Exploring the Photophysical Properties of Iridium (III) Complexes Using TD-DFT: A Comprehensive Study

Exploring the Photophysical Properties of Iridium (III) Complexes Using TD-DFT: A Comprehensive Study | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Exploring the Photophysical Properties of Iridium (III) Complexes Using TD-DFT: A Comprehensive Study Ren Xinqi, Shiwei Yin This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4984416/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 12 Dec, 2024 Read the published version in Theoretical Chemistry Accounts → Version 1 posted 8 You are reading this latest preprint version Abstract Organic light-emitting diodes (OLEDs) are prominent in various applications, including screen displays, medical devices, and chemical sensors, due to their low power consumption, fast response speed, and high-resolution capability. Phosphorescent emitters, especially cyclometalated Ir(III) complexes, are particularly significant in OLEDs because they enable internal quantum efficiencies of up to 100% through strong spin-orbit coupling (SOC). This study focuses on the accurate characterization of singlet and triplet metal-to-ligand charge transfer (MLCT) states in Ir(III) complexes, which is essential for optimizing their performance. Using a combination of quantum mechanical methods, particularly time-dependent density functional theory (TDDFT) with optimally tuned range-separated functionals and the full-electron scalar relativistic Douglas-Kroll-Hess (DKH2) Hamiltonian, we evaluate the electronic structures and MLCT states of eight Ir(III) complexes. Our results highlight the efficacy of the tuned ω *B97X functional in predicting MLCT energies and higher-energy absorption peaks, demonstrating its superiority over conventional functionals like PBE0 and B3LYP. The inclusion of relativistic effects and SOC in our models ensures alignment with experimental absorption spectra, providing reliable benchmarks for computational approaches. This comprehensive analysis not only advances the understanding of MLCT transitions in phosphorescent materials but also aids in the design of new Ir(III) complexes with enhanced photophysical properties. Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 1.Introduction Organic light emitting diodes (OLEDs) are widely used in screen displays 1 , medical devices 2 , chemical sensors 3 , and other fields due to their advantages such as low power consumption 4 , fast response speed 5 , and high-resolution capability 2 . Among them, phosphorescent emitters have attracted wide attention because heavy-atom leads to the SOC between triplet (T) and singlet (S) states, which effectively promotes the non-radiative inter-system crossover from the first singlet excited state (S 1 ) to the lowest triplet state (T 1 ) and enhances the radiative transition from T 1 to the ground state (S 0 ). Thus, the internal quantum efficiency of 100% is readily achieved in phosphorescent OLEDs 6 – 7 . These phosphorescent emitters are mainly composed of heavy metal elements such as Iridium (Ir) 8 – 10 , Platinum (Pt) 11 , and Osmium (Os) 10 . Among them, cyclometalated Ir(III) complexes are of particular interest due to their relatively short triplet state lifetimes and tunable emission wavelengths 12 – 13 . The superior photophysical properties of these complexes are governed by their electronic transitions, especially metal-to-ligand charge transfer (MLCT) transitions. 14 – 16 MLCT transitions involve the electron transfer from a metal center to a ligand. In iridium complexes, these transitions are significant due to the strong SOC inherent to heavy transition metals like Ir(III). This SOC facilitates intersystem crossing between singlet and triplet states, making the characterization of both ¹MLCT and ³MLCT states critical. The singlet MLCT (¹MLCT) involves an electronic transition where the spin multiplicity remains unchanged (singlet to singlet), while the triplet MLCT (³MLCT) involves a transition to a triplet state, where the spin multiplicity changes. Thus, accurate assignment and understanding of these MLCT transitions, encompassing both singlet (¹MLCT) and triplet (³MLCT) states, are essential for optimizing the performance and tailoring the properties of these materials. Quantum mechanical (QM) methods, particularly time-dependent density functional theory (TDDFT), are indispensable for investigating the electronic structures and excited states of transition metal complexes. TDDFT extends the capabilities of ground-state DFT to excited states, enabling detailed studies of electronic transitions. However, conventional DFT functionals often inadequately describe CT electron transitions due to limitations in handling long-range electron-electron interactions 17 and self-interaction errors 18 . These inaccuracies are especially pronounced in systems with significant charge-transfer character, such as MLCT states in transition metal complexes. To end this, the tuned range-separated functionals are proposed to deal with the excited states with CT characters. 19 – 20 Furthermore, Ir is a heavy transition metal and elements in this part of the periodic table exhibit significant relativistic effect. The relativistic effect results in strong SOC and the notable splitting and mixing of singlet and triplet electronic states, making the electronic transitions from ³MLCT to S 0 possible. Experimental absorption spectra of Ir(III) complexes inherently include relativistic effects. To ensure that computational simulations accurately reflect experimental data, these effects must be included in the models. This alignment is crucial for validating computational methods and for the reliable interpretation of experimental results. In recent years, an increasing number of researchers have employed theoretical calculations to systemically consider the ligand effects on the optical properties such as absorption spectra, emission spectra and quantum yields of Ir(III) complexes. 21 – 23 However, the selection of DFT functionals and the impact of relativistic effects on MLCT electronic transitions are seldom studied for transition metal complexes. 24 – 25 Experimental absorption is primarily related to the geometric structures under the ground state (S 0 ), and does not involve the more complex relaxation processes that occur in the excited states. And experimental absorption data, particularly for ³MLCT and ¹MLCT states, serve as excellent benchmark data for evaluating different computational approaches. This benchmarking helps identify the most suitable computational techniques for studying Ir(III) complexes and designing the new complexes with optimized performance. In this study, we firstly selected eight Ir(III) complexes including facial ( fac ) and meridional ( mer ) Ir(C^N) 3 -type 26 – 27 complexes: fac -Ir(ppy) 3 28–29 , mer -Ir(ppy) 3 29 , fac -Ir(tpy) 3 29 , mer -Ir(tpy) 3 29 , fac -Ir(piq) 3 30 , mer -Ir(piq) 3 29 and Ir(C^N) 2 LX-type complexes 31 – 32 : Ir(ppy) 2 acac 33 and Ir(tpy) 2 acac 33 as a mini-benchmarking dataset whose absorption data for MLCT states can be found in literatures. The detailed structures of these eight Ir(III) complexes are showed in Fig. 1 . In this paper, the tuned optimal range-separated ω *B97X functional in combination with the full-electron scalar relativistic Douglas-Kroll-Hess (DKH2) Hamiltonian of 2nd order 34 is applied to calculate the electronic structure and MLCT excited states of these molecules in Fig. 1 . As a comparison, some widely used DFT functionals including hybrid GGA such as PBE0 and B3LYP and range-separated hybrid GGA functionals such as ω B97X and CAM-B3LYP in combination with DKH2 also are applied to calculate the absorption spectra of these Ir(III) complexes. In addition, the effects of relativistic Hamiltonian and SOC on MLCT states are discussed in results section. 2.Theory and computational details 2.1 Optimally Tuned Range-Separated Functionals To accurately describe charge transfer (CT) states, optimally tuned range-separated functionals are employed. Conventional functionals often underestimate the energies of excited states, but range-separated functionals address these issues by distinguishing between short-range and long-range exchange interactions, separated by the range-separation parameter ω . The key feature of these functionals is their ability to balance DFT and Hartree-Fock (HF) contributions. When electron-electron distance (r₁₂) is small, the short-range exchange is dominated by DFT. As r₁₂ increases, the exchange gradually shifts to HF, providing an accurate description of long-range interactions. The parameter ω controls this balance, enhancing the accuracy of predicting CT energies. To determine the optimal ω value, the ionization potential ( IP ) tuning method is used. This method adjusts the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) energies to match the IP and electron affinity ( EA ) of the system. The optimization minimizes the following function: $$J\left( \omega \right)=\hbox{min} \left\{ {\left| {{E_{HOMO}}(\omega ) - IP(N)} \right|+\left| {{E_{LUMO}}(\omega ) - IP(N+1)} \right|} \right\}$$ 1 where E HOMO and E LUMO are the energies of the HOMO and LUMO, respectively. By minimizing these functions, the optimal ω parameter is found, ensuring accurate predictions of electronic transitions and improving the description of CT states. Additionally, this approach eliminates spurious behavior because the exact exchange has the correct asymptotic character and cancels the self-interaction exactly. 35 – 38 2.2 Computational details Geometry optimizations The ground state structures of molecules in Fig. 1 were separately optimized using the hybrid PBE0 39 , B3LYP 40 and range-separated ω B97X 41 , CAM-B3LYP 42 functionals. All the calculations are performed using the Stuttgart/Dresden ECP basis set (SDD) 43 for heavy-metal Ir atom and D95 basis set for all other atoms. The geometry optimizations are carried out by G16 program. 44 Excited state calculations Based on the optimized structures, the TD-DFT method was applied to simulate the absorption spectra of Ir(III) complexes. All-electron relativistic approaches using the DKH2 Hamiltonian were employed to account for relativistic effects, with the SARC-DKH-TZVP all-electron basis set used for Ir, and the DKH-def2-TZVP(-f) basis set used for other nonmetallic atoms. To assign the ³MLCT states, the SOC effect was also considered during the TD-DFT calculations. 45 Standard functionals such as PBE0, B3LYP, ω B97X and CAM-B3LYP were separately utilized to calculate the excited electronic structures of the Ir(III) complexes. The optimally tuned range-separated functionals were based on the standard range-separated ω B97X functional. The molecule-specific ω parameters were optimized using the optDFTw program v1.0 and the ORCA interface written by Dr. Zikuan Wang. 46 We refer to this optimally tuned range-separated functionals as ω *B97X. All the TD-DFT calculations were performed using the ORCA 5.0 package. 