English

• 0.   Introduction

  The organic light-emitting diode (OLED) industry and solid-state light-emitting sector have accorded special attention to transition metal complexes in recent years due to their spin-orbit coupling ability, which facilitates the blending of the singlet and triplet states^[1-5]. On this basis, the quantum yield in electroluminescent devices can attain 100%, rendering these complexes ideal for use as electroluminescent materials. Moreover, the emission wavelength and efficiency of these materials can be fine-tuned, making them favored in various electroluminescent applications. Compared with other transition metal complexes, Ir(Ⅲ) complexes have better performance in areas such as coordination with ligands, phosphorescence lifetime, and wavelength tunability^[6-10]. These strength that enable them to cover the entire visible spectrum enhance their promise as luminescent materials in electroluminescent devices^[11-14]. In a word, Ir(Ⅲ) complexes, which can offer a trio of fundamental hues, are highly sought-after phosphorescent substances in the OLED sector, proven to be invaluable in electroluminescent phosphors^[15-18].

  Through extensive research, a series of luminescent materials in red, green, and blue have been designed and synthesized^[19-23]. Some of these have been utilized in the fabrication of organic electroluminescent devices, with excellent performance. However, high-performance red light-emitting materials, in contrast to the green and blue ones, are still in short supply, unable to satisfy the practical needs, which has become a significant obstacle to the promotion of OLED technology and remains a focal point in the further investigation of organic electroluminescent materials^[24]. PtOEP, the earliest red phosphorescent material applied in OLEDs, exhibits a deep red hue, with near-saturated red organic phosphorescent properties. However, the efficiency roll-off property of it is visible^[25-26]. This phenomenon can be attributed to two main factors: firstly, the minimal energy difference between the lowest excited state and the ground state of red light-emitting dyes leads to more effective non-radiative deactivation of the excited state dye molecules, resulting in a relatively low fluorescence quantum yield for most red light-emitting material^[27-29]; secondly, the energy level difference between the highest occupied molecular orbital (HOMO) and the lowest occupied molecular orbital (LUMO) of the red light-emitting dyes is also negligible, making it more challenging to match the energy levels between the red light-emitting materials and the carrier transport layer, which hinders the effective recombination of electrons and holes in the light-emitting layer^[30-32].

  Therefore, in this work, we employed six complexes on Ir(Ⅲ) consisting of two main ligands (piq and fpiq, piq=1-phenylisoquinoline, fpiq=1-(4-fluorophenyl) isoquinoline), and three auxiliary ligands (acac, tmd, and tpip, acac=(3Z)-4-hydroxypent-3-en-2-one, tmd=(4Z)-5-hydroxy-2, 2, 6, 6-tetramethylhept-4-en-3-one, tpip=tetraphenylimido-diphosphonate) to analyze their electronic configuration, frontier molecular orbital (FMO) properties, absorption and emission spectra, and energy transfer processes through density functional theory (DFT) and time-dependent density-functional theory (TD-DFT). It is expected that our research can shed light on the production of materials in the future. Furthermore, by introducing the F atom, which can reduce the HOMO energy level^[33], to the main ligand, leading to the development of another main ligand fpiq, we hope that the properties of complexes with fpiq ligand better than the complexes with piq ligand, which has been successfully synthesized through experimentation^[34].

  1.   Methodology

  Every computation utilized Gaussian09, applying stringent self-adjoint field convergence limits for both gradient and wave function convergence. DFT and TD-DFT were responsible for fine-tuning the ground and triple excited state geometries of the complexes, using CH₂Cl₂ solution for spectral data collection. Furthermore, frequency analysis verified the complexes′ stable structures, revealing no imaginary frequency across all configurations at both the energy minimum and maximum levels. Detailed methodologies of the research are included in the Supporting information.

