English

• 0.   Introduction

  For more than a decade, Ir(Ⅲ) complexes have gained significant attention in organic light-emitting diodes (OLEDs) due to their excellent features, such as high quantum efficiency, excellent thermal and chemical stability, and a wide scope of emissive colors, demonstrating potential applications in flat-panel displays and solid-state lighting sources^[1-2]. Up to now, the comprehensive performance of Ir(Ⅲ)-complex-based green/red-light phosphors has approached commercial standards, exemplified by compounds such as Ir(ppy)₃ and Ir(dfppy)₂(acac) (green: ppy=2-phenylpyridine, dfppy=4, 6-difluorophenylpyridine, acac=acetylacetonate) and Ir(piq)₃ (red: piq=1-phenylisoquinolato)^[3-17]. However, the use of Ir(Ⅲ)-complex-based blue-light phosphors in commercial applications has rarely been reported^[18-21]. This is primarily because, on the one hand, the wide energy gap leads to insufficient emission efficiency for blue-light phosphors. On the other hand, the efficiency roll-off effect prevents their effective use in solid-state lighting sources and even flat-panel displays^[22-23].

  Generally, improving the luminescence efficiency of blue-light phosphors through ligand adjustment is challenging, as it is an inherent property of the wide energy gap. Conversely, introducing electron-withdrawing or electron-donating groups into the ligand can adjust the charge transfer mode, thereby reducing the phosphorescence lifetime. This lifetime is a key factor in determining whether the material exhibits the efficiency roll-off effect^[24]. In 2011, Zhu et al. proposed a strategy to reduce the phosphorescence lifetime of a blue Ir(Ⅲ) complex (Ir(dfppy)₂(tpip): dfppy=4, 6-difluorophenylpyridine, tpip=tetraphenylimidodiphosphinate), thereby mitigating its efficiency roll-off effect^[24]. The literature reports excellent performance for this complex, characterized by an emission maximum at 485 nm, CIE color coordinates of (0.15, 0.36), and a triplet state (T₁) lifetime of 0.77 μs. However, the analysis of the complex′s photophysical properties is limited.

  For Ir(dfppy)₂(tpip), what attracts us is not only its aforementioned excellent performance but also its broad emission spectrum band (430-600 nm), which necessarily corresponds to richer charge transfer modes. Interestingly, research on the thermal activation delayed fluorescence (TADF) properties of transition metal complexes has been extremely limited since Kawai et al. first proposed this phenomenon for such complexes in 2006^[25-36].

  In this article, using the classic blue Ir(Ⅲ) complexes FIrpic (pic=picolinic acid) and Ir(dfppy)₂(tpip) as parent compounds, we extracted their auxiliary ligands and introduced a benzene ring into the main ligand phenylpyridine to provide rich frontier molecular orbitals (FMOs). We designed six blue Ir complexes: (Phppy)₂Ir(pic) (1), (F₃Phppy)₂Ir(pic) (2), (Phppy)₂Ir(tmd) (3), (F₃Phppy)₂Ir(tmd) (4), (Phppy)₂Ir(tpip) (5), and (F₃Phppy)₂ Ir(tpip) (6), where Phppy=2-(biphenyl-4-yl)pyridine, tmd=2,2,6,6-tetramethyl-3,5-heptanedione). We investigated the electronic structures, fragment-composed FMOs, absorption spectra, and emission spectra (fluorescence and phosphorescence) properties of Ir(Ⅲ) complexes 1-6 using density functional theory (DFT) and time-dependent density functional theory (TDDFT) methods. To investigate the TADF property of the designed complexes, the spin-orbit coupling (SOC) matrix elements were also calculated. We anticipate that the materials we designed can be synthesized in the future.