47 3.Results and Discussion 3.1 Ground State Geometry Figure 1 shows eight phosphorescent Ir(III) complexes. The heavy-metal Ir coordinates with ligands including 2-phenylpyridine (ppy), 1-phenylisoquinolinato (piq), benzo[h]quinolinato (bzq), 2,4-pentanedione (acac), 2-(4,6-difluorophenyl) pyridinato (46dfppy), and 2-(p-tolyl) pyridinato (tpy) to form six-coordinate complexes. Four different functionals including PBE0, B3LYP, ω B97X, and CAM-B3LYP are utilized to optimize the ground-state geometries of eight molecules. Table 1 presents the structural parameters of fac -Ir(ppy) 3 , mer -Ir(tpy) 3 , and fac -Ir(piq) 3 obtained from different functionals and X-ray crystallography measurements 15 , 29 – 30 . Figure 1 shows the structure of the selected molecule and the key atomic labels. Due to the C 3 symmetry of the facial configuration including fac -Ir(ppy) 3 and fac -Ir(piq) 3 , the Ir-C and Ir-N bond lengths are identical. Thus, for the facial configuration, we only analyze one Ir-C and one Ir-N bond length due to the C 3 symmetry. In contrast, for the meridional configuration with C 1 symmetry, we analyze all three Ir-C and Ir-N bond lengths. From Table 1 , we can find that the maximum errors between calculated and experimental values in bond lengths and angles obtained from different functionals are as follows: ω B97X is 0.096 Å and 1.4 degrees, CAM-B3LYP is 0.123 Å and 1.8 degrees, PBE0 is 0.108 Å and 1.7 degrees, and B3LYP is 0.143 Å and 1.6 degrees. Compared with X-ray crystallography data 15 , 29 – 30 , the computed bond length deviations are all below 0.15 Å, and the angle deviations are below 2 degrees. These indicate that the ground state structures of the complexes obtained from DFT calculations are relatively reliable, and the choice of functional has a minor impact on the results. The minor variations in bond lengths and angles across different functionals, all remaining within acceptable error margins compared to X-ray crystallography data, underscore the robustness of DFT in modeling the ground structures of these complexes. Given the high accuracy and consistency of the ω B97X functional, as evidenced by its minimal deviations in bond lengths and angles, it is deemed the most suitable for further studies. The ω B97X functional, with its optimal tuning and balance between short-range and long-range interactions, provides a nuanced and accurate description of the electronic environment in these complexes. Therefore, subsequent studies will employ the ground-state geometries optimized with ω B97X for further electron structure calculations, including time-dependent DFT (TD-DFT) simulations of absorption spectra. Table 1 Comparison of the calculated bond lengths (in Å) and bond angles (in degrees) for the molecular geometry of the Ir(III) complex optimized using different functional approaches with experimental values obtained from X-ray crystallography. ω B97X CAM-B3LYP PBE0 B3LYP exp. mer- Ir(tpy) 3 Bond Lengths (Å) Ir-C1 2.176 2.102 2.090 2.115 2.151 29 Ir-N1 2.080 2.167 2.152 2.187 2.044 29 Ir-C2 2.065 2.087 2.076 2.098 2.065 29 Ir-N2 2.103 2.073 2.057 2.084 2.076 29 Ir-C3 2.086 2.109 2.008 2.026 2.086 29 Ir-N3 2.106 2.058 2.042 2.066 2.010 29 fac- Ir(ppy) 3 Bond Lengths (Å) Ir-C 2.031 2.033 2.022 2.041 2.033 48 Ir-N 2.155 2.146 2.130 2.162 2.158 48 fac- Ir(piq) 3 Bond Lengths (Å) Ir-N1 2.154 2.145 2.130 2.161 2.135 30 Ir-C2 2.029 2.030 2.019 2.038 2.009 30 N1-C1 1.375 1.372 1.370 1.376 1.374 30 N1-C3 1.350 1.354 1.361 1.368 1.339 30 Bond Angles (degree) N1-Ir-C2 78.4 78.3 78.5 78.2 78.5 30 Ir-N1-C1 123.4 123.0 123.1 123.2 124.8 30 Ir-N1-C3 115.3 115.7 115.9 115.7 115.1 30 3.2 Effects of functionals on Frontier Molecular Orbitals (FMO) The molecular orbital wavefunctions of the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) of fac -Ir(ppy) 3 calculated by DKH2 Hamiltonian in combination with the five different functionals including PBE0, B3LYP, ω B97X, CAM-B3LYP and optimally tuned ω* B97X are respectively showed in Fig. 2 . From Fig. 2 , we can see that all five functionals produce wavefunctions with the same C 3 symmetric distributions for both the HOMO and LUMO. The HOMO is a mixture of d-type orbitals on the Ir atom and π-type orbitals on the three ppy ligands, while the LUMO consists of typical π-type orbitals equally distributed across the three ligands. This demonstrates that all calculated FMOs from five different DFT functionals belong to C 3 symmetry. Compared with the vertical IP values in Fig. 2 , we can readily observe that the range-separated ω B97X and CAM-B3LYP functionals underestimate the energy of the HOMO, while the PBE0 and B3LYP functionals significantly overestimate it. The HOMO energy from ω *B97X is very close to the vertical IP values. In terms of the vertical EA values, the range-separated ω B97X functional overestimates the LUMO energy, while PBE0 and B3LYP notably underestimate it. The LUMO energy from the ω *B97X functional is very close to the vertical EA values. Regarding the band gap between HOMO and LUMO, ω B97X overestimates the gap, while PBE0 and B3LYP notably underestimate it. The CAM-B3LYP and ω *B97X provide similar band gaps that align well with the energy difference between IP and EA . In short summary, the tuned range-separated ω *B97X functional satisfies with Koopman's Theorem, indicating that the energies of the HOMO and LUMO are consistent with the vertical IP and EA values. 3.3 Effects of DFT functionals on 1/3 MLCT MLCT assignments All-electron scalar relativistic DKH2 Hamiltonian combined with five DFT functionals ( ω B97X, CAM-B3LYP, PBE0, B3LYP, and tuned ω *B97X) were applied to calculate the lowest excited triplet (T 1 ) and singlet (S 1 ) states. The electron-hole wavefunctions for the transition from S 1 /T 1 to the ground state (S 0 ) were analyzed using Multwfn 3.8 49 . Using fac -Ir(ppy) 3 as an example, the isosurface of electron-hole wavefunctions is shown in Fig. 3 . Figure 3 demonstrates that the electron-hole wavefunctions for the S 1 and T 1 states exhibit DFT functional-dependent characteristics. For example, the DFT functionals B3LYP and ω *B97X produce C 3 symmetric electron-hole wavefunctions, with the electron (green) and hole (blue) wavefunctions equally distributed on the three ppy ligands. The DFT functionals ω B97X and CAM-B3LYP slightly break the C 3 symmetry of the electron-hole wavefunctions, while PBE0 strongly breaks the C 3 symmetry, causing the electron (green) wavefunction to be primarily located on the first (I) ppy ligand. Regardless of the electron-hole wavefunctions from different functionals for S 1 or T 1 , the hole (blue) wavefunctions are located on the Ir atom and its surrounding ppy ligands, and the electron wavefunctions are located on the ppy ligands. The electron-hole wavefunctions for fac -Ir(ppy) 3 indicate that both S 1 and T 1 exhibit typical MLCT electron transition characteristics. The isosurfaces of electron-hole wavefunctions for other Ir complexes, shown in Figure S1 also demonstrate similar MLCT electron transition characteristics for S 1 and T 1 states. Therefore, we assign the S 1 and T 1 states as the ¹MLCT and ³MLCT states, respectively. Functional-dependent energies of 1/3 MLCT According to the energies of S 1 and T 1 obtained from various DFT functionals, we compared them with their respective observed 3 MLCT and 1 MLCT absorption peaks. The deviations (Δ E ) of the calculated values from the experimental data are shown in Fig. 4 (a for ³MLCT, b for ¹MLCT). For the same DFT functional, Δ E for ³MLCT and ¹MLCT exhibits ligand-dependent characteristics. Examining the Δ E results from the range-separated ω B97X functional, we find that for ³MLCT, Ir(ppy) 2 acac has the largest Δ E (~ 0.31 eV) and Ir(bzq) 2 acac has the smallest Δ E (~ 0.03 eV). For ¹MLCT, fac -Ir(piq) 3 has the largest Δ E (~ 1.2 eV) and fac -Ir(tpy) 3 has the smallest Δ E (~ 0.90 eV). Generally speaking, the range-separated functionals ω B97X and CAM-B3LYP overestimate the transition energies of 1/3 MLCT, while the hybrid functionals PBE0 and B3LYP underestimate them. The optimally tuned range-separated ω *B97X functional shows very good agreement with experimental ³MLCT and ¹MLCT, possibly because its frontier orbitals satisfy Koopman's Theorem. Looking closely at the Δ E of ¹MLCT, we can see that PBE0 also performs well in predicting ¹MLCT. Under the framework of TD-DFT, the transition energy of MLCT is mainly related to the energy gap of frontier orbitals and the two-electron correlation and exchange interaction. 50 According to the analysis of frontier orbital energies, it is clear why ω B97X and CAM-B3LYP overestimate the transition energies of 1/3 MLCT, while PBE0 and B3LYP underestimate them. PBE0's good performance in predicting ¹MLCT may be due to the error cancellation effect of the overestimation of two-electron interactions and the underestimation of the energy gap. The poor two-electron interaction behavior of the PBE0 functional is evident from the previous analysis of the electron-hole wavefunction, where the electron-hole wavefunction of ¹MLCT for the C 3 symmetric fac -Ir(ppy) 3 notably breaks the C 3 symmetry. Considering the transition energies of ¹/³MLCT and the symmetry of the electron-hole wavefunction, we conclude that the tuned range-separated ω B97X functional performs the best in evaluating the ¹/³MLCT states of Ir(III) complexes. Therefore, for the following study of absorption spectra, we focus on the tuned range-separated ω B97X functional. 3.4 Evaluation of Higher-Energy Absorption Peaks Using the ω *B97X Functional We have demonstrated that the ω B97X functional can accurately identify the ¹MLCT and ³MLCT energies in the absorption spectra of Ir(III) complexes. Next, we explore whether the ω B97X functional can accurately identify absorption peaks at higher energy levels in the absorption spectra, beyond the MLCT states. To assess this, we calculated the wavelengths of significant oscillator strengths using the ω *B97X functional and compared them with experimentally observed wavelengths of high absorbance peaks. Table 2 presents these comparisons and includes the mean absolute deviation (MAD) between the calculated and experimental data for each complex. From Table 2 , it is evident that the ω B97X functional not only accurately predicts the MLCT state wavelengths but also effectively models absorption peaks at higher energy levels. For instance, the maximum MAD observed is 10.7 nm for Ir(bzq) 2 acac, while the minimum MAD is 2.0 nm for mer -Ir(ppy) 3 . These small average discrepancies demonstrate the precision of the ω B97X functional in simulating high-energy absorption peaks. The ability of the ω *B97X functional to accurately predict these higher-energy absorption peaks is significant for several reasons. First, it underscores the functional's robustness and reliability across a broader spectrum of electronic transitions, not just those limited to MLCT states. This broader applicability enhances the utility of the ω *B97X functional in computational chemistry, making it a valuable tool for predicting electronic properties in a wide range of complexes. Additionally, accurate simulation of high-energy absorption peaks aids in the experimental synthesis of new Ir(III) phosphorescent complexes. By providing precise theoretical predictions, researchers can better design and synthesize complexes with desired photophysical properties, potentially leading to the development of more efficient and tunable phosphorescent materials. In summary, our study shows that the ω *B97X functional not only excels in predicting ¹MLCT and ³MLCT energies but also accurately identifies higher-energy absorption peaks. This capability enhances its value as a predictive tool in computational chemistry, aiding in the design and synthesis of new Ir(III) phosphorescent complexes with optimized photophysical properties. Table 2 Wavelengths corresponding to the large absorption intensities of the Ir(III) complexes obtained from experiments and ω *B97X functional calculations, along with the Mean Absolute Deviation (MAD) in eV between the calculated and experimental values. λ abs /nm 3 MLCT 1 MLCT Higher MLCT MAD fac -Ir(ppy) 3 exp. 29 488 455 405 377 341 283 cal. 484 460 403 368 343 288 4.5 mer -Ir(ppy) 3 exp. 29 488 457 410 382 339 cal. 486 458 410 383 333 2.0 fac -Ir(piq) 3 exp. 30 600 550 483 430 354 333 cal. 611 560 482 444 344 332 7.8 fac -Ir(tpy) 3 exp. 29 485 450 410 374 347 cal. 484 459 403 366 344 5.6 mer -Ir(tpy) 3 exp. 29 485 451 420 383 336 cal. 487 459 416 384 336 3.0 fac -Ir(46dfppy) 3 exp. 29 456 428 388 353 312 cal. 460 424 378 340 304 7.8 Ir(bzq) 2 acac exp. 33 500 470 360 cal. 511 483 368 10.7 Ir(ppy) 2 acac exp. 33 497 460 412 345 cal. 498 464 410 338 3.5 3.5 Relativistic Effects of Ir Complexes In addition to the choice of functionals, the relativistic effects of Ir(III) complexes, including SOC and scalar relativistic effects, significantly impact the absorption spectra. Spin-Orbit Coupling (SOC) Effects Figure 5 shows the absorption spectra of fac -Ir(ppy) 3 calculated using the ω *B97X functional coupled with DKH2 Hamiltonian. The red curve represents the absorption spectra with SOC, while the blue curve represents the spectra without SOC. As we know, SOC becomes more pronounced with increasing atomic number. For Ir(III) complexes, SOC strongly influences the splitting and mixing of electronic states. This is particularly relevant for MLCT transitions, where SOC can mix singlet and triplet states, affecting the absorption and emission spectra. Ignoring the SOC effect prevents the mixture of triplet and singlet states, making the ³MLCT transition from S 0 to T 1 forbidden according to spin symmetry. Therefore, we can observe that the ³MLCT absorption peak at the low energy level of the absorption spectra disappears when the SOC effect is not considered, leaving only the ¹MLCT absorption peak. The red shift ~ 0.21eV of 1 MLCT for the calculation including SOC is due to strong SOC affecting on the energy levels in fac -Ir(ppy) 3 molecule. The similar situations are happened on other Ir(III) complexes shown as in Figure S2. Scalar Relativistic Effects Relativistic effects shift the energy levels of orbitals, which can alter the electronic structure of the molecules. For Ir atom, the relativistic stabilization of the 6s orbital and the destabilization of the 5d orbitals are significant, which results in decreasing energies of inner molecular orbitals and increasing the energies of occupied valance orbitals in Ir complexes. 