  2.   Results and discussion

  2.1   Geometries in the ground state S₀ and the lowest-lying triplet state T₁

  The structures and designations of the complexes are depicted in Fig. 1: (piq)₂Ir(acac) (1), (piq)₂Ir(tmd) (2), (piq)₂Ir(tpip) (3), (fpiq)₂Ir(acac) (4), (fpiq)₂Ir(tmd) (5), (fpiq)₂Ir(tpip) (6). Fig. 2 offers a detailed view of the enhanced ground state structure of complex 1, including the sequential arrangement of specific essential atoms. Table 1 presents a comprehensive overview of the primary geometric parameters of the ground state (S₀). Furthermore, it is noteworthy that complexes 1 and 4 possess the identical auxiliary ligand, acac; complexes 2 and 5 have the same auxiliary ligand, tmd; complexes 3 and 6 share the same auxiliary ligand, tpip; and complexes 1-3 and 4-6 all employ the main ligands, piq and fpiq, correspondingly.

  Figure 1

  

  Figure 1.  Sketch structures of the ligands and formulae of the complexes

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  Figure 2

  

  Figure 2.  Molecular geometric structure of complex 1

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  Table 1

  

  Table 1.  Main optimized geometries (S₀ and T₁) of the complexes

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  Complex	State	Selected bond distancea/nm							Selected bond angleb/(°)
  		R1	R2	R3	R4	R5	R6		A1	A2	A3	A4	A5
  1	S0	2.00	2.00	2.06	2.06	2.21	2.21		79.7	99.3	86.3	94.7	178.7
  	T1	2.00	1.99	2.08	2.03	2.20	2.21		79.7	99.4	86.4	94.8	177.5
  2	S0	2.00	2.00	2.06	2.06	2.20	2.20		79.7	99.4	86.0	95.0	178.7
  	T1	2.00	1.99	2.08	2.03	2.20	2.20		79.7	99.3	86.0	95.1	178.7
  3	S0	1.99	1.99	2.06	2.06	2.27	2.27		80.6	96.5	91.4	92.3	175.7
  	T1	1.98	1.99	2.03	2.08	2.27	2.27		81.3	97.4	89.0	93.7	177.2
  4	S0	2.00	2.00	2.06	2.06	2.20	2.20		79.8	99.1	86.4	94.7	178.4
  	T1	2.00	2.00	2.07	2.02	2.20	2.20		79.7	98.9	86.9	94.6	177.4
  5	S0	2.00	2.00	2.06	2.06	2.19	2.19		79.8	99.1	86.8	93.5	176.2
  	T1	2.00	2.00	2.08	2.03	2.19	2.19		79.7	98.8	86.6	94.9	177.2
  6	S0	1.99	1.99	2.06	2.07	2.27	2.26		80.0	98.8	86.6	93.0	176.0
  	T1	1.99	1.99	2.26	2.08	2.26	2.26		81.3	97.8	88.4	92.1	176.3
  a R1=Ir—C1, R2=Ir—C2, R3=Ir—N1, R4=Ir—N2, R5=Ir—O1, R6=Ir—O2; b A1=N1—Ir—C1, A2=N1—Ir—C2, A3=N1—Ir—O1, A4=N1—Ir—O2, A5=N1—Ir—N2.

  The geometry of S₀ and T₁ excited states of the complexes was optimized using the DFT method^[35]. As shown in Table 1, each complex preserves a quasi-octahedral geometry around the metal center, which can contribute to optimizing the electroluminescence performance, as observed in other typical six-coordinated Ir(Ⅲ) complexes. Regarding the disparities and resemblances among these complexes, we undertook an extensive array of meticulous observations, comparisons, and deliberations, focusing on the crucial bond lengths and bond angles. Analysis of the data, as shown in Table 1, indicates that complexes 3 and 6 have longer Ir—O bond lengths in the ground state than complexes 1 and 4, as well as 2 and 5, owing to the stronger electron-releasing capacity of tpip compared to acac and tmd. Furthermore, when comparing complexes 1, 4, 2, 5, and 3, 6, it is evident that the Ir—O bond lengths of the complexes with piq as the main ligand are greater than those of the complexes with fpiq as the main ligand. This difference stems from the substitution of the H atom in the phenyl group of piq with an F atom in fpiq, a modification that enhances the electron-accepting capacity of the F atom, thereby lowering the HOMO energy level. The changes in the length of the Ir—C bond on the main ligand of (piq)₂Ir(acac) and (fpiq)₂Ir(acac) show no statistical significance (0.000 2 nm), and the alteration in Ir—N bond is still negligible (0.000 1 nm) when contrasted with piq and fpiq. Similarly, the difference in Ir—C bond length is only 0.000 1 nm, and the difference in Ir—N bond length is 0.000 2 nm for complexes 2 and 5. However, for complexes 3 and 6, the difference between the Ir—C bond length and the Ir—N bond length is identical (0-0.000 2 nm). The results of the comparison demonstrate a longer Ir—C bond when using piq as the main ligand, and a shorter Ir—N bond when fpiq is applied. Despite the formation of Ir—C bonds necessitating substantial energy and thereby augmenting the connection complexity, the Ir—C bond length remains nearly constant under S₀ and T₁ states, suggesting robust stability of the compound. Additionally, the parameters of S₀ and T₁ of complexes 1-6 are compared to the structure parameters under the triplet excited state in Table 1. Only slight changes are observed in S₀ and T₁ states, indicating a weak breakthrough barrier. A few of the S₀ and T₁ states demonstrate noteworthy modifications, implying electron transition. All these suggest strong stability of these Ir(Ⅲ) complexes^[18].