  1.   Results and discussion

  1.1   Design concept

  As is well known, FIrpic is a classic blue electroluminescent material, holding a leading position among blue emitters in key performance metrics. These include an emission maximum at approximately 472 nm, a high maximum current efficiency of 53.6 cd·A^-1, and a high maximum external quantum efficiency (EQE) of 30.0% at 100 cd·m^{-2 [22]}. These data demonstrate the rationality of the structural design of FIrpic. However, its severe efficiency roll-off effect prevents it from reaching commercial standards. Zhu et al. replaced the pic ligand in FIrpic with tpip and experimentally synthesized Ir(dfppy)₂(tpip)^[24]. This modification concentrated the FMOs towards the main ligand and the metal center, shortened the charge transfer distance, and mitigated the efficiency roll-off effect of the emitter, which increases the triplet intra-ligand charge transfer (³ILCT) component while decreasing the triplet ligand-to-ligand charge transfer (³LLCT) component. However, it also caused a redshift of the emission spectrum (to 485 nm)^[24]. This systematic design explores the distinct roles of main ligands (Phppy vs F₃Phppy) and ancillary ligands (pic, tmd, and tpip). Qualitatively: (1) extending conjugation in the main ligand (Phppy) increases FMO contributions and induces a blue shift in absorption; (2) introducing strong electron-withdrawing fluorine groups (F₃Phppy) effectively compresses the energy gap between the singlet excited state (S₁) and T₁ ($ \Delta {E}_{{S}_{1}{T}_{1}} $), enhancing TADF potential; (3) employing the strong electron-withdrawing ancillary ligand tpip significantly localizes FMOs on the main ligand and metal center, shortening the charge transfer distance and reducing ³LLCT character, which is key to suppressing efficiency roll-off, albeit accompanied by an emission redshift. The ancillary ligand tmd exhibits intermediate electron-withdrawing ability, with effects lying between those of pic and tpip.

  In previous work, we carefully studied the effect of tpip ligands on the FMOs in Ir(Ⅲ) complexes. We found that although tpip ligands increased the ³ILCT contribution, the ³LLCT component persisted. This persistence is the main reason for the observed emission spectrum redshift^[37-40]. We speculate two primary reasons for this phenomenon: firstly, the structure of the main ligands might be too small to provide sufficient FMOs; secondly, the electron-withdrawing group tpip might be insufficient to fully concentrate the FMOs on the main ligands and the metal center. To verify the correctness of this hypothesis, we introduced the main ligand Phppy (providing more active orbitals for the FMOs) to address the first point, and the main ligand F₃Phppy (containing the electron-withdrawing fluorine group) to address the second point in this study (Fig.1).

  Figure 1

  

  Figure 1.  (a) Sketch maps and (b) the optimized ground state (S₀) geometrical structures of the complexes

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  1.2   Geometries in the S₀ and the lowest-lying T₁

  To ensure the reliability of the calculation results, we employed the established computational methodology previously used for FIrpic^[41-43]. The S₀ and T₁ geometries were optimized using the DFT and TDDFT methods, respectively, with the Becke three-parameter Lee-Yang-Parr (B3LYP) exchange-correlation functional^[44-46]. No symmetry constraints were applied to these complexes.

  Sketch maps depicting the optimized S₀ geometrical structures of the complexes are shown in Fig.1. Key geometric parameters for the S₀ and T₁ are summarized in Table 1. As shown in Table 1, the molecular structures of complexes 1-6 exhibit slight distortions in their S₀. The bond lengths of Ir—C and Ir—N maintain good symmetry, while minor changes (<9.38°) are observed in bond angles ∠N1—Ir—C1, ∠N1—Ir—C2, ∠N1—Ir—N3/∠N1—Ir—O1, and ∠N1—Ir—O/∠N1—Ir—O2. Furthermore, the S₀ structures of all complexes maintain a regular octahedral configuration, effectively preventing π-π stacking——a key factor contributing to the efficiency roll-off effect. Compared to the S₀ of complexes 1-6, the T₁ structures of complexes 1-3 undergo significant deformation, while complexes 4-6 show nearly no structural changes. This suggests that complexes 1-3 require a larger energy barrier to undergo radiative transitions.

