4.21

50.30 53.89 45.81 3.59 8.08 52.30 54.66 52.13 2.36 2.53

Note: B1(1–2), B2 (1–3), B3 (1–4), B4 (6–7), B5 (7–8), A1 (2-1-4), A2 (1-4-6), A3 (4-6-7), A4 (6-7-8), A5 (7-8-10), D1 (3-1-4-5), D2 (6-7-8-9).

Fig. 2. Geometric comparisons between S0 and S1 for B-oCz and B-oTC in both gas phase and solid phase. The RMSD values are also illustrated.

Kji ¼

V 2ji ħ

rffiffiffiffiffiffiffiffiffiffiffi � π exp KB Tλ

ΔGji þ λ 4λKB T

�2 � ¼

V 2ji ħ

rffiffiffiffiffiffiffiffiffiffiffi � π exp KB Tλ

� ΔGΔ : KB T

reorganization energy which is defined as the relaxation energy for both states. ΔGji is the energy difference between the final state and the initial state, and the temperature T is set as 298 K in this work.

(5)

here Vji is the spin-orbit coupling between the initial state and the final state which is calculated using DALTON program [24]. λ is the 3

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Fig. 3. Contour surface of the RDG function for B-oCz (a) and B-oTC (b). The colors represent strength of intramolecular interaction. Distances between the donor groups and the R1 unit of B-oCz (c) and B-oTC (d).

3. Results and discussions

(68.9� and 52.3� ). It indicates that adding two tert-butyl groups in the donor group has more significant influence on the geometry when they are in aggregation state. Similar trend can also be found for the excited states (S1 and T1). It indicates that different environment can induce significant geometric variation of organic molecules. In addition, the dihedral angle variations for B-oCz when it is excited from S0 to S1 are also a little larger than that for B-oTC. The root of the mean of squared displacement (RMSD) between two states for B-oCz and B-oTC in both gas and solid phase are calculated using Multiwfn [25]. The RMSD values between S0 and S1 for B-oCz and B-oTC in both gas and solid phase are illustrated in Fig. 2. It is found that the RMSD values for B-oTC are similar to those for B-oCz in gas phase, although tert-butyl groups are involved in the B-oTC molecule. It means that the tert-butyl groups have no contribution to the geometric variation when the molecule is excited. However, the RMSD values for both molecules in solid phase are much smaller than that in gas phase. In addition, the RMSD values for B-oTC are also much smaller than those for B-oCz. It further indicates that solid environment can limit the geometric variation when the molecule is excited. The addition of the tert-butyl in the donor group can induce different environment for the molecule and also different confinement

3.1. Geometry structures The geometric structures of the ground state (S0), S1 and T1 are optimized in both solid state and in vacuum. Some typical structure parameters (with definition shown in Fig. 1(a) and (b)) are listed in Table 1. It is found that the variation of bond lengths is quite limited when the molecule is excited from S0 to S1 or T1. The differences for the bond lengths of two molecules in vacuum and that in solid phase are also quite small. However, the bond angles and dihedral angles changed significantly when molecules are excited from one state to another. The variations for most bond angles and dihedral angles that happened be­ tween two states in vacuum are larger than that in solid phase. Here we focus on the dihedral angles between D unit and the aryl ring R2 (marked with D1) as well as the dihedral angles between two aryl rings (R1 and R2) in the triarylboron group (marked with D2). It is found that both D1 (79.7� ) and D2 (52.2� ) in S0 for B-oCz in gas phase are similar to the values for B-oTC (76.4� and 50.3� ). However, the two angles in solid phase (84.9� and 63.1� ) for B-oCz are quite different from that for B-oTC 4

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Dispersion

Total

for geometric variation. In addition, the geometric differences between S1 and T1 in gas phase are larger than that in solid phase except for the D1 of B-oTC, which predicts larger relaxation energy in gas phase than in solid phase.