51 The scalar relativistic effects can usually be considered by effective core potential (ECP) and all-electron relativistic approaches. To demonstrate this effect, we respectively calculate the absorption spectra of Ir complexes with all-electron DKH2 and without DKH2 Hamiltonian. As a contrast, Def2-TZVP ECP basis set also is applied to calculate the fronter molecular orbitals of Ir(III) complexes. Figure 6 shows the absorption spectra and HOMO-LUMO orbitals with and without the DKH2 Hamiltonian for fac -Ir(ppy) 3 , as well as the fronter orbitals using ECP method. The black curve represents spectra without the DKH2 Hamiltonian correction, and the red curve represents spectra with the DKH2 Hamiltonian correction, both accounting for SOC effects. From the absorption spectra in Fig. 6 (a), we observe that the high-energy level absorption peaks are similar with and without scalar relativistic effect, but the absorption intensities differ. However, for the lower-energy MLCT states, the spectrum without the DKH2 Hamiltonian correction is notably blue-shifted, affecting the accuracy of the absorption spectra. The similar situations are happened on other Ir(III) complexes shown as in Figure S3. Figure 6 (b) shows that the energy levels of HOMO are similar with each other when the relativistic effect is considering by DKH2 Hamiltonian or ECP, while the HOMO energy without DKH2 indeed is significantly lower around 0.24eV. The smaller HOMO-LUMO energy gap for DKH2 method results in the red-shift MLCT energy transition compared with all-electron non-relativistic DFT calculation. In summary, both SOC and scalar relativistic effects are crucial for accurately modeling the electronic structure and absorption spectra of Ir(III) complexes. Ignoring these effects can lead to significant deviations from experimental results, underscoring the importance of including relativistic corrections in computational studies of transition metal complexes. 4.Conclusions In this study, we systematically evaluated the electronic structures and photophysical properties of eight Ir(III) complexes using a variety of DFT functionals, with a particular focus on the tuned range-separated ω *B97X functional. Our primary objectives were to assess the accuracy of these functionals in predicting the lowest excited singlet (¹MLCT) and triplet (³MLCT) states, as well as to explore the effects of relativistic corrections and spin-orbit coupling (SOC) on these electronic transitions. The optimized ground-state geometries obtained using different DFT functionals (PBE0, B3LYP, ω B97X and CAM-B3LYP) showed good agreement with experimental X-ray crystallography data, with minor variations confirming the reliability of these methods for modeling such complexes. Our analysis of the electron-hole wavefunctions for the S 1 and T 1 states reaffirmed the metal-to-ligand charge transfer (MLCT) nature of these transitions. The results demonstrated that the ω *B97X functional, due to its optimal tuning, provided the most accurate predictions for both ¹MLCT and ³MLCT states. This was further supported by the comparison of calculated absorption spectra with experimental data, where the ω *B97X functional not only accurately identified the MLCT states but also effectively modeled higher-energy absorption peaks. The inclusion of relativistic effects, specifically scalar relativistic Douglas-Kroll-Hess (DKH2) Hamiltonian and SOC, proved essential in aligning computational simulations with experimental observations. The results underscored the significance of these effects in accurately describing the electronic transitions in Ir(III) complexes, given the substantial relativistic effects inherent to heavy transition metals like iridium. In conclusion, the ω *B97X functional, coupled with appropriate relativistic corrections, emerged as a robust and reliable computational approach for studying the photophysical properties of Ir(III) complexes. This study highlights the importance of carefully selecting and tuning DFT functionals to achieve accurate predictions of electronic transitions in phosphorescent materials. The insights gained here not only advance our understanding of Ir(III) complexes but also pave the way for the design and synthesis of new phosphorescent materials with optimized properties for various applications in display technologies, medical devices, and chemical sensors. Declarations Associated Content Supporting information These materials are available free of charge via the Internet. Isosurfaces of electron-hole wave functions for the Ir(III) complexes calculated using different DFT functionals, where green represents electron density and blue represents hole density are shown in Figure S1. The effect of spin-orbital coupling (SOC) on absorption spectrum Ir(III) complexes are shown in Figure S2. The impact of scalar relativistic effects on the absorption spectra of Ir(III) complexes are shown in Figure S3. Author Information Corresponding Author *E-mail: [email protected] Acknowledges SW Yin thanks National Science Foundation of China (Grant No. 22273054) for the financial supporting. Author Contribution Xinqin Ren did ORCA calculations and prepared the all the figures and Shiwei Yin wrote the manuscript text. All authors reviewed the manuscript. References Kang, K.; Byeon, I.; Kim, Y. G.; Choi, J.-r.; Kim, D., Nanostructures in Organic Light-Emitting Diodes: Principles and Recent Advances in the Light Extraction Strategy. Laser & Photonics Reviews 2024, 2400547. Hong, G.; Gan, X.; Leonhardt, C.; Zhang, Z.; Seibert, J.; Busch, J. M.; Bräse, S., A Brief History of OLEDs—Emitter Development and Industry Milestones. Adv. Mater. (Weinheim, Fed. Repub. Ger.) 2021, 33 (9), 2005630. Miyamoto, K.-i.; Kaneko, K.; Matsuo, A.; Wagner, T.; Kanoh, S. i.; Schöning, M. J.; Yoshinobu, T., Miniaturized chemical imaging sensor system using an OLED display panel. 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Tsuboyama, A.; Iwawaki, H.; Furugori, M.; Mukaide, T.; Kamatani, J.; Igawa, S.; Moriyama, T.; Miura, S.; Takiguchi, T.; Okada, S.; Hoshino, M.; Ueno, K., Homoleptic Cyclometalated Iridium Complexes with Highly Efficient Red Phosphorescence and Application to Organic Light-Emitting Diode. Journal of the American Chemical Society 2003, 125 (42), 12971–12979. Li, J.; Djurovich, P. I.; Alleyne, B. D.; Yousufuddin, M.; Ho, N. N.; Thomas, J. C.; Peters, J. C.; Bau, R.; Thompson, M. E., Synthetic Control of Excited-State Properties in Cyclometalated Ir(III) Complexes Using Ancillary Ligands. Inorganic Chemistry 2005, 44 (6), 1713–1727. Chen, Z.-q.; Bian, Z.-q.; Huang, C.-h., Functional IrIII Complexes and Their Applications. 2010, 22 (13), 1534–1539. Lamansky, S.; Djurovich, P.; Murphy, D.; Abdel-Razzaq, F.; Lee, H.-E.; Adachi, C.; Burrows, P. E.; Forrest, S. R.; Thompson, M. E., Highly Phosphorescent Bis-Cyclometalated Iridium Complexes: Synthesis, Photophysical Characterization, and Use in Organic Light Emitting Diodes. Journal of the American Chemical Society 2001, 123 (18), 4304–4312. Hong, G.; Dolg, M.; Li, L., A comparison of scalar-relativistic ZORA and DKH density functional schemes: monohydrides, monooxides and monofluorides of La, Lu, Ac and Lr. Chemical Physics Letters 2001, 334 (4), 396–402. Baer, R.; Livshits, E.; Salzner, U., Tuned Range-Separated Hybrids in Density Functional Theory. Annu. Rev. Phys. Chem. 2010, 61 (Volume 61, 2010), 85–109. Kronik, L.; Stein, T.; Refaely-Abramson, S.; Baer, R., Excitation Gaps of Finite-Sized Systems from Optimally Tuned Range-Separated Hybrid Functionals. J. Chem. Theory Comput. 2012, 8 , 1515–1531. Sun, H.; Zhong, C.; Brédas, J.-L., Reliable Prediction with Tuned Range-Separated Functionals of the Singlet–Triplet Gap in Organic Emitters for Thermally Activated Delayed Fluorescence. J. Chem. Theory Comput. 2015, 11 (8), 3851–3858. Zhang, C.-R.; Sears, J. S.; Yang, B.; Aziz, S. G.; Coropceanu, V.; Brédas, J.-L., Theoretical Study of the Local and Charge-Transfer Excitations in Model Complexes of Pentacene.C60 Using Tuned Range-Separated Hybrid Functionals. J. Chem. Theory Comput. 2014, 10 , 2379–2388. Adamo, C.; Barone, V., Toward reliable density functional methods without adjustable parameters: The PBE0 model. The Journal of Chemical Physics 1999, 110 (13), 6158–6170. Becke, A. D., Density-functional thermochemistry. III. The role of exact exchange. The Journal of Chemical Physics 1993, 98 (7), 5648–5652. Chai, J.-D.; Head-Gordon, M., Systematic optimization of long-range corrected hybrid density functionals. The Journal of Chemical Physics 2008, 128 (8). Yanai, T.; Tew, D. P.; Handy, N. C., A new hybrid exchange–correlation functional using the Coulomb-attenuating method (CAM-B3LYP). Chemical Physics Letters 2004, 393 (1), 51–57. Dunning, T. H.; Hay, P. J., Gaussian Basis Sets for Molecular Calculations. In Methods of Electronic Structure Theory , Schaefer, H. F., Ed. Springer US: Boston, MA, 1977; pp 1–27. M. J. Frisch, G. W. T., H. B. Schlegel, G. E. Scuseria, M. A. Robb, J. R. Cheeseman, G. Scalmani, V. Barone, G. A. Petersson, H. Nakatsuji, X. Li, M. Caricato, A. V. Marenich, J. Bloino, B. G. Janesko, R. Gomperts, B. Mennucci, H. P. Hratchian, J. V. Ortiz, A. F. Izmaylov, J. L. Sonnenberg, D. Williams-Young, F. Ding, F. Lipparini, F. Egidi, J. Goings, B. Peng, A. Petrone, T. Henderson, D. Ranasinghe, V. G. Zakrzewski, J. Gao, N. Rega, G. Zheng, W. Liang, M. Hada, M. Ehara, K. Toyota, R. Fukuda, J. Hasegawa, M. Ishida, T. Nakajima, Y. Honda, O. Kitao, H. Nakai, T. Vreven, K. Throssell, J. A. Montgomery, Jr., J. E. Peralta, F. Ogliaro, M. J. Bearpark, J. J. Heyd, E. N. Brothers, K. N. Kudin, V. N. Staroverov, T. A. Keith, R. Kobayashi, J. Normand, K. Raghavachari, A. P. Rendell, J. C. Burant, S. S. Iyengar, J. Tomasi, M. Cossi, J. M. Millam, M. Klene, C. Adamo, R. Cammi, J. W. Ochterski, R. L. Martin, K. Morokuma, O. Farkas, J. B. Foresman, and D. J. Fox Gaussian 16, Revision B.01 , Gaussian, Inc., Wallingford CT: 2016. de Souza, B.; Farias, G.; Neese, F.; Izsák, R., Predicting Phosphorescence Rates of Light Organic Molecules Using Time-Dependent Density Functional Theory and the Path Integral Approach to Dynamics. J. Chem. Theory Comput. 2019, 15 (3), 1896–1904. Lu, T. optDFTw program v1.0. http://sobereva.com/346 . Neese, F.; Wennmohs, F.; Becker, U.; Riplinger, C., The ORCA quantum chemistry program package. J. Chem. Phys. 2020, 152 (22), 224108. Berger, R. J. F.; Stammler, H.