  Table 1

  

  Table 1.  Main geometry structural parameters of S₀ and T₁ of the complexes under DFT and TDDFT level*

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  Complex	State	Selected bond length / nm							Selected bond angle / (°)
  		R1	R2	R3	R4	R5	R6		A1	A2	A3	A4	A5
  1	S0	0.20	0.20	0.20	0.20	0.21	0.21		174.87	80.70	94.73	89.88	91.20
  	T1	0.20	0.19	0.20	0.20	0.22	0.21		175.86	82.12	95.46	88.00	92.35
  2	S0	0.20	0.20	0.20	0.20	0.21	0.21		175.02	80.62	94.89	89.78	91.33
  	T1	0.20	0.19	0.20	0.20	0.22	0.21		176.46	82.13	95.97	87.10	92.71
  3	S0	0.20	0.20	0.20	0.20	0.21	0.21		176.59	80.74	96.86	93.33	89.17
  	T1	0.20	0.20	0.20	0.19	0.22	0.22		177.54	96.82	80.59	94.64	87.56
  4	S0	0.20	0.20	0.20	0.20	0.21	0.21		176.49	80.68	96.79	93.37	89.42
  	T1	0.20	0.20	0.20	0.20	0.21	0.21		176.49	80.72	96.89	93.19	89.19
  5	S0	0.20	0.20	0.20	0.20	0.22	0.22		174.98	80.88	95.61	94.59	88.93
  	T1	0.20	0.20	0.20	0.20	0..2	0.22		174.98	80.89	95.62	94.58	88.92
  6	S0	0.20	0.20	0.20	0.20	0.22	0.22		175.02	80.83	95.68	94.33	89.23
  	T1	0.25	0.20	0.20	0.20	0.22	0.22		175.02	80.83	95.68	94.33	89.23
  *R1: Ir—N1, R2: Ir—C1, R3: Ir—N2, R4: Ir—C2, R5: Ir—N3/Ir—O1, R6: Ir—O/Ir—O2; A1: ∠N1—Ir—N2, A2: ∠N1—Ir—C1, A3: ∠N1—Ir—C2, A4: ∠N1—Ir—N3/∠N1—Ir—O1, A5: ∠N1—Ir—O/∠N1—Ir—O2.

  1.3   FMO properties

  It is known that charge transitions within the FMOs of the S₀ of complexes——which represent the system′s most active orbitals——will be accompanied by optical radiation or non-radiation processes. Therefore, we discuss the S₀ electronic structure, focusing on the highest occupied molecular orbit (HOMO)/lowest unoccupied molecular orbit (LUMO) distribution, energy levels, and energy gaps. These for complexes 1-6 are shown in Fig.2; their fragment-composed FMOs are in Table S1-S6 (Supporting information).

  Figure 2

  

  Figure 2.  Electronic structures on the HOMOs and LUMOs of S₀, energy levels, and energy gaps (E_g) between HOMO and LUMO of the complexes 1-6

  The lines of green and the lines of red are HOMO and LUMO energy levels, respectively.

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  In FIrpic′s S₀, HOMO localizes on Ir and the main ligand phenyl, LUMO localizes on auxiliary ligands^[41-43]. Compared to it, complex 1′s extra main ligand phenyl increases main ligands′ HOMO/LUMO contributions via more FMOs, with this amplified in complex 2 by electron-withdrawing fluorine (Fig.2, Table S1-S6). For complexes 3 and 4, replacing the auxiliary ligand pic with tmd increases the proportion of FMO components localized on the main ligands, while significantly reducing the proportion on the auxiliary ligands. Similarly, the FMOs of complexes 5-6 are almost entirely localized on the main ligands. This indicates that complexes 5-6 exhibit low efficiency roll-off characteristics, attributable to the strongly electron-withdrawing group tpip. This phenomenon demonstrates that introducing a phenyl group into the main ligand shifts the FMOs toward the main ligand, and fluorination of this phenyl group amplifies the effect. Additionally, adjusting the electron-donating ability of the auxiliary ligand achieves the same outcome.

  The energies of different states and the energy gaps between states for complexes 1-6 are listed in Table 2. Our calculation results show that the energy levels of each electronic state in the complexes are reasonably distributed. The $ \Delta {E}_{{S}_{1}{T}_{1}} $ are 1.174, 1.069, 1.156, 1.005, 0.861, and 0.752 eV, respectively.