68.58 75.32

41.88 12.99

3.2. Intramolecular interaction

Table 2 Interaction energy between the donor group and the R1 unit in B-oCz and B-oTC. (Unit: KJ/mol). System

Electronic

Repulsive

B-oCz B-oTC

59.53 35.93

50.93 52.38

In order to visualize the intramolecular interaction between the donor and the acceptor, the reduced density gradient (RDG) function is adopted. The RDG formula is written as:

Table 3 Absorption and emission wavelengths calculated. The oscillator strength of S1 and the energy gap between S1 and T1 are also listed. Experimental results are in the parentheses [16]. System B-oCz B-oTC

Gas Solid Gas Solid

λab (nm)

λem (nm)

f

ΔES1-T1 (eV)

366 370 (400) 380 391 (400)

470 448 (465) 469 456 (476)

0.0070 0.0036 0.0092 0.0096

0.33 0.13 (0.06) 0.27 0.14 (0.05)

RDG ¼

jrρðrÞ j 1 4 2ð3π 2 Þ2 ρðrÞ 3

here ρðrÞ is the electronic density [26]. By analyzing the RDG values, one can easily distinguish the region near the nuclei, the region near the chemical bonds, the weak interaction region and the molecular edge. This method can also highlight the areas of π-π intramolecular interac­ tion in the system and help to visualize the region that is associated with intramolecular π-π interaction. From Fig. 3, we can significantly find the weak interaction between D unit and R1 for both B-oCz and B-oTC

Fig. 4. Vertical excited energy for B-oCz in both gas phase (a) and solid phase (b) as well as for B-oTC in both gas phase (c) and solid phase (d). 5

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Fig. 5. Electron distribution of natural transition orbitals (NTOs) for the S1 state of B-oCz in both gas phase (a) and solid phase (b) as well as B-oTC in both gas phase (c) and solid phase (d). The values above the arrows are the contribution of two orbitals to S1 and the values bellow is the component ratio of the localized exci­ tation (LE).

molecules, while the differences between two molecules are not clear enough. The decomposition of interaction energy between D unit and R1 in both B-oCz and B-oTC is calculated based on the method of force field where UFF force field is used for the Boron atom and the AMBER force field for other atoms. The interaction energy is decomposed into three parts: the electrostatic interaction energy, the repulsion energy and the dispersion energy (As shown in Table 2). It is found that the dispersion between D and R1 shows significant effect for both molecules. The electronic interaction in B-oCz is much more strong than that in B-oTC, which may be due to closer distance between D and R1 in B-oCz than that in B-oTC (as shown in Fig. 3 (c) and (d)). Since the positive inter­ action energy represents destabilization. The larger values for the total interaction energy in B-oCz than that in B-oTC indicate stronger intra­ molecular interaction in B-oCz. It also means that the addition of the tert-butyl in the donor group will stabilize the molecules.

27]. The oscillator strengths of two molecules calculated in both phases are all quite small, which is a typical property for TADF molecules. The adiabatic energy gaps between S1 and T1 (ΔES1-T1) for both molecules in solid phase are also calculated, which are a little larger than experi­ mental values [16]. The ΔES1-T1 values calculated for two molecules in gas phase are both larger than those calculated in solid phase, which indicates that aggregation could induce smaller S1-T1 energy gap. Although the energy gap for B-oTC is a little smaller than that for B-oCz in gas phase, the values in solid phase for both molecules are almost the same. It further indicates that intermolecular interaction could influence the electronic structures of molecules. Fig. 4 illustrates the vertical excitation energy for both molecules in gas and solid phase. It is found that there is only one triplet state lower in energy than S1 for both molecules and the second triplet excited state is much higher in energy than that in gas phase. Consequently, we deduce that the ISC and RISC process mainly happens between S1 and T1. The excitation energy values for both S1 and T1 are higher in solid phase than that in gas phase. The energy for the triplet state is more significantly enhanced in solid phase, which results in smaller energy gap between S1 and T1 in solid phase. This is also in accordance with the adiabatic en­ ergy gap as shown in Table 3. The transition properties of both S1 and T1 in gas and solid phase are also illustrated in Fig. 5. It is found that S1 for both molecules are typical charge transfer (CT) states with electron mainly transferred from the acceptor units to the donor group and R2. For T1, both local excitation (LE) and CT characters are found. Electrons are mainly transferred from R2 to the D unit, while LE only involves the transition in the R2 unit. From the values below the arrow in the figure, we found that the LE component is decreased in solid phase for both molecules. The variation of transition properties of the excited state could induce change of the energy gap, the spin-orbit coupling and also the decay rates. In theory, triplet states with CT character could induce smaller S1-T1 energy gap