  2.2   FMO properties

  The primary cause behind the varied photophysical and photochemical characteristics of these complexes lies within the configuration of the electron cloud, that is, the altered configuration of the FMOs. Information regarding the FMOs is displayed in Fig. 3. Modifying the luminescence hue of the complexes usually involves altering the substituent, either by switching the substituent itself or by adding another one that pulls or pushes electrons. The lowest excited state is characterized by electron transition from a HOMO to a LUMO. The following segment will concentrate on examining the electron distribution, energy states, and band voids in HOMOs and LUMOs, along with the band gap. In our research, Gaussian software is utilized to implement the TD-DFT technique for determining the contribution rates of the HOMO in complexes 1-6^[36-38]. To unveil the optical and chemical characteristics of these complexes, a theoretical analysis of their FMO properties was performed. The primary distribution of HOMO occurs within main ligands and central metal ions (piq: 22%/22%, 22%/22%, 22%/21%; fpiq: 23%/23%, 23%/23%, 23%/22%; Ir: 51%/51%, 52%/48%, 48%/50%); auxiliary ligands constitute just a minor segment (acac: 5%, 5%; tmd: 6%, 6%; tpip: 5%, 5%). LUMO is mainly distributed on main ligands (piq: 47%/47%, 47%/47%, 59%/35%; fpiq: 47%/47%, 47%/47%, 55%/39%). The transition mode of each excited state is ascertained based on the composition of the orbitals involved.

  Figure 3

  

  Figure 3.  Presentation of energy levels, energy gaps and orbital composition distribution of HOMOs and LUMOs for the complexes

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  The MLCT (metal-to-ligand charge transfer) is the process of transferring charge from a metal atom/ion to a ligand. While the ILCT represents the charge transfer in the same ligand, the charge transfer between the two ligands is documented as LLCT. The charge transfer transitions of complexes 1-6 are the following: (piq)₂Ir(acac): Ir/piq-2/piq-1/acac → piq-1/piq-2 (³LLCT/³ILCT/³MLCT); (piq)₂Ir(tmd): Ir/piq-2/piq-1/tmd → piq-1/piq-2 (³LLCT/³ILCT/³MLCT); (piq)₂Ir(tpip): Ir/piq-2/piq-1/tpip → piq-1/piq-2 (³LLCT/³ILCT/³MLCT); (fpiq)₂Ir(acac): Ir/fpiq-2/fpiq-1/acac → fpiq-1/fpiq-2 (³LLCT/³ILCT/³MLCT); (fpiq)₂Ir(tmd): Ir/fpiq-2/fpiq-1/tmd → fpiq-1/fpiq-2 (³LLCT/³ILCT/³MLCT); (fpiq)₂Ir(tpip): Ir/fpiq-2/fpiq-1/tpip → fpiq-1/fpiq-2 (³LLCT/³ILCT/³MLCT). The energy levels of HOMO and LUMO are primarily found on the main ligands, rather than on the auxiliary ligands. Complexes 1-6 have introduced relatively strong electron-donating ligands such as acac, tmd, and tpip. Besides causing redshift or blueshift in the absorption spectrum, this also leads to the movement of FMOs towards the main ligand, directly resulting in ³LLCT, ³ILCT, and ³MLCT dominating the absorption spectral characteristics without the emergence of other absorption characteristics. Furthermore, the electron cloud distribution of the LUMO converges inward significantly, and the material molecules possess a 3D spatial structure, which increases the steric hindrance between the material molecules and reduces the probability of exciton collisions. Therefore, this complex may exhibit the characteristic of low-efficiency roll-off during the luminescence process^[39-41].