  Table 2

  

  Table 2.  Energy levels of the S₀, the lowest singlet S₁, and the lowest T₁ under the M06-2X functional

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  Complex	$ {E}_{{S}_{0}} $ / eV	$ {E}_{{S}_{1}} $ / eV	$ {E}_{{T}_{1}} $ / eV	Δ$ \Delta {E}_{{S}_{0}{S}_{1}} $ / eV	$ \Delta {E}_{{S}_{0}{T}_{1}} $ / eV	$ \Delta {E}_{{S}_{1}{T}_{1}} $ / eV
  1	-5.261	-1.722	-2.896	3.539	2.365	1.174
  2	-5.280	-1.784	-2.853	3.496	2.427	1.069
  3	-5.065	-1.563	-2.719	3.502	2.346	1.156
  4	-5.077	-1.675	-2.680	3.402	2.397	1.005
  5	-5.016	-1.522	-2.383	3.494	2.633	0.861
  6	-5.034	-1.641	-2.393	3.393	2.641	0.752
  $E_{S_0}, E_{S_1}$, and $E_{T_1}$ are the energies of S0, the lowest S1, and the lowest T1 under the M06-2X functional, respectively; and are the energy gaps between different states (S0 and S1, S0 and T1, respectively).

  Fluorination of the phenyl group on the main ligand causes a slight decrease in $ \Delta {E}_{{S}_{1}{T}_{1}} $ (ca. 0.1 eV). Furthermore, $ \Delta {E}_{{S}_{1}{T}_{1}} $ decreases as the electron-donating ability of the auxiliary ligand increases. Notably, the $ \Delta {E}_{{S}_{1}{T}_{1}} $ values for complexes 5-6 (which feature the tpip auxiliary ligand) reach levels conducive to the TADF phenomenon (0.861 and 0.752 eV)^[47].

  Based on the FMO composition and energy gap analysis (Fig.2, Table 2 and S1-S6), the performance tendencies of the six complexes are summarized as follows: complexes 1-2 with the weakly electron-withdrawing ancillary ligand pic are prone to ³LLCT and exhibit a higher risk of efficiency roll-off; complexes 3-4 with the moderately electron-withdrawing tmd show improvement; complexes 5-6 with the strongly electron-withdrawing tpip display the lowest tendency for efficiency roll-off due to highly localized FMOs and significantly reduced ³LLCT. Notably, complex 6 combines the low $ \Delta {E}_{{S}_{1}{T}_{1}} $ (0.752 eV) from F₃Phppy and the strong FMO localization from tpip, predicting both low efficiency roll-off and TADF characteristics.

  1.4   Photophysical properties

  The calculated absorption spectra, along with their oscillator strengths, assignments, and excitation energies, are listed in Table S7. The FMO properties are listed in Table S1-S6. For clarity, only the leading excited states (with large configuration interaction coefficients) are listed. The calculated phosphorescent emissions of the complexes in CH₂Cl₂ solution are listed in Table 3.

  Table 3

  

  Table 3.  Phosphorescent emission parameters of the complexes in CH₂Cl₂ solution under the TDDFT/M06-2X calculations

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  Complex	Energy / eV	Wavelength / nm	Major	Contribution rate / %	Character
  1	2.37	524.25	HOMO→LUMO	55.7	3MLCT*+3LLCT+3ILCT
  			HOMO→LUMO+1	36.8
  2	2.43	510.78	HOMO→LUMO	55.8	3MLCT+3LLCT+3ILCT
  			HOMO→LUMO+1	35.6
  3	2.35	528.50	HOMO→LUMO	60.2	3MLCT+3LLCT+3ILCT
  			HOMO→LUMO+1	28.7
  4	2.40	517.23	HOMO→LUMO	59.6	3MLCT+3LLCT+3ILCT
  			HOMO→LUMO+2	30.0
  5	2.63	470.85	HOMO→LUMO	57.0	3MLCT+3LLCT+3ILCT
  			HOMO→LUMO+2	33.5
  6	2.64	469.39	HOMO→LUMO	58.2	3MLCT+3LLCT+3ILCT
  			HOMO→LUMO+2	31.7
  *3MLCT: the triplet metal-to-ligand charge transfer.

  In addition, Ir(Ⅲ) complexes typically exhibit main peaks and shoulder peaks in their emission spectra. The main peak primarily corresponds to fluorescence emission, while the shoulder peak primarily corresponds to phosphorescence emission. Thus, the fluorescence emission spectra of the complexes were also calculated and are shown in Fig.3, together with the absorption spectra of complexes 1-6.