3.3. Excited state properties The absorption and emission wavelengths for two molecules calcu­ lated in both gas phase and solid phase are calculated (as shown in Table 3). It is found that the absorption wavelengths calculated in gas phase are quite similar to those calculated in solid phase for both mol­ ecules. The emission wavelengths for B-oCz and B-oTC in solid phase are both smaller than that calculated in gas phase. It means that environ­ ment has more significant influence on the excited state than the ground state for both molecules. As shown in Table 3, both absorption and emission wavelengths calculated with BMK functional are in good agreement with experimental values [16], which confirms the reason­ ability of the theoretical method. In addition, both absorption and emission wavelengths of two molecules are quite similar, which in­ dicates weak influence of tert-butyl on emission colors of this kind of molecules, which is a little different from other TADF molecules [17,18, 6

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Table 4 Spin-orbit coupling between S1 and T1 based on the geometry of S1 and T1 of B-oCz and B-oTC. The reorganization energy, the ISC and RISC rates are also listed. System B-oCz B-oTC

(cm Gas Solid Gas Solid

1

)

0.055 0.035 0.127 0.158

(cm

1

)

0.156 0.064 0.142 0.102

480 102 387 143

B-oCz B-oTC

Gas Solid Gas Solid

Knr (s 1)

Kr (s

1

2.49 � 109 1.23 � 1010 3.39 � 1011 2.57 � 107

2.11 � 106 1.20 � 106 2.79 � 106 3.09 � 106

KISC (s 7.0 9.2 4.8 1.7

1

) 6

� 10 � 106 � 106 � 107

KRISC (s

1

1.5 1.9 1.6 3.1

1

� � � �

)

10 104 102 104

that the reorganization energy values for both molecules in solid phase are smaller than that in gas phase. The ISC rates for both molecules in solid phase are also a little larger than that in gas phase, while the RISC rates in solid phase are much larger than that in gas phase. It further confirms that small S1-T1 energy gap is important for RISC process. The decay rates for S1 in both gas and solid phase are also calculated (shown in Table 5). It is found that the radiative rates for both molecules in gas and solid phases are in the order of 106. It is found that aggre­ gation has weak influence on the radiative rate of two molecules. The nonradiative rate for S1 is much larger than the radiative rate, which implies that the luminescent efficiency is not too high especially for BoCz. In addition, the nonradiative rate of B-oCz in solid phase is about one order larger than that calculated in gas phase, which implies an ACQ phenomenon, which is also consistent with experimental results [16]. For B-oTC, the nonradiative rate in solid phase is greatly decreased, which shows different aggregation effect with that of B-oCz. However significant enhancement of efficiency can be found for the B-oTC molecule than B-oCz in solid phase, which should mainly be induced by lower nonradiative rate for B-oTC. The reason that the nonradiative

Table 5 Non-radiative rates and radiative rates for S1 of B-oCz and B-oTC. System

Reorganization energy (meV)

)

and spin-orbit coupling [28]. Our calculation results confirmed that more CT components in T1 could induce smaller S1-T1 energy gap (as shown in Table 3). The spin-orbit coupling values between S1 and T1 are listed in Table 4. It is found that the values become a little smaller in solid phase than that in gas phase except for the value for B-oTC. This is also in consistence with the results that weak SOC be­ tween two states with CT character was found by Monkman’s group [29]. Based on the four-site energy method [30], the reorganization energy between S1 and T1 is calculated (as shown in Table 4). It is found

Fig. 6. Huang-Rhys factors of every vibration modes for the S1 state of B-oCz in both gas phase (a) and solid phase (b). The reorganization energy contribution from every vibration mode to the relaxation of S1 of B-oCz in both gas phase (c) and solid phase (d) are also illustrated. The modes with significant contribution are marked. 7

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Fig. 7. Huang-Rhys factors of every vibration modes for the S1 state of B-oTC in both gas phase (a) and solid phase (b). The reorganization energy contribution from every vibration mode to the relaxation of S1 of B-oTC in both gas phase (c) and solid phase (d) are also illustrated. The modes with significant contribution are marked.