  2.3   Ionization potentials and electron affinities

  The performance of OLED devices hinges on their charge injection, transmission, balance, and exciton recombination. Therefore, our ongoing analysis will focus on various complexes with the subsequent dataset. The assessment of the hole barrier employs ionization potential (E_I); a lower E_I facilitates the hole's transition from the hole transport layer (HTL) to the luminescent layer, while electron affinity (E_A) serves to evaluate the electron barrier. Elevated E_A levels increase the likelihood of electron transition from the electron transition layer (ETL), with recombination energy (λ) as a measure for equilibrium and the rate of charge transfer; electron extraction potential (E_EE) represents the energy variance between a neutral molecule and an anion derived from the anion; similarly, the hole extraction potential (E_HE) reflects the energy gap between a neutral molecule and the cationic state, indicating the ease of hole extraction; stabilizing energy (E_S) forecasts the energy involved in charge self-trapping; Table 2 showcases a comparative analysis of E_A and E_I data for complexes 1-6. Among them, (piq)₂Ir(tpip) (3) has the lowest E_I, indicating it accepts holes more easily than others. On the contrary, (fpiq)₂Ir(tpip) (6) has the highest E_A, suggesting it accepts electrons more easily. Complexes 1-3 exhibit a reduced E_HE for easier hole acceptance, while complexes 4-6 possess a greater E_EE for better electron absorption.

  Table 2

  

  Table 2.  E_I, E_A, E_EE, λ, E_HE, and E_S for the six complexes calculated at DFT/B3LYP/LANL2DZ level* eV

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  Complex	EI,v	EI,a	EHE	ES,h	EA,v	EA,a	EEE	ES,e	λh	λe
  1	5.93	5.84	5.73	0.09	0.68	0.76	0.83	0.08	0.20	0.15
  2	5.91	5.81	5.70	0.10	0.72	0.79	0.87	0.07	0.21	0.15
  3	5.83	5.71	5.58	0.12	0.67	0.82	0.90	0.15	0.25	0.23
  4	6.15	6.07	5.97	0.08	0.77	0.85	0.92	0.08	0.18	0.15
  5	6.13	6.04	5.94	0.09	0.80	0.88	0.96	0.08	0.19	0.16
  6	6.04	5.92	5.79	0.12	0.75	0.89	0.96	0.14	0.25	0.21
  * The suffixes v, a, h, and e indicate vertical, adiabatic values, hole, and electron.

  The E_S values for complexes 1, 2, 4, and 5 are significantly lower compared to those of complexes 3 and 6, suggesting reduced undesired losses in their luminescent state. Drawing from Marcus and Hush^[42-45], the value of k can be calculated using this equation^[46]:

  $ k=\left(\frac{\mathtt{π}}{k_{\mathrm{B}} T}\right)^{\frac{1}{2}} \frac{V^2}{h} \exp \left(-\frac{\lambda}{4 k_{\mathrm{B}} T}\right)=A \exp \left(-\frac{\lambda}{4 k_{\mathrm{B}} T}\right) $

  (1)

  In this formula, k_B symbolizes Boltzmann′s constant, T signifies temperature, λ denotes the recombination energy, and V is the coupling matrix element. Within the given formula, k varies with λ and V. When in a solid state, the range of electron transition between molecules is limited. As depicted in Fig. 4, the expression of λ_h is as follows^[46-48]:

  $ \lambda_{\mathrm{h}}=\lambda_0+\lambda_{+}=\left(E^*{ }_0-E_0\right)+\left(E^*{ }_{+}-E_{+}\right)=E_{\mathrm{I}, \mathrm{P}}-E_{\mathrm{HE}} $

  (2)