  Figure 3

  

  Figure 3.  (a) Absorption spectra and (b) fluorescence emission spectra of the complexes 1-6

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  As shown in Table S7 and Fig.3, the positions of the strongest absorption peaks for complexes 1-6, generated by the excitation of multiple electronic states, are 347, 325, 322, 321, 307, and 326 nm, respectively. Compared to FIrpic, the absorption spectra of complexes 1-2 show a blue shift (ca. 78 nm), attributed to the introduction of phenyl groups into the main ligand^[43]. For complexes 3-6, as electron-withdrawing groups are introduced via the auxiliary ligands, the frontier orbital components gradually shift towards the main ligand and the metal center, and the original ¹LLCT charge transfer transition transforms into ¹ILCT. Consequently, compared to complexes 1-2, the blue shift in the absorption spectra of complexes 3-6 is less pronounced.

  Interestingly, as reported in the literature, Ir complexes typically undergo a blue shift in their absorption and emission spectra upon fluorination of the main ligand^[48]. In this work, complexes 1-2 (with pic as the auxiliary ligand) follow this pattern. For complexes 3-4 (with tmd as the auxiliary ligand), fluorination of the main ligand has almost no effect on the absorption spectrum. Uniquely, complexes 5-6 (with tpip as the auxiliary ligand) exhibit a red shift in their absorption spectra. The reason for this anomalous phenomenon is that the tmd and tpip groups possess strong electron-withdrawing abilities, causing the FMOs of complexes 3-6 to localize on both the main ligand and the metal center. Therefore, fluorination of the main ligand affects both the HOMO and LUMO.

  Complexes 1-6 show fluorescence emission peaks (412-390 nm, Fig.3) and phosphorescence peaks (524.25-469.39 nm, Table 3; blue/blue-green). Their emission spectra have a main fluorescence peak (determining color) and a phosphorescent shoulder. Enhanced auxiliary ligand electron-donating ability causes significant blue shifts in emission; main ligand fluorination has little effect, due to weakened ³LLCT and strengthened ³ILCT. Notably, complexes 5-6 have absorption shoulder peaks (363, 367 nm) near their fluorescence peaks (389, 390 nm), suggesting possible TADF.

  The efficiency roll-off in OLEDs, particularly problematic for blue emitters, is primarily caused by exciton-exciton annihilation at high current densities. Its severity is critically linked to the material′s phosphorescence lifetime (τ). According to the well-established model by Adachi et al.: efficiency roll-off is proportional to τ²/d², where d is the exciton diffusion distance^[27]. This highlights that shortening τ is a highly effective strategy to suppress roll-off. Strikingly, Zhu et al. experimentally measured an exceptionally short τ (0.77 μs) for Ir(dfppy)₂(tpip)^[24], a complex structurally analogous to our designed 5-6 (both featuring the key tpip ancillary ligand). This value is significantly lower than the typical τ (1.4 μs) observed for the benchmark blue emitter FIrpic^[49]. Applying the relationship above, a reduction in τ from 1.40 to 0.77 μs (a decrease of ca. 45%) would theoretically suppress efficiency roll-off by approximately 70% under comparable exciton diffusion conditions. This compelling experimental evidence strongly corroborates our theoretical prediction that the tpip ligand effectively mitigates efficiency roll-off. The physical origin lies in the strong electron-withdrawing nature of tpip, which localizes FMOs on the main ligand and metal center (Fig.2, Table S5-S6), thereby reducing long-range ³LLCT processes and shortening the excited-state lifetime, τ.

  To further validate the TADF properties of the complexes, SOC matrix elements (<T|H_SOC|S>, shown in Table 4) were calculated. The results show that the <T|H_SOC|S> between the S₁ and T₁ states for complexes 3 and 6 are below 10 cm^-1. This small SOC matrix element <T|H_SOC|S> facilitates the reverse intersystem crossing (RISC) process between the S₁ and T₁ states for these complexes. However, for complex 3, the $ \Delta {E}_{{S}_{1}{T}_{1}} $ (1.156 eV, Table 2) is too large for RISC to occur efficiently. Consequently, while the calculated data confirms the presence of the TADF phenomenon in complex 6, it cannot be confirmed for complex 3.