-G.; Neumann, B.; Mitzel, N. W., fac-Ir(ppy)3: Structures in the Gas-Phase and of a New Solid Modification. European Journal of Inorganic Chemistry 2010, 2010 (11), 1613–1617. Lu, T.; Chen, F., Multiwfn: A multifunctional wavefunction analyzer. J. Comput. Chem. 2011, 33 (5), 580–592. Dreuw, A.; Head-Gordon, M., Single-Reference ab Initio Methods for the Calculation of Excited States of Large Molecules. Chem. Rev. 2005, 105 , 4009–4037. Powell, B. J., Theories of phosphorescence in organo-transition metal complexes – From relativistic effects to simple models and design principles for organic light-emitting diodes. Coord. Chem. Rev. 2015, 295 , 46–79. Additional Declarations No competing interests reported. Supplementary Files SI.docx Onlinefloatimage7.png TOC Cite Share Download PDF Status: Published Journal Publication published 12 Dec, 2024 Read the published version in Theoretical Chemistry Accounts → Version 1 posted Editorial decision: Revision requested 22 Oct, 2024 Reviews received at journal 17 Oct, 2024 Reviewers agreed at journal 27 Sep, 2024 Reviewers agreed at journal 13 Sep, 2024 Reviewers invited by journal 13 Sep, 2024 Editor assigned by journal 27 Aug, 2024 Submission checks completed at journal 27 Aug, 2024 First submitted to journal 27 Aug, 2024 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-4984416","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":359800372,"identity":"f9016b45-f2e6-4099-834b-cd7737398918","order_by":0,"name":"Ren Xinqi","email":"","orcid":"","institution":"Shaanxi Normal University","correspondingAuthor":false,"prefix":"","firstName":"Ren","middleName":"","lastName":"Xinqi","suffix":""},{"id":359800375,"identity":"b764fe8b-91de-4a67-b8c4-cad3a3b226c3","order_by":1,"name":"Shiwei Yin","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAwklEQVRIiWNgGAWjYDACZjBpA+WxEa8ljRQtEHCYBC0Gx3kPMP5sO29vLt1jwPCh7DAD/+wGAloO8yUw87bdTtw554wB44xzhxkk7hwgpIXHgJlx2+0Egxs5BkC9hxkMJBIIa2H8ue2cPVjLX2K1MPBuO8C4AaSFkRgtkiCH8f5LTtxwI63gYM+5dB6JGwS08J0H+vrHGTugw5I3PvhRZi3HP4OAFoUDDOw/YJwDQMyDXz0QyDcQVDIKRsEoGAUjHgAAYWo//oVPp/gAAAAASUVORK5CYII=","orcid":"","institution":"Shaanxi Normal University","correspondingAuthor":true,"prefix":"","firstName":"Shiwei","middleName":"","lastName":"Yin","suffix":""}],"badges":[],"createdAt":"2024-08-27 12:14:22","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-4984416/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-4984416/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1007/s00214-024-03169-y","type":"published","date":"2024-12-12T15:57:36+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":65714808,"identity":"59433079-cec9-489a-a155-c9c198ac5038","added_by":"auto","created_at":"2024-10-01 15:26:16","extension":"jpeg","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":488375,"visible":true,"origin":"","legend":"\u003cp\u003eThe structural diagram of the studied Ir(III) complexes with Ir atoms in brown, C atoms in gray, and N atoms in blue. Hydrogen atoms are hidden for clarity, and specific atomic numbers are labeled in the figure.\u003c/p\u003e","description":"","filename":"floatimage1.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-4984416/v1/4f7d299607a0b0500794421b.jpeg"},{"id":65713437,"identity":"cd056fcd-eba0-4581-a27c-e62cbce336b5","added_by":"auto","created_at":"2024-10-01 15:18:15","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":67424,"visible":true,"origin":"","legend":"\u003cp\u003eIsosurfaces of frontier molecular orbital wavefunctions of \u003cem\u003efac\u003c/em\u003e-Ir(ppy)\u003csub\u003e3\u003c/sub\u003e calculated using different DFT functionals. The red dashed lines correspond to the vertical \u003cem\u003eIP\u003c/em\u003e and \u003cem\u003eEA\u003c/em\u003e energies calculated with the tuned \u003cem\u003eω\u003c/em\u003e*B97X functional. Red and blue represent positive and negative phases of the orbital wave function, respectively.\u003c/p\u003e","description":"","filename":"Onlinefloatimage2.png","url":"https://assets-eu.researchsquare.com/files/rs-4984416/v1/fe0d44f049eb8204a510d84f.png"},{"id":65713442,"identity":"ff4bb3b5-f84f-4e2d-b316-126b324f669a","added_by":"auto","created_at":"2024-10-01 15:18:16","extension":"jpeg","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":699714,"visible":true,"origin":"","legend":"\u003cp\u003eIsosurfaces of electron-hole wave functions for the \u003cem\u003efac\u003c/em\u003e-Ir(ppy)\u003csub\u003e3\u003c/sub\u003e complex calculated using different DFT functionals, where green represents electron density and blue represents hole density. The first and second rows respectively represent electron transitions from the ground state to the T\u003csub\u003e1\u003c/sub\u003e (first) and S\u003csub\u003e1\u003c/sub\u003e (second) states.\u003c/p\u003e","description":"","filename":"floatimage3.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-4984416/v1/e442d1c163246c4a912e7468.jpeg"},{"id":65713440,"identity":"4f50235b-6f02-4bc5-8299-ffd6f3ede9d9","added_by":"auto","created_at":"2024-10-01 15:18:15","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":21712,"visible":true,"origin":"","legend":"\u003cp\u003eDFT functional-dependent deviations(Δ\u003cem\u003eE\u003c/em\u003e) of experimental and calculated transition energies of MLCT states. (a) The deviations of \u003csup\u003e3\u003c/sup\u003eMLCT, eight symbols represent eight studied Ir(III) complexes; (b) The deviations of \u003csup\u003e1\u003c/sup\u003eMLCT, eight symbols represent molecule-specific optimally tuned \u003cem\u003eω\u003c/em\u003e* values (in Bohr\u003csup\u003e-1\u003c/sup\u003e).\u003c/p\u003e","description":"","filename":"Onlinefloatimage4.png","url":"https://assets-eu.researchsquare.com/files/rs-4984416/v1/0792ee2996b31a58146a521b.png"},{"id":65713438,"identity":"559895c9-67b5-4064-964d-31d44236e036","added_by":"auto","created_at":"2024-10-01 15:18:15","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":22848,"visible":true,"origin":"","legend":"\u003cp\u003eThe effect of spin-orbital coupling (SOC) on absorption spectrum of \u003cem\u003efac\u003c/em\u003e-Ir(ppy)\u003csub\u003e3\u003c/sub\u003e. The red and blue curves represent the absorption spectra obtained with and without SOC effect, respectively. The red and blue bars represent the oscillator strengths of excited states obtained with and without SOC, respectively. The number in parentheses means the transition energy in eV unit.\u003c/p\u003e","description":"","filename":"Onlinefloatimage5.png","url":"https://assets-eu.researchsquare.com/files/rs-4984416/v1/ad822a738bf3c7c234783b7f.png"},{"id":65713443,"identity":"0252ae29-76e6-4f70-9661-9dd374e2c8f3","added_by":"auto","created_at":"2024-10-01 15:18:16","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":47959,"visible":true,"origin":"","legend":"\u003cp\u003e(a) The impact of scalar relativistic effects on the absorption spectra of \u003cem\u003efac\u003c/em\u003e-Ir(ppy)\u003csub\u003e3\u003c/sub\u003e. The red curve represents the absorption spectrum calculated using the DKH2 Hamiltonian, while the black curve represents the spectrum without DKH2 corrections. The red and black bars indicate the oscillator strengths corresponding to the spectra obtained with and without DKH2, respectively. (b) Comparison of frontier molecular orbitals calculated with and without the DKH2 Hamiltonian and using Def2-TZVP pseudopotentials. The number in parentheses means the transition energy in eV unit.\u003c/p\u003e","description":"","filename":"Onlinefloatimage6.png","url":"https://assets-eu.researchsquare.com/files/rs-4984416/v1/54a6c730e1e8abdaa7c1f7ff.png"},{"id":71552454,"identity":"2d652839-0e79-4d52-b176-11d1e612b032","added_by":"auto","created_at":"2024-12-16 16:06:18","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2192200,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4984416/v1/f6800f13-7634-4171-8d11-80d841f96b7f.pdf"},{"id":65713441,"identity":"2911a8a4-19cc-442a-b70f-a7c72e77ff73","added_by":"auto","created_at":"2024-10-01 15:18:16","extension":"docx","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":2751608,"visible":true,"origin":"","legend":"","description":"","filename":"SI.docx","url":"https://assets-eu.researchsquare.com/files/rs-4984416/v1/3dbd7a3a9e8687ba44e4c2c2.docx"},{"id":65713436,"identity":"a34d24dd-b1ab-48e3-b1b5-97f930b25838","added_by":"auto","created_at":"2024-10-01 15:18:15","extension":"png","order_by":2,"title":"","display":"","copyAsset":false,"role":"supplement","size":69428,"visible":true,"origin":"","legend":"\u003cp\u003eTOC\u003c/p\u003e","description":"","filename":"Onlinefloatimage7.png","url":"https://assets-eu.researchsquare.com/files/rs-4984416/v1/74362b0e3498c5a14671fc9d.png"}],"financialInterests":"No competing interests reported.","formattedTitle":"Exploring the Photophysical Properties of Iridium (III) Complexes Using TD-DFT: A Comprehensive Study","fulltext":[{"header":"1.Introduction","content":"\u003cp\u003eOrganic light emitting diodes (OLEDs) are widely used in screen displays\u003csup\u003e\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u003c/sup\u003e, medical devices\u003csup\u003e\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e\u003c/sup\u003e, chemical sensors\u003csup\u003e\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e\u003c/sup\u003e, and other fields due to their advantages such as low power consumption\u003csup\u003e\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e\u003c/sup\u003e, fast response speed\u003csup\u003e\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e\u003c/sup\u003e, and high-resolution capability\u003csup\u003e\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e\u003c/sup\u003e. Among them, phosphorescent emitters have attracted wide attention because heavy-atom leads to the SOC between triplet (T) and singlet (S) states, which effectively promotes the non-radiative inter-system crossover from the first singlet excited state (S\u003csub\u003e1\u003c/sub\u003e) to the lowest triplet state (T\u003csub\u003e1\u003c/sub\u003e) and enhances the radiative transition from T\u003csub\u003e1\u003c/sub\u003e to the ground state (S\u003csub\u003e0\u003c/sub\u003e). Thus, the internal quantum efficiency of 100% is readily achieved in phosphorescent OLEDs\u003csup\u003e\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e\u003c/sup\u003e. These phosphorescent emitters are mainly composed of heavy metal elements such as Iridium (Ir)\u003csup\u003e\u003cspan additionalcitationids=\"CR9\" citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e\u003c/sup\u003e, Platinum (Pt)\u003csup\u003e\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e\u003c/sup\u003e, and Osmium (Os)\u003csup\u003e\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e\u003c/sup\u003e. Among them, cyclometalated Ir(III) complexes are of particular interest due to their relatively short triplet state lifetimes and tunable emission wavelengths\u003csup\u003e\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eThe superior photophysical properties of these complexes are governed by their electronic transitions, especially metal-to-ligand charge transfer (MLCT) transitions.\u003csup\u003e\u003cspan additionalcitationids=\"CR15\" citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e\u003c/sup\u003e MLCT transitions involve the electron transfer from a metal center to a ligand. In iridium complexes, these transitions are significant due to the strong SOC inherent to heavy transition metals like Ir(III). This SOC facilitates intersystem crossing between singlet and triplet states, making the characterization of both \u0026sup1;MLCT and \u0026sup3;MLCT states critical. The singlet MLCT (\u0026sup1;MLCT) involves an electronic transition where the spin multiplicity remains unchanged (singlet to singlet), while the triplet MLCT (\u0026sup3;MLCT) involves a transition to a triplet state, where the spin multiplicity changes. Thus, accurate assignment and understanding of these MLCT transitions, encompassing both singlet (\u0026sup1;MLCT) and triplet (\u0026sup3;MLCT) states, are essential for optimizing the performance and tailoring the properties of these materials.