  Figure 4

  

  Figure 4.  Schematic description of internal recombination energy (λ) for hole transfer

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  Within the aforementioned formula, E₀ and E₊ represent the constant energies of molecules and cations, while E₀^* and E₊^* signify the energy levels of neutral molecules and cations in cationic structures. The energy of the hole transmission composite matches the disparity between vertical E_I and E_HE. Besides, when considering electron transition, a similar formulation applies, highlighting the parallels between hole and charge transfer mechanisms. The recombination energy λ, serving as the material for the emission layer (EML), maintains equilibrium amidst the process of hole injection and electron injection. Table 2 reveals that complexes 1-6 typically exhibit hole transfer (λ_h) values surpassing electron transfer (λ_e) values, indicating their substantial superiority over hole transport in electron transport characteristics. Within this group of substances, (piq)₂Ir(tpip) (3) exhibits the least variance in λ_h and λ_e values, owing to its steadier recombination energies compared to other transition metal-emitting and organic materials, making it an ideal choice for OLED light-emitting materials.

  2.4   Absorption and emission of the complexes in CH₂Cl₂ media

  The absorption spectra, distribution, and excitation of the complexes in CH₂Cl₂ solution, along with their corresponding oscillator strengths, are detailed in Table 3. Based on the optimized ground-state geometry, the minimum energy emissions and minimum oblique absorption bands of complexes 1-6 were calculated to facilitate the study of the effects of ligands on the photophysical properties, as shown in Fig. 5, which features a fitted Gaussian-type absorption curve.

  Table 3

  

  Table 3.  Phosphorescent emissions of the complexes in CH₂Cl₂ solution, together with experimental values

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  Complex	Emission	Major contribution	Character
  1	656 nm/1.89 eV	L→H(58%)	3MLCT/3ILCT/3LLCT
  1	654 nm/1.90 eV	L→H(57%)	3MLCT/3ILCT/3LLCT
  3	661 nm/1.88 eV	L→H(58%)	3MLCT/3ILCT/3LLCT
  4	667 nm/1.86 eV	L→H(63%)	3MLCT/3ILCT/3LLCT
  5	667 nm/1.86 eV	L→H(63%)	3MLCT/3ILCT/3LLCT
  6	669 nm/1.86 eV	L→H(63%)	3MLCT/3ILCT/3LLCT

  Figure 5

  

  Figure 5.  Simulated absorption spectra of the complexes in CH₂Cl₂ with calculated data

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  According to Table S1, the fundamental singlet absorptions wavelengths and the oscillator strengths for complexes 1-6 are situated at 503 nm (f=0.003), 505 nm (f=0.002), 512 nm (f=0.070), 477 nm (f=0.006), 478 nm (f=0.005), and 485 nm (f=0.073), respectively. The primary transitions refer to the transitions from the HOMO to the LUMO. Through individual comparisons of complexes 1-4, 2-5, and 3-6, it is discovered that adding an F atom to the main ligand results in a blue shift in fpiq relative to piq. An analysis of complexes 1-3 and 4-6 reveals that auxiliary ligand tpip, when interacting with the same main ligand, has a higher probability than acac and tmd of triggering a blue shift in the complex due to the strong electron-withdrawing nature of the F atom^[49].

  The oscillator strength f_1→2 moving from a lower state |1m₁〉 to an upper state |2m₂〉 can be determined by^[11-14]

  $ f_{1 \rightarrow 2}=\frac{2 m_e}{3 \hbar^2}\left(E_2-E_1\right) \sum_{m_2} \sum_{a=x, y, z}\left.\left|\left\langle 1 m_1\right| R_a\right| 2 m_2\right\rangle\left.\right|^ 2 $

  (3)

  where $ \hbar$ represents the reduced Planck′s constant, and m_e denotes an electron′s mass. This presupposes that quantum states |nm_n〉, where n=1, 2, ⋯, possess multiple degenerate sub-states labeled as m_n. These are deemed degenerate when they possess identical energy E_n. The aggregate of all N electrons′ x coordinates γ_i,α constitutes the operator R_α^[15-18]:

  $ R_\alpha=\sum\limits_{i=1}^N \gamma_{i, \alpha} $

  (4)

  For every sub-state |1m₁〉, the oscillator′s intensity remains consistent.