  Table 4

  

  Table 4.  SOC matrix elements of the complexes $\Delta E_{S_0 T_1}$

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  Complex	<S1|Hsoc|T1> / cm-1	<S1|Hsoc|T2> / cm-1	<S1|Hsoc|T3> / cm-1
  1	55.78	67.67	117.86
  2	49.78	89.19	124.28
  3	6.61	79.96	822.29
  4	10.42	46.56	843.64
  5	23.33	181.74	813.78
  6	8.09	136.56	817.62

  2.   Conclusions

  To investigate the efficiency roll-off effect and thermally activated delayed fluorescence (TADF) characteristics of Ir(Ⅲ) complexes, we theoretically designed and calculated complexes 1-6, focusing on their geometrical structures, FMO properties, absorption spectra, emission spectra (fluorescence and phosphorescence), and SOC effects. The results show that the S₀ molecular structures of all complexes exhibit a regular octahedral configuration, which structurally reduces the efficiency roll-off effect. Significant differences between the ground and excited state molecular structures of complexes 1-3 indicate that they require overcoming higher energy barriers during light emission.

  Furthermore, introducing phenyl groups into the main ligands broadens their steric volume, facilitating the shift of FMOs towards the main ligands and the Ir center. Introducing tpip auxiliary ligands shifts almost all FMOs onto the main ligands, shortening the charge transfer distance and thereby achieving the goal of reducing the efficiency roll-off effect for complexes 5-6.

  Critically, the strong electron-withdrawing ancillary ligand tpip localizes FMOs on the main ligand and metal (reducing ³LLCT), leading to a significant shortening of the phosphorescence lifetime τ (experimentally demonstrated to be >45% reduction in analogous tpip complexes^[24]). According to the Adachi model, this translates to a substantial suppression of efficiency roll-off by ca. 70%. Simultaneously, the fluorinated main ligand F₃Phppy compresses the $ \Delta {E}_{{S}_{1}{T}_{1}} $ gap to 0.75 eV in complex 6, enabling TADF^[49].

  Analysis of photophysical properties reveals that introducing phenyl groups into the main ligands causes a blue shift in the absorption spectra. Conversely, fluorination of these phenyl groups has little effect on the spectral shift because the FMOs are primarily localized on the main ligands and the Ir atom. Finally, the calculated <T|H_SOC|S> values, S₁-T₁ energy gaps, and emission spectra collectively indicate that complex 6 displays TADF properties.

  
  Acknowledgments: The authors are grateful to the financial aid from the National Natural Science Foundation of China (Grant No.21701047), Science and Technology Research Foundation of Jilin Provincial Department of Education (Grants No. JJKH20250944KJ, JJKH20191024KJ), and the Science and Technology Development Foundation of Jilin Province of China (Grants No.20220101039JC, 20180520191JH). Supporting information is available at http://www.wjhxxb.cn
  
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  Figure 1  (a) Sketch maps and (b) the optimized ground state (S₀) geometrical structures of the complexes

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  Figure 2  Electronic structures on the HOMOs and LUMOs of S₀, energy levels, and energy gaps (E_g) between HOMO and LUMO of the complexes 1-6

  The lines of green and the lines of red are HOMO and LUMO energy levels, respectively.

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  Figure 3  (a) Absorption spectra and (b) fluorescence emission spectra of the complexes 1-6

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  Table 1.  Main geometry structural parameters of S₀ and T₁ of the complexes under DFT and TDDFT level*