\u003c/p\u003e \u003cp\u003eQuantum mechanical (QM) methods, particularly time-dependent density functional theory (TDDFT), are indispensable for investigating the electronic structures and excited states of transition metal complexes. TDDFT extends the capabilities of ground-state DFT to excited states, enabling detailed studies of electronic transitions. However, conventional DFT functionals often inadequately describe CT electron transitions due to limitations in handling long-range electron-electron interactions\u003csup\u003e\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e\u003c/sup\u003e and self-interaction errors\u003csup\u003e\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e\u003c/sup\u003e. These inaccuracies are especially pronounced in systems with significant charge-transfer character, such as MLCT states in transition metal complexes. To end this, the tuned range-separated functionals are proposed to deal with the excited states with CT characters.\u003csup\u003e\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e\u003c/sup\u003e\u003c/p\u003e \u003cp\u003eFurthermore, Ir is a heavy transition metal and elements in this part of the periodic table exhibit significant relativistic effect. The relativistic effect results in strong SOC and the notable splitting and mixing of singlet and triplet electronic states, making the electronic transitions from \u0026sup3;MLCT to S\u003csub\u003e0\u003c/sub\u003e possible. Experimental absorption spectra of Ir(III) complexes inherently include relativistic effects. To ensure that computational simulations accurately reflect experimental data, these effects must be included in the models. This alignment is crucial for validating computational methods and for the reliable interpretation of experimental results. In recent years, an increasing number of researchers have employed theoretical calculations to systemically consider the ligand effects on the optical properties such as absorption spectra, emission spectra and quantum yields of Ir(III) complexes.\u003csup\u003e\u003cspan additionalcitationids=\"CR22\" citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e\u003c/sup\u003e However, the selection of DFT functionals and the impact of relativistic effects on MLCT electronic transitions are seldom studied for transition metal complexes.\u003csup\u003e\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e\u003c/sup\u003e\u003c/p\u003e \u003cp\u003eExperimental absorption is primarily related to the geometric structures under the ground state (S\u003csub\u003e0\u003c/sub\u003e), and does not involve the more complex relaxation processes that occur in the excited states. And experimental absorption data, particularly for \u0026sup3;MLCT and \u0026sup1;MLCT states, serve as excellent benchmark data for evaluating different computational approaches. This benchmarking helps identify the most suitable computational techniques for studying Ir(III) complexes and designing the new complexes with optimized performance. In this study, we firstly selected eight Ir(III) complexes including \u003cem\u003efacial\u003c/em\u003e (\u003cem\u003efac\u003c/em\u003e) and \u003cem\u003emeridional\u003c/em\u003e (\u003cem\u003emer\u003c/em\u003e) Ir(C^N)\u003csub\u003e3\u003c/sub\u003e-type\u003csup\u003e\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e\u003c/sup\u003e complexes: \u003cem\u003efac\u003c/em\u003e-Ir(ppy)\u003csub\u003e3\u003c/sub\u003e\u003csup\u003e28\u0026ndash;29\u003c/sup\u003e, \u003cem\u003emer\u003c/em\u003e-Ir(ppy)\u003csub\u003e3\u003c/sub\u003e\u003csup\u003e29\u003c/sup\u003e, \u003cem\u003efac\u003c/em\u003e-Ir(tpy)\u003csub\u003e3\u003c/sub\u003e\u003csup\u003e29\u003c/sup\u003e, \u003cem\u003emer\u003c/em\u003e-Ir(tpy)\u003csub\u003e3\u003c/sub\u003e\u003csup\u003e29\u003c/sup\u003e, \u003cem\u003efac\u003c/em\u003e-Ir(piq)\u003csub\u003e3\u003c/sub\u003e\u003csup\u003e30\u003c/sup\u003e, \u003cem\u003emer\u003c/em\u003e-Ir(piq)\u003csub\u003e3\u003c/sub\u003e\u003csup\u003e29\u003c/sup\u003e and Ir(C^N)\u003csub\u003e2\u003c/sub\u003eLX-type complexes\u003csup\u003e\u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e\u003c/sup\u003e: Ir(ppy)\u003csub\u003e2\u003c/sub\u003eacac\u003csup\u003e\u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e\u003c/sup\u003e and Ir(tpy)\u003csub\u003e2\u003c/sub\u003eacac\u003csup\u003e\u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e\u003c/sup\u003e as a mini-benchmarking dataset whose absorption data for MLCT states can be found in literatures. The detailed structures of these eight Ir(III) complexes are showed in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eIn this paper, the tuned optimal range-separated \u003cem\u003eω\u003c/em\u003e*B97X functional in combination with the full-electron scalar relativistic Douglas-Kroll-Hess (DKH2) Hamiltonian of 2nd order\u003csup\u003e\u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e\u003c/sup\u003e is applied to calculate the electronic structure and MLCT excited states of these molecules in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e. As a comparison, some widely used DFT functionals including hybrid GGA such as PBE0 and B3LYP and range-separated hybrid GGA functionals such as \u003cem\u003eω\u003c/em\u003eB97X and CAM-B3LYP in combination with DKH2 also are applied to calculate the absorption spectra of these Ir(III) complexes. In addition, the effects of relativistic Hamiltonian and SOC on MLCT states are discussed in results section.\u003c/p\u003e"},{"header":"2.Theory and computational details","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003e2.1 Optimally Tuned Range-Separated Functionals\u003c/h2\u003e \u003cp\u003eTo accurately describe charge transfer (CT) states, optimally tuned range-separated functionals are employed. Conventional functionals often underestimate the energies of excited states, but range-separated functionals address these issues by distinguishing between short-range and long-range exchange interactions, separated by the range-separation parameter \u003cem\u003eω\u003c/em\u003e.\u003c/p\u003e \u003cp\u003eThe key feature of these functionals is their ability to balance DFT and Hartree-Fock (HF) contributions. When electron-electron distance (r₁₂) is small, the short-range exchange is dominated by DFT. As r₁₂ increases, the exchange gradually shifts to HF, providing an accurate description of long-range interactions. The parameter \u003cem\u003eω\u003c/em\u003e controls this balance, enhancing the accuracy of predicting CT energies.\u003c/p\u003e \u003cp\u003eTo determine the optimal \u003cem\u003eω\u003c/em\u003e value, the ionization potential (\u003cem\u003eIP\u003c/em\u003e) tuning method is used. This method adjusts the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) energies to match the \u003cem\u003eIP\u003c/em\u003e and electron affinity (\u003cem\u003eEA\u003c/em\u003e) of the system. The optimization minimizes the following function:\u003cdiv id=\"Equ1\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ1\" name=\"EquationSource\"\u003e\n$$J\\left( \\omega \\right)=\\hbox{min} \\left\\{ {\\left| {{E_{HOMO}}(\\omega ) - IP(N)} \\right|+\\left| {{E_{LUMO}}(\\omega ) - IP(N+1)} \\right|} \\right\\}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e1\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere \u003cem\u003eE\u003c/em\u003e\u003csub\u003e\u003cem\u003eHOMO\u003c/em\u003e\u003c/sub\u003e and \u003cem\u003eE\u003c/em\u003e\u003csub\u003e\u003cem\u003eLUMO\u003c/em\u003e\u003c/sub\u003e are the energies of the HOMO and LUMO, respectively. By minimizing these functions, the optimal \u003cem\u003eω\u003c/em\u003e parameter is found, ensuring accurate predictions of electronic transitions and improving the description of CT states. Additionally, this approach eliminates spurious behavior because the exact exchange has the correct asymptotic character and cancels the self-interaction exactly.\u003csup\u003e\u003cspan additionalcitationids=\"CR36 CR37\" citationid=\"CR35\" class=\"CitationRef\"\u003e35\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e38\u003c/span\u003e\u003c/sup\u003e\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003e2.2 Computational details\u003c/h2\u003e \u003cp\u003e \u003cb\u003eGeometry optimizations\u003c/b\u003e \u003c/p\u003e \u003cp\u003eThe ground state structures of molecules in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e were separately optimized using the hybrid PBE0\u003csup\u003e39\u003c/sup\u003e, B3LYP\u003csup\u003e\u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e40\u003c/span\u003e\u003c/sup\u003e and range-separated \u003cem\u003eω\u003c/em\u003eB97X\u003csup\u003e\u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e41\u003c/span\u003e\u003c/sup\u003e, CAM-B3LYP\u003csup\u003e\u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e42\u003c/span\u003e\u003c/sup\u003e functionals. All the calculations are performed using the Stuttgart/Dresden ECP basis set (SDD)\u003csup\u003e\u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e43\u003c/span\u003e\u003c/sup\u003e for heavy-metal Ir atom and D95 basis set for all other atoms. The geometry optimizations are carried out by G16 program.\u003csup\u003e\u003cspan citationid=\"CR44\" class=\"CitationRef\"\u003e44\u003c/span\u003e\u003c/sup\u003e\u003c/p\u003e \u003cp\u003e \u003cb\u003eExcited state calculations\u003c/b\u003e \u003c/p\u003e \u003cp\u003eBased on the optimized structures, the TD-DFT method was applied to simulate the absorption spectra of Ir(III) complexes. All-electron relativistic approaches using the DKH2 Hamiltonian were employed to account for relativistic effects, with the SARC-DKH-TZVP all-electron basis set used for Ir, and the DKH-def2-TZVP(-f) basis set used for other nonmetallic atoms. To assign the \u0026sup3;MLCT states, the SOC effect was also considered during the TD-DFT calculations.\u003csup\u003e\u003cspan citationid=\"CR45\" class=\"CitationRef\"\u003e45\u003c/span\u003e\u003c/sup\u003e Standard functionals such as PBE0, B3LYP, \u003cem\u003eω\u003c/em\u003eB97X and CAM-B3LYP were separately utilized to calculate the excited electronic structures of the Ir(III) complexes. The optimally tuned range-separated functionals were based on the standard range-separated \u003cem\u003eω\u003c/em\u003eB97X functional. The molecule-specific \u003cem\u003eω\u003c/em\u003e parameters were optimized using the optDFTw program v1.0 and the ORCA interface written by Dr. Zikuan Wang.\u003csup\u003e\u003cspan citationid=\"CR46\" class=\"CitationRef\"\u003e46\u003c/span\u003e\u003c/sup\u003e We refer to this optimally tuned range-separated functionals as \u003cem\u003eω\u003c/em\u003e*B97X. All the TD-DFT calculations were performed using the ORCA 5.0 package.\u003csup\u003e\u003cspan citationid=\"CR47\" class=\"CitationRef\"\u003e47\u003c/span\u003e\u003c/sup\u003e\u003c/p\u003e \u003c/div\u003e"},{"header":"3.Results and Discussion","content":"\u003cdiv id=\"Sec6\" class=\"Section2\"\u003e \u003ch2\u003e3.1 Ground State Geometry\u003c/h2\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e shows eight phosphorescent Ir(III) complexes. The heavy-metal Ir coordinates with ligands including 2-phenylpyridine (ppy), 1-phenylisoquinolinato (piq), benzo[h]quinolinato (bzq), 2,4-pentanedione (acac), 2-(4,6-difluorophenyl) pyridinato (46dfppy), and 2-(p-tolyl) pyridinato (tpy) to form six-coordinate complexes. Four different functionals including PBE0, B3LYP, \u003cem\u003eω\u003c/em\u003eB97X, and CAM-B3LYP are utilized to optimize the ground-state geometries of eight molecules. Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e presents the structural parameters of \u003cem\u003efac\u003c/em\u003e-Ir(ppy)\u003csub\u003e3\u003c/sub\u003e, \u003cem\u003emer\u003c/em\u003e-Ir(tpy)\u003csub\u003e3\u003c/sub\u003e, and \u003cem\u003efac\u003c/em\u003e-Ir(piq)\u003csub\u003e3\u003c/sub\u003e obtained from different functionals and X-ray crystallography measurements\u003csup\u003e\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e, \u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e\u003c/sup\u003e. Figure\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e shows the structure of the selected molecule and the key atomic labels.\u003c/p\u003e \u003cp\u003eDue to the \u003cem\u003eC\u003c/em\u003e\u003csub\u003e3\u003c/sub\u003e symmetry of the \u003cem\u003efacial\u003c/em\u003e configuration including \u003cem\u003efac\u003c/em\u003e-Ir(ppy)\u003csub\u003e3\u003c/sub\u003e and \u003cem\u003efac\u003c/em\u003e-Ir(piq)\u003csub\u003e3\u003c/sub\u003e, the Ir-C and Ir-N bond lengths are identical. Thus, for the \u003cem\u003efacial\u003c/em\u003e configuration, we only analyze one Ir-C and one Ir-N bond length due to the \u003cem\u003eC\u003c/em\u003e\u003csub\u003e3\u003c/sub\u003e symmetry. In contrast, for the \u003cem\u003emeridional\u003c/em\u003e configuration with \u003cem\u003eC\u003c/em\u003e\u003csub\u003e1\u003c/sub\u003e symmetry, we analyze all three Ir-C and Ir-N bond lengths. From Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e, we can find that the maximum errors between calculated and experimental values in bond lengths and angles obtained from different functionals are as follows: \u003cem\u003eω\u003c/em\u003eB97X is 0.096 \u0026Aring; and 1.4 degrees, CAM-B3LYP is 0.123 \u0026Aring; and 1.8 degrees, PBE0 is 0.108 \u0026Aring; and 1.7 degrees, and B3LYP is 0.143 \u0026Aring; and 1.6 degrees. Compared with X-ray crystallography data\u003csup\u003e\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e, \u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e\u003c/sup\u003e, the computed bond length deviations are all below 0.15 \u0026Aring;, and the angle deviations are below 2 degrees.\u003c/p\u003e \u003cp\u003eThese indicate that the ground state structures of the complexes obtained from DFT calculations are relatively reliable, and the choice of functional has a minor impact on the results. The minor variations in bond lengths and angles across different functionals, all remaining within acceptable error margins compared to X-ray crystallography data, underscore the robustness of DFT in modeling the ground structures of these complexes.\u003c/p\u003e \u003cp\u003eGiven the high accuracy and consistency of the \u003cem\u003eω\u003c/em\u003eB97X functional, as evidenced by its minimal deviations in bond lengths and angles, it is deemed the most suitable for further studies. The \u003cem\u003eω\u003c/em\u003eB97X functional, with its optimal tuning and balance between short-range and long-range interactions, provides a nuanced and accurate description of the electronic environment in these complexes. Therefore, subsequent studies will employ the ground-state geometries optimized with \u003cem\u003eω\u003c/em\u003eB97X for further electron structure calculations, including time-dependent DFT (TD-DFT) simulations of absorption spectra.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eComparison of the calculated bond lengths (in \u0026Aring;) and bond angles (in degrees) for the molecular geometry of the Ir(III) complex optimized using different functional approaches with experimental values obtained from X-ray crystallography.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"7\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cem\u003eω\u003c/em\u003eB97X\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eCAM-B3LYP\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003ePBE0\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eB3LYP\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003eexp.\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"6\" rowspan=\"7\"\u003e \u003cp\u003e\u003cem\u003emer-\u003c/em\u003eIr(tpy)\u003csub\u003e3\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colspan=\"5\" nameend=\"c7\" namest=\"c3\"\u003e \u003cp\u003eBond Lengths (\u0026Aring;)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eIr-C1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e2.176\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e2.102\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e2.090\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e2.115\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e2.151\u003csup\u003e29\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eIr-N1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e2.080\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e2.167\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e2.152\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e2.187\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e2.044\u003csup\u003e29\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eIr-C2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e2.065\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e2.087\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e2.076\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e2.098\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e2.065\u003csup\u003e29\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eIr-N2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e2.103\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e2.073\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e2.057\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e2.084\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e2.076\u003csup\u003e29\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eIr-C3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e2.086\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e2.109\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e2.008\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e2.026\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e2.086\u003csup\u003e29\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eIr-N3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e2.106\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e2.058\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e2.042\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e2.066\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e2.010\u003csup\u003e29\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"2\" rowspan=\"3\"\u003e \u003cp\u003e\u003cem\u003efac-\u003c/em\u003eIr(ppy)\u003csub\u003e3\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colspan=\"5\" nameend=\"c7\" namest=\"c3\"\u003e \u003cp\u003eBond Lengths (\u0026Aring;)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eIr-C\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e2.031\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e2.033\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e2.022\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e2.041\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e2.033\u003csup\u003e48\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eIr-N\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e2.155\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e2.146\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e2.130\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e2.162\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e2.158\u003csup\u003e48\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"8\" rowspan=\"9\"\u003e \u003cp\u003e\u003cem\u003efac-\u003c/em\u003eIr(piq)\u003csub\u003e3\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colspan=\"5\" nameend=\"c7\" namest=\"c3\"\u003e \u003cp\u003eBond Lengths (\u0026Aring;)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eIr-N1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e2.154\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e2.145\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e2.130\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e2.161\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e2.135\u003csup\u003e30\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eIr-C2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e2.029\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e2.030\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e2.019\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e2.038\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e2.009\u003csup\u003e30\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eN1-C1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1.375\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e1.372\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1.370\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e1.376\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e1.374\u003csup\u003e30\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eN1-C3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1.350\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e1.354\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1.361\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e1.368\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e1.339\u003csup\u003e30\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colspan=\"5\" nameend=\"c7\" namest=\"c3\"\u003e \u003cp\u003eBond Angles (degree)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eN1-Ir-C2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e78.4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e78.3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e78.5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e78.2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e78.5\u003csup\u003e30\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eIr-N1-C1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e123.4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e123.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e123.1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e123.2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e124.8\u003csup\u003e30\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eIr-N1-C3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e115.3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e115.7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e115.9\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e115.7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e115.1\u003csup\u003e30\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec7\" class=\"Section2\"\u003e \u003ch2\u003e3.2 Effects of functionals on Frontier Molecular Orbitals (FMO)\u003c/h2\u003e \u003cp\u003eThe molecular orbital wavefunctions of the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) of \u003cem\u003efac\u003c/em\u003e-Ir(ppy)\u003csub\u003e3\u003c/sub\u003e calculated by DKH2 Hamiltonian in combination with the five different functionals including PBE0, B3LYP, \u003cem\u003eω\u003c/em\u003eB97X, CAM-B3LYP and optimally tuned \u003cem\u003eω*\u003c/em\u003eB97X are respectively showed in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e. From Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e, we can see that all five functionals produce wavefunctions with the same \u003cem\u003eC\u003c/em\u003e\u003csub\u003e3\u003c/sub\u003e symmetric distributions for both the HOMO and LUMO. The HOMO is a mixture of d-type orbitals on the Ir atom and π-type orbitals on the three ppy ligands, while the LUMO consists of typical π-type orbitals equally distributed across the three ligands. This demonstrates that all calculated FMOs from five different DFT functionals belong to \u003cem\u003eC\u003c/em\u003e\u003csub\u003e3\u003c/sub\u003e symmetry.