Fig. 8. Vibration modes marked in Figs. 6 and 7. 8

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Fig. 9. Two typical stacking modes in B-oCz crystal (a) and (b) as well as B-oTC crystal (c) and (d).

process in B-oTC solid can be effectively suppressed should have close relationship with intermolecular interaction and also the electron-vibration coupling which will be analyzed in the following section.

come from the swing of the whole unit groups (D and A groups), while the high-frequency modes (marked with 2, 4, 5 and 7 in Figs. 6 and 7) are mostly contributed by the C–H stretching vibration. The lowfrequency modes are more easily to be suppressed than the highfrequency modes since less energy is needed. In addition, the swing of the whole D and ary groups should be easy to be hindered by sur­ rounding molecules in solid phase. While different stacking modes of molecules in solid phase will induce different environment effect. Two typical stacking modes of molecules in B-oCz and B-oTC crystals are shown in Fig. 9. It is found there are both similarities and differences in stacking modes for two molecular crystals. The R1 units in both mole­ cules overlap with each other to form π-π stacking modes (as shown in Fig. 9(a) and (c)). The two D units and R1 have no effect on each other, so these two stacking manners have no significant effect on the swing of the whole D and R1 groups. For the other stacking mode in B-oCz crystal (as shown in Fig. 9(b)), the D and R1 units in one molecule are almost perpendicular to the D and R1 units of the other molecule, which also has little influence on the swing of whole D and R1 units. However, the staggered stacking manner of D and R1 units in two molecules can effectively hinder the out-of-plane swing of whole D and R1 units (as shown in Fig. 9(d)). This is the direct reason that the low-frequency modes are greatly suppressed in solid phase. Different stacking pat­ terns of molecules in solid phase may induce different influence on the nonradiative process.

3.4. Intermolecular interaction The Huang-Rhys factor and reorganization energy for every vibra­ tion modes of two molecules are calculated and shown in Fig. 6 and Fig. 7. It is found that the Huang-Rhys factors for B-oCz are contributed by two groups of vibration modes: the low-frequency modes (e.g. 47.51 and 38.05 cm 1) and the high-frequency modes (e.g. 3062 and 3071 cm 1). However, the Huang-Rhys factors for B-oTC are mainly contributed by low-frequency modes (e.g. 51.57 and 32.61 cm 1). Comparing the Huang-Rhys factors for B-oCz in gas, we find that the Huang-Rhys factor is only decreased by 2–5 times in solid phase. However, the Huang-Rhys factor for B-oTC is decreased by 10 times in solid phase. The reorganization energy values for both molecules are also quite different. The reorganization energy for B-oCz is mainly contributed by high-frequency modes, while it mostly comes from the low-frequency modes for B-oTC. The reorganization energy for B-oTC in solid phase is also decreased more than 10 times, while it is only decreased by 5 times for B-oCz in solid phase than that in gas phase. Since smaller reorganization energy can induce smaller nonradiative rate, it is the reason why significant decreased nonradiative rate can be found for B-oTC in solid phase than in gas phase. In addition, the reor­ ganization energy for B-oTC is also much smaller than that for B-oCz in solid phase, and that is also the reason why the nonradiative rate for BoTC is also much smaller than that for B-oCz. To figure out the reason why different contributions of vibration modes to Huang-Rhys factors and the reorganization energy for B-oCz and B-oTC can induce different variation of nonradiative rates in gas and solid phases, the vibration modes are analyzed in detail. The vibration modes with significant contribution to the Huang-Rhys factors and the reorganization energy are shown in Fig. 8. It is found that the lowfrequency modes (marked with 1, 3, 8 and 9 in Figs. 6 and 7) mainly

4. Conclusions In summary, the light-emitting properties of B-oCz and B-oTC in both gas and solid phases are investigated based on first-principles and QM/ MM calculations. The introduction of tert-butyl has weak effect on the emission colors and fluorescence rates, while the non-radiative process is significantly influenced. For B-oCz, only high-frequency modes contribute to the reorganization energy, while the reorganization energy for B-oTC includes both low-frequency and high-frequency modes. For B-oCz, the stacking patterns in solid are not favorable for suppression of high-frequency vibrations, and the ACQ phenomenon is confirmed. 9

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Since the intermolecular interaction in B-oTC can effectively hinder the low-frequency vibration in solid phase, the nonradiative process can be effectively suppressed in solid phase, and effective suppression of ACQ is expected for the B-oTC molecule in solid phase. Our theoretical study gives reasonable explanation of experimental results. In addition, the influence mechanism of the tert-butyl on molecular luminescent prop­ erties is revealed.

[12] [13] [14]

Declaration of competing interest

[15]

There are no conflicts of interest to declare.

[16]

Acknowledgement This work is supported by the Shandong Provincial Natural Science Foundation, China (ZR2019MA056) and National Natural Science Foundation of China (Grant Nos. 11874242, 11974216). Thanks to the supporting of Taishan Scholar Project of Shandong Province and the General Financial Grant from the China Postdoctoral Science Founda­ tion (Grant No. 2018M642689).

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