  Complex	State	Selected bond length / nm							Selected bond angle / (°)
  		R1	R2	R3	R4	R5	R6		A1	A2	A3	A4	A5
  1	S0	0.20	0.20	0.20	0.20	0.21	0.21		174.87	80.70	94.73	89.88	91.20
  	T1	0.20	0.19	0.20	0.20	0.22	0.21		175.86	82.12	95.46	88.00	92.35
  2	S0	0.20	0.20	0.20	0.20	0.21	0.21		175.02	80.62	94.89	89.78	91.33
  	T1	0.20	0.19	0.20	0.20	0.22	0.21		176.46	82.13	95.97	87.10	92.71
  3	S0	0.20	0.20	0.20	0.20	0.21	0.21		176.59	80.74	96.86	93.33	89.17
  	T1	0.20	0.20	0.20	0.19	0.22	0.22		177.54	96.82	80.59	94.64	87.56
  4	S0	0.20	0.20	0.20	0.20	0.21	0.21		176.49	80.68	96.79	93.37	89.42
  	T1	0.20	0.20	0.20	0.20	0.21	0.21		176.49	80.72	96.89	93.19	89.19
  5	S0	0.20	0.20	0.20	0.20	0.22	0.22		174.98	80.88	95.61	94.59	88.93
  	T1	0.20	0.20	0.20	0.20	0..2	0.22		174.98	80.89	95.62	94.58	88.92
  6	S0	0.20	0.20	0.20	0.20	0.22	0.22		175.02	80.83	95.68	94.33	89.23
  	T1	0.25	0.20	0.20	0.20	0.22	0.22		175.02	80.83	95.68	94.33	89.23
  *R1: Ir—N1, R2: Ir—C1, R3: Ir—N2, R4: Ir—C2, R5: Ir—N3/Ir—O1, R6: Ir—O/Ir—O2; A1: ∠N1—Ir—N2, A2: ∠N1—Ir—C1, A3: ∠N1—Ir—C2, A4: ∠N1—Ir—N3/∠N1—Ir—O1, A5: ∠N1—Ir—O/∠N1—Ir—O2.

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  Table 2.  Energy levels of the S₀, the lowest singlet S₁, and the lowest T₁ under the M06-2X functional

  Complex	$ {E}_{{S}_{0}} $ / eV	$ {E}_{{S}_{1}} $ / eV	$ {E}_{{T}_{1}} $ / eV	Δ$ \Delta {E}_{{S}_{0}{S}_{1}} $ / eV	$ \Delta {E}_{{S}_{0}{T}_{1}} $ / eV	$ \Delta {E}_{{S}_{1}{T}_{1}} $ / eV
  1	-5.261	-1.722	-2.896	3.539	2.365	1.174
  2	-5.280	-1.784	-2.853	3.496	2.427	1.069
  3	-5.065	-1.563	-2.719	3.502	2.346	1.156
  4	-5.077	-1.675	-2.680	3.402	2.397	1.005
  5	-5.016	-1.522	-2.383	3.494	2.633	0.861
  6	-5.034	-1.641	-2.393	3.393	2.641	0.752
  $E_{S_0}, E_{S_1}$, and $E_{T_1}$ are the energies of S0, the lowest S1, and the lowest T1 under the M06-2X functional, respectively; and are the energy gaps between different states (S0 and S1, S0 and T1, respectively).

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  Table 3.  Phosphorescent emission parameters of the complexes in CH₂Cl₂ solution under the TDDFT/M06-2X calculations

  Complex	Energy / eV	Wavelength / nm	Major	Contribution rate / %	Character
  1	2.37	524.25	HOMO→LUMO	55.7	3MLCT*+3LLCT+3ILCT
  			HOMO→LUMO+1	36.8
  2	2.43	510.78	HOMO→LUMO	55.8	3MLCT+3LLCT+3ILCT
  			HOMO→LUMO+1	35.6
  3	2.35	528.50	HOMO→LUMO	60.2	3MLCT+3LLCT+3ILCT
  			HOMO→LUMO+1	28.7
  4	2.40	517.23	HOMO→LUMO	59.6	3MLCT+3LLCT+3ILCT
  			HOMO→LUMO+2	30.0
  5	2.63	470.85	HOMO→LUMO	57.0	3MLCT+3LLCT+3ILCT
  			HOMO→LUMO+2	33.5
  6	2.64	469.39	HOMO→LUMO	58.2	3MLCT+3LLCT+3ILCT
  			HOMO→LUMO+2	31.7
  *3MLCT: the triplet metal-to-ligand charge transfer.

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  Table 4.  SOC matrix elements of the complexes $\Delta E_{S_0 T_1}$

  Complex	<S1|Hsoc|T1> / cm-1	<S1|Hsoc|T2> / cm-1	<S1|Hsoc|T3> / cm-1
  1	55.78	67.67	117.86
  2	49.78	89.19	124.28
  3	6.61	79.96	822.29
  4	10.42	46.56	843.64
  5	23.33	181.74	813.78
  6	8.09	136.56	817.62

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