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eCompared with the vertical \u003cem\u003eIP\u003c/em\u003e values in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e, we can readily observe that the range-separated \u003cem\u003eω\u003c/em\u003eB97X and CAM-B3LYP functionals underestimate the energy of the HOMO, while the PBE0 and B3LYP functionals significantly overestimate it. The HOMO energy from \u003cem\u003eω\u003c/em\u003e*B97X is very close to the vertical \u003cem\u003eIP\u003c/em\u003e values. In terms of the vertical \u003cem\u003eEA\u003c/em\u003e values, the range-separated \u003cem\u003eω\u003c/em\u003eB97X functional overestimates the LUMO energy, while PBE0 and B3LYP notably underestimate it. The LUMO energy from the \u003cem\u003eω\u003c/em\u003e*B97X functional is very close to the vertical \u003cem\u003eEA\u003c/em\u003e values. Regarding the band gap between HOMO and LUMO, \u003cem\u003eω\u003c/em\u003eB97X overestimates the gap, while PBE0 and B3LYP notably underestimate it. The CAM-B3LYP and \u003cem\u003eω\u003c/em\u003e*B97X provide similar band gaps that align well with the energy difference between \u003cem\u003eIP\u003c/em\u003e and \u003cem\u003eEA\u003c/em\u003e. In short summary, the tuned range-separated \u003cem\u003eω\u003c/em\u003e*B97X functional satisfies with Koopman's Theorem, indicating that the energies of the HOMO and LUMO are consistent with the vertical \u003cem\u003eIP\u003c/em\u003e and \u003cem\u003eEA\u003c/em\u003e values.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec8\" class=\"Section2\"\u003e \u003ch2\u003e3.3 Effects of DFT functionals on \u003csup\u003e1/3\u003c/sup\u003eMLCT\u003c/h2\u003e \u003cp\u003e \u003cb\u003eMLCT assignments\u003c/b\u003e \u003c/p\u003e \u003cp\u003eAll-electron scalar relativistic DKH2 Hamiltonian combined with five DFT functionals (\u003cem\u003eω\u003c/em\u003eB97X, CAM-B3LYP, PBE0, B3LYP, and tuned \u003cem\u003eω\u003c/em\u003e*B97X) were applied to calculate the lowest excited triplet (T\u003csub\u003e1\u003c/sub\u003e) and singlet (S\u003csub\u003e1\u003c/sub\u003e) states. The electron-hole wavefunctions for the transition from S\u003csub\u003e1\u003c/sub\u003e/T\u003csub\u003e1\u003c/sub\u003e to the ground state (S\u003csub\u003e0\u003c/sub\u003e) were analyzed using Multwfn 3.8\u003csup\u003e49\u003c/sup\u003e. Using \u003cem\u003efac\u003c/em\u003e-Ir(ppy)\u003csub\u003e3\u003c/sub\u003e as an example, the isosurface of electron-hole wavefunctions is shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e. Figure\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e demonstrates that the electron-hole wavefunctions for the S\u003csub\u003e1\u003c/sub\u003e and T\u003csub\u003e1\u003c/sub\u003e states exhibit DFT functional-dependent characteristics. For example, the DFT functionals B3LYP and \u003cem\u003eω\u003c/em\u003e*B97X produce \u003cem\u003eC\u003c/em\u003e\u003csub\u003e3\u003c/sub\u003e symmetric electron-hole wavefunctions, with the electron (green) and hole (blue) wavefunctions equally distributed on the three ppy ligands. The DFT functionals \u003cem\u003eω\u003c/em\u003eB97X and CAM-B3LYP slightly break the \u003cem\u003eC\u003c/em\u003e\u003csub\u003e3\u003c/sub\u003e symmetry of the electron-hole wavefunctions, while PBE0 strongly breaks the \u003cem\u003eC\u003c/em\u003e\u003csub\u003e3\u003c/sub\u003e symmetry, causing the electron (green) wavefunction to be primarily located on the first (I) ppy ligand.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eRegardless of the electron-hole wavefunctions from different functionals for S\u003csub\u003e1\u003c/sub\u003e or T\u003csub\u003e1\u003c/sub\u003e, the hole (blue) wavefunctions are located on the Ir atom and its surrounding ppy ligands, and the electron wavefunctions are located on the ppy ligands. The electron-hole wavefunctions for \u003cem\u003efac\u003c/em\u003e-Ir(ppy)\u003csub\u003e3\u003c/sub\u003e indicate that both S\u003csub\u003e1\u003c/sub\u003e and T\u003csub\u003e1\u003c/sub\u003e exhibit typical MLCT electron transition characteristics. The isosurfaces of electron-hole wavefunctions for other Ir complexes, shown in Figure \u003cspan refid=\"MOESM1\" class=\"InternalRef\"\u003eS1\u003c/span\u003e also demonstrate similar MLCT electron transition characteristics for S\u003csub\u003e1\u003c/sub\u003e and T\u003csub\u003e1\u003c/sub\u003e states. Therefore, we assign the S\u003csub\u003e1\u003c/sub\u003e and T\u003csub\u003e1\u003c/sub\u003e states as the \u0026sup1;MLCT and \u0026sup3;MLCT states, respectively.\u003c/p\u003e \u003cp\u003e \u003cb\u003eFunctional-dependent energies of\u003c/b\u003e \u003csup\u003e\u003cb\u003e1/3\u003c/b\u003e\u003c/sup\u003e\u003cb\u003eMLCT\u003c/b\u003e\u003c/p\u003e \u003cp\u003eAccording to the energies of S\u003csub\u003e1\u003c/sub\u003e and T\u003csub\u003e1\u003c/sub\u003e obtained from various DFT functionals, we compared them with their respective observed \u003csup\u003e\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e\u003c/sup\u003eMLCT and \u003csup\u003e\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u003c/sup\u003eMLCT absorption peaks. The deviations (Δ\u003cem\u003eE\u003c/em\u003e) of the calculated values from the experimental data are shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e (a for \u0026sup3;MLCT, b for \u0026sup1;MLCT). For the same DFT functional, Δ\u003cem\u003eE\u003c/em\u003e for \u0026sup3;MLCT and \u0026sup1;MLCT exhibits ligand-dependent characteristics.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eExamining the Δ\u003cem\u003eE\u003c/em\u003e results from the range-separated \u003cem\u003eω\u003c/em\u003eB97X functional, we find that for \u0026sup3;MLCT, Ir(ppy)\u003csub\u003e2\u003c/sub\u003eacac has the largest Δ\u003cem\u003eE\u003c/em\u003e (~\u0026thinsp;0.31 eV) and Ir(bzq)\u003csub\u003e2\u003c/sub\u003eacac has the smallest Δ\u003cem\u003eE\u003c/em\u003e (~\u0026thinsp;0.03 eV). For \u0026sup1;MLCT, \u003cem\u003efac\u003c/em\u003e-Ir(piq)\u003csub\u003e3\u003c/sub\u003e has the largest Δ\u003cem\u003eE\u003c/em\u003e (~\u0026thinsp;1.2 eV) and \u003cem\u003efac\u003c/em\u003e-Ir(tpy)\u003csub\u003e3\u003c/sub\u003e has the smallest Δ\u003cem\u003eE\u003c/em\u003e (~\u0026thinsp;0.90 eV). Generally speaking, the range-separated functionals \u003cem\u003eω\u003c/em\u003eB97X and CAM-B3LYP overestimate the transition energies of \u003csup\u003e1/3\u003c/sup\u003eMLCT, while the hybrid functionals PBE0 and B3LYP underestimate them.\u003c/p\u003e \u003cp\u003eThe optimally tuned range-separated \u003cem\u003eω\u003c/em\u003e*B97X functional shows very good agreement with experimental \u0026sup3;MLCT and \u0026sup1;MLCT, possibly because its frontier orbitals satisfy Koopman's Theorem. Looking closely at the Δ\u003cem\u003eE\u003c/em\u003e of \u0026sup1;MLCT, we can see that PBE0 also performs well in predicting \u0026sup1;MLCT. Under the framework of TD-DFT, the transition energy of MLCT is mainly related to the energy gap of frontier orbitals and the two-electron correlation and exchange interaction.\u003csup\u003e\u003cspan citationid=\"CR50\" class=\"CitationRef\"\u003e50\u003c/span\u003e\u003c/sup\u003e According to the analysis of frontier orbital energies, it is clear why \u003cem\u003eω\u003c/em\u003eB97X and CAM-B3LYP overestimate the transition energies of \u003csup\u003e1/3\u003c/sup\u003eMLCT, while PBE0 and B3LYP underestimate them.\u003c/p\u003e \u003cp\u003ePBE0's good performance in predicting \u0026sup1;MLCT may be due to the error cancellation effect of the overestimation of two-electron interactions and the underestimation of the energy gap. The poor two-electron interaction behavior of the PBE0 functional is evident from the previous analysis of the electron-hole wavefunction, where the electron-hole wavefunction of \u0026sup1;MLCT for the \u003cem\u003eC\u003c/em\u003e\u003csub\u003e3\u003c/sub\u003e symmetric \u003cem\u003efac\u003c/em\u003e-Ir(ppy)\u003csub\u003e3\u003c/sub\u003e notably breaks the \u003cem\u003eC\u003c/em\u003e\u003csub\u003e3\u003c/sub\u003e symmetry.\u003c/p\u003e \u003cp\u003eConsidering the transition energies of \u0026sup1;/\u0026sup3;MLCT and the symmetry of the electron-hole wavefunction, we conclude that the tuned range-separated \u003cem\u003eω\u003c/em\u003eB97X functional performs the best in evaluating the \u0026sup1;/\u0026sup3;MLCT states of Ir(III) complexes. Therefore, for the following study of absorption spectra, we focus on the tuned range-separated \u003cem\u003eω\u003c/em\u003eB97X functional.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec9\" class=\"Section2\"\u003e \u003ch2\u003e3.4 Evaluation of Higher-Energy Absorption Peaks Using the \u003cem\u003eω\u003c/em\u003e*B97X Functional\u003c/h2\u003e \u003cp\u003eWe have demonstrated that the \u003cem\u003eω\u003c/em\u003eB97X functional can accurately identify the \u0026sup1;MLCT and \u0026sup3;MLCT energies in the absorption spectra of Ir(III) complexes. Next, we explore whether the \u003cem\u003eω\u003c/em\u003eB97X functional can accurately identify absorption peaks at higher energy levels in the absorption spectra, beyond the MLCT states. To assess this, we calculated the wavelengths of significant oscillator strengths using the \u003cem\u003eω\u003c/em\u003e*B97X functional and compared them with experimentally observed wavelengths of high absorbance peaks. Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e presents these comparisons and includes the mean absolute deviation (MAD) between the calculated and experimental data for each complex.\u003c/p\u003e \u003cp\u003eFrom Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e, it is evident that the \u003cem\u003eω\u003c/em\u003eB97X functional not only accurately predicts the MLCT state wavelengths but also effectively models absorption peaks at higher energy levels. For instance, the maximum MAD observed is 10.7 nm for Ir(bzq)\u003csub\u003e2\u003c/sub\u003eacac, while the minimum MAD is 2.0 nm for \u003cem\u003emer\u003c/em\u003e-Ir(ppy)\u003csub\u003e3\u003c/sub\u003e. These small average discrepancies demonstrate the precision of the \u003cem\u003eω\u003c/em\u003eB97X functional in simulating high-energy absorption peaks.\u003c/p\u003e \u003cp\u003eThe ability of the \u003cem\u003eω\u003c/em\u003e*B97X functional to accurately predict these higher-energy absorption peaks is significant for several reasons. First, it underscores the functional's robustness and reliability across a broader spectrum of electronic transitions, not just those limited to MLCT states. This broader applicability enhances the utility of the \u003cem\u003eω\u003c/em\u003e*B97X functional in computational chemistry, making it a valuable tool for predicting electronic properties in a wide range of complexes.\u003c/p\u003e \u003cp\u003eAdditionally, accurate simulation of high-energy absorption peaks aids in the experimental synthesis of new Ir(III) phosphorescent complexes. By providing precise theoretical predictions, researchers can better design and synthesize complexes with desired photophysical properties, potentially leading to the development of more efficient and tunable phosphorescent materials.\u003c/p\u003e \u003cp\u003eIn summary, our study shows that the \u003cem\u003eω\u003c/em\u003e*B97X functional not only excels in predicting \u0026sup1;MLCT and \u0026sup3;MLCT energies but also accurately identifies higher-energy absorption peaks. This capability enhances its value as a predictive tool in computational chemistry, aiding in the design and synthesis of new Ir(III) phosphorescent complexes with optimized photophysical properties.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eWavelengths corresponding to the large absorption intensities of the Ir(III) complexes obtained from experiments and \u003cem\u003eω\u003c/em\u003e*B97X functional calculations, along with the Mean Absolute Deviation (MAD) in eV between the calculated and experimental values.