  Table 3 displays the emission specifics, acquired at the TD-DFT/M062X/LanL2DZ & 6-31G* level. Complexes 1-6 primarily exhibit charge-transfer features such as ³MLCT, ³LLCT, and ³ILCT, characterized by emission levels at 656, 654, 661, 667, 667, and 669 nm^[50]. Specialists have successfully created a main ligand closely resembling the main ligands fpiq and piq^[33]. The range of experimental values for the complexes with this main ligand spans from 620 to 658 nm, in contrast to the range of 654 to 669 nm observed for complexes 1-6. The alignment between experimental and theoretical values suggests the reliability and trustworthiness of our theoretical predictions.

  The complex (fpiq)₂Ir(tpip) (6) has a low-efficiency roll-off property. Consequently, we hypothesized initially that (fpiq)₂Ir(tpip) characteristics mirror those of other complexes due to their similar molecular configurations, FMO features, absorption and emission spectra, believing that each complex possesses low-efficiency roll-off features. Nonetheless, the experimental results exhibit a certain spectrum of variances with limited precision. Therefore, our approach focuses more on offering a broad overview rather than establishing detailed prerequisites.

  2.5   Application prospects in OLEDs

  Typically, OLED apparatuses are structured in three tiers: HTL, EML, and ETL. We are about to elucidate the real-world use of these substances in OLED gadgets. Fig. 6 displays the states of electron transition and energy levels of these substances in OLED device setups.

  Figure 6

  

  Figure 6.  OLED structure designed in this work

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  ITO is celebrated for its exceptional electrical conductivity and clarity. It is employed in our research, with a 5.2 eV work function as the anode. For the cathode selection, the commonly used LiF/Al working function at 5.2 eV is determined. In this context, TAPC (di-[4-(N, N-dipolymer-amino)-phenyl]-cyclohexane) and TmPyPb (1, 3, 5-triphenylbenzene) are utilized for HTL and ETL. Furthermore, mCP (1, 3-bis(carbazole-9-acyl) benzene) typically serves as the matrix for the EML.

  Fig. 6 illustrates that the energy levels of HOMO in complexes 1-6 exceeded those in the host mCP (0.64-0.82 eV), inhibiting the luminescence emitted by the material of the host, and the energy levels of their LUMO are lower than those of the host (0.78-1.00 eV). Consequently, the dopant creates a trap for holes and electrons, postponing electron and hole movement in the EML due to doping^[51]. Consequently, it is ascertainable that complexes 1-6 will improve the balance of carrier injection and transition. In other words, the complexes examined in this study are highly appropriate for application in OLED technology.

  3.   Conclusions

  Our research has strived to determine the geometric configuration, absorption, and emission characteristics of Ir(Ⅲ) metal ions using DFT and TD-DFT techniques. Through the research, a conclusion is drawn that these substances are apt for producing OLED in the form of low-efficiency roll-off materials. It is also found by calculating phosphorescent emissions that all of them are red-emitting substances. Furthermore, by introducing F atoms into the main ligand and substituting the secondary ligand, the gap in the HOMO-LUMO band may be changed, and thereby their glowing hue may be influenced. Ionization potentials and electron affinities of these complexes have wonderful results. Among them, (fpiq)₂Ir (tpip) performs the most outstandingly. Specialists have successfully created complexes whose structures closely resemble those in our study. Our aspiration is that the research will offer fresh concepts for subsequent investigations.

  
  Acknowledgments: This work was supported by the Science and Technology Development of Jilin Province of China (Grant No.20220101039JC), the Education Department of Jilin Province (Grant No.JJKH20230506KJ), the Natural Science Foundation of Shandong Province (Grant No.ZR2020BM016), and the Science Fund of Shandong Laboratory of Advanced Materials and Green Manufacturing (Yantai) (Grant No.AMGM2023A07). Supporting information is available at http://www.wjhxxb.cn
  
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  Figure 1  Sketch structures of the ligands and formulae of the complexes

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  Figure 2  Molecular geometric structure of complex 1

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  Figure 3  Presentation of energy levels, energy gaps and orbital composition distribution of HOMOs and LUMOs for the complexes

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  Figure 4  Schematic description of internal recombination energy (λ) for hole transfer

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  Figure 5  Simulated absorption spectra of the complexes in CH₂Cl₂ with calculated data

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  Figure 6  OLED structure designed in this work

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  Table 1.  Main optimized geometries (S₀ and T₁) of the complexes

  Complex	State	Selected bond distancea/nm							Selected bond angleb/(°)
  		R1	R2	R3	R4	R5	R6		A1	A2	A3	A4	A5
  1	S0	2.00	2.00	2.06	2.06	2.21	2.21		79.7	99.3	86.3	94.7	178.7
  	T1	2.00	1.99	2.08	2.03	2.20	2.21		79.7	99.4	86.4	94.8	177.5
  2	S0	2.00	2.00	2.06	2.06	2.20	2.20		79.7	99.4	86.0	95.0	178.7
  	T1	2.00	1.99	2.08	2.03	2.20	2.20		79.7	99.3	86.0	95.1	178.7
  3	S0	1.99	1.99	2.06	2.06	2.27	2.27		80.6	96.5	91.4	92.3	175.7
  	T1	1.98	1.99	2.03	2.08	2.27	2.27		81.3	97.4	89.0	93.7	177.2
  4	S0	2.00	2.00	2.06	2.06	2.20	2.20		79.8	99.1	86.4	94.7	178.4
  	T1	2.00	2.00	2.07	2.02	2.20	2.20		79.7	98.9	86.9	94.6	177.4
  5	S0	2.00	2.00	2.06	2.06	2.19	2.19		79.8	99.1	86.8	93.5	176.2
  	T1	2.00	2.00	2.08	2.03	2.19	2.19		79.7	98.8	86.6	94.9	177.2
  6	S0	1.99	1.99	2.06	2.07	2.27	2.26		80.0	98.8	86.6	93.0	176.0
  	T1	1.99	1.99	2.26	2.08	2.26	2.26		81.3	97.8	88.4	92.1	176.3
  a R1=Ir—C1, R2=Ir—C2, R3=Ir—N1, R4=Ir—N2, R5=Ir—O1, R6=Ir—O2; b A1=N1—Ir—C1, A2=N1—Ir—C2, A3=N1—Ir—O1, A4=N1—Ir—O2, A5=N1—Ir—N2.

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  Table 2.  E_I, E_A, E_EE, λ, E_HE, and E_S for the six complexes calculated at DFT/B3LYP/LANL2DZ level* eV

  Complex	EI,v	EI,a	EHE	ES,h	EA,v	EA,a	EEE	ES,e	λh	λe
  1	5.93	5.84	5.73	0.09	0.68	0.76	0.83	0.08	0.20	0.15
  2	5.91	5.81	5.70	0.10	0.72	0.79	0.87	0.07	0.21	0.15
  3	5.83	5.71	5.58	0.12	0.67	0.82	0.90	0.15	0.25	0.23
  4	6.15	6.07	5.97	0.08	0.77	0.85	0.92	0.08	0.18	0.15
  5	6.13	6.04	5.94	0.09	0.80	0.88	0.96	0.08	0.19	0.16
  6	6.04	5.92	5.79	0.12	0.75	0.89	0.96	0.14	0.25	0.21
  * The suffixes v, a, h, and e indicate vertical, adiabatic values, hole, and electron.

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  Table 3.  Phosphorescent emissions of the complexes in CH₂Cl₂ solution, together with experimental values

  Complex	Emission	Major contribution	Character
  1	656 nm/1.89 eV	L→H(58%)	3MLCT/3ILCT/3LLCT
  1	654 nm/1.90 eV	L→H(57%)	3MLCT/3ILCT/3LLCT
  3	661 nm/1.88 eV	L→H(58%)	3MLCT/3ILCT/3LLCT
  4	667 nm/1.86 eV	L→H(63%)	3MLCT/3ILCT/3LLCT
  5	667 nm/1.86 eV	L→H(63%)	3MLCT/3ILCT/3LLCT
  6	669 nm/1.86 eV	L→H(63%)	3MLCT/3ILCT/3LLCT

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