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"9\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c9\" colnum=\"9\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colspan=\"6\" nameend=\"c8\" namest=\"c3\"\u003e \u003cp\u003e\u003cem\u003eλ\u003c/em\u003e\u003csub\u003eabs\u003c/sub\u003e /nm\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c9\"\u003e\u0026nbsp;\u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003csup\u003e3\u003c/sup\u003eMLCT\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003csup\u003e1\u003c/sup\u003eMLCT\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"4\" nameend=\"c8\" namest=\"c5\"\u003e \u003cp\u003eHigher MLCT\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003eMAD\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003e\u003cem\u003efac\u003c/em\u003e-Ir(ppy)\u003csub\u003e3\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eexp.\u003csup\u003e29\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e488\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e455\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e405\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e377\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e341\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e283\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003ecal.\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e484\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e460\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e403\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e368\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e343\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e288\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e4.5\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003e\u003cem\u003emer\u003c/em\u003e-Ir(ppy)\u003csub\u003e3\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eexp.\u003csup\u003e29\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e488\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e457\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e410\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e382\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e339\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003ecal.\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e486\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e458\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e410\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e383\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e333\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e2.0\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003e\u003cem\u003efac\u003c/em\u003e-Ir(piq)\u003csub\u003e3\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eexp.\u003csup\u003e30\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e600\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e550\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e483\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e430\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e354\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e333\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003ecal.\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e611\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e560\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e482\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e444\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e344\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e332\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e7.8\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003e\u003cem\u003efac\u003c/em\u003e-Ir(tpy)\u003csub\u003e3\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eexp.\u003csup\u003e29\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e485\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e450\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e410\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e374\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e347\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003ecal.\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e484\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e459\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e403\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e366\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e344\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e5.6\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003e\u003cem\u003emer\u003c/em\u003e-Ir(tpy)\u003csub\u003e3\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eexp.\u003csup\u003e29\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e485\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e451\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e420\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e383\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e336\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003ecal.\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e487\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e459\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e416\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e384\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e336\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e3.0\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003e\u003cem\u003efac\u003c/em\u003e-Ir(46dfppy)\u003csub\u003e3\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eexp.\u003csup\u003e29\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e456\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e428\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e388\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e353\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e312\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003ecal.\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e460\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e424\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e378\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e340\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e304\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e7.8\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eIr(bzq)\u003csub\u003e2\u003c/sub\u003eacac\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eexp.\u003csup\u003e33\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e500\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e470\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e360\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003ecal.\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e511\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e483\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e368\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e10.7\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eIr(ppy)\u003csub\u003e2\u003c/sub\u003eacac\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eexp.\u003csup\u003e33\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e497\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e460\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e412\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e345\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003ecal.\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e498\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e464\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e410\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e338\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e3.5\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec10\" class=\"Section2\"\u003e \u003ch2\u003e3.5 Relativistic Effects of Ir Complexes\u003c/h2\u003e \u003cp\u003eIn addition to the choice of functionals, the relativistic effects of Ir(III) complexes, including SOC and scalar relativistic effects, significantly impact the absorption spectra.\u003c/p\u003e \u003cp\u003e \u003cb\u003eSpin-Orbit Coupling (SOC) Effects\u003c/b\u003e \u003c/p\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e shows the absorption spectra of \u003cem\u003efac\u003c/em\u003e-Ir(ppy)\u003csub\u003e3\u003c/sub\u003e calculated using the \u003cem\u003eω\u003c/em\u003e*B97X functional coupled with DKH2 Hamiltonian. The red curve represents the absorption spectra with SOC, while the blue curve represents the spectra without SOC. As we know, SOC becomes more pronounced with increasing atomic number. For Ir(III) complexes, SOC strongly influences the splitting and mixing of electronic states. This is particularly relevant for MLCT transitions, where SOC can mix singlet and triplet states, affecting the absorption and emission spectra. Ignoring the SOC effect prevents the mixture of triplet and singlet states, making the \u0026sup3;MLCT transition from S\u003csub\u003e0\u003c/sub\u003e to T\u003csub\u003e1\u003c/sub\u003e forbidden according to spin symmetry. Therefore, we can observe that the \u0026sup3;MLCT absorption peak at the low energy level of the absorption spectra disappears when the SOC effect is not considered, leaving only the \u0026sup1;MLCT absorption peak. The red shift\u0026thinsp;~\u0026thinsp;0.21eV of \u003csup\u003e\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u003c/sup\u003eMLCT for the calculation including SOC is due to strong SOC affecting on the energy levels in \u003cem\u003efac\u003c/em\u003e-Ir(ppy)\u003csub\u003e3\u003c/sub\u003e molecule. The similar situations are happened on other Ir(III) complexes shown as in Figure S2.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003cb\u003eScalar Relativistic Effects\u003c/b\u003e \u003c/p\u003e \u003cp\u003eRelativistic effects shift the energy levels of orbitals, which can alter the electronic structure of the molecules. For Ir atom, the relativistic stabilization of the 6s orbital and the destabilization of the 5d orbitals are significant, which results in decreasing energies of inner molecular orbitals and increasing the energies of occupied valance orbitals in Ir complexes.\u003csup\u003e\u003cspan citationid=\"CR51\" class=\"CitationRef\"\u003e51\u003c/span\u003e\u003c/sup\u003e The scalar relativistic effects can usually be considered by effective core potential (ECP) and all-electron relativistic approaches. To demonstrate this effect, we respectively calculate the absorption spectra of Ir complexes with all-electron DKH2 and without DKH2 Hamiltonian. As a contrast, Def2-TZVP ECP basis set also is applied to calculate the fronter molecular orbitals of Ir(III) complexes. Figure\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e shows the absorption spectra and HOMO-LUMO orbitals with and without the DKH2 Hamiltonian for \u003cem\u003efac\u003c/em\u003e-Ir(ppy)\u003csub\u003e3\u003c/sub\u003e, as well as the fronter orbitals using ECP method. The black curve represents spectra without the DKH2 Hamiltonian correction, and the red curve represents spectra with the DKH2 Hamiltonian correction, both accounting for SOC effects.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eFrom the absorption spectra in Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e(a), we observe that the high-energy level absorption peaks are similar with and without scalar relativistic effect, but the absorption intensities differ. However, for the lower-energy MLCT states, the spectrum without the DKH2 Hamiltonian correction is notably blue-shifted, affecting the accuracy of the absorption spectra. The similar situations are happened on other Ir(III) complexes shown as in Figure S3. Figure\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e(b) shows that the energy levels of HOMO are similar with each other when the relativistic effect is considering by DKH2 Hamiltonian or ECP, while the HOMO energy without DKH2 indeed is significantly lower around 0.24eV. The smaller HOMO-LUMO energy gap for DKH2 method results in the red-shift MLCT energy transition compared with all-electron non-relativistic DFT calculation.\u003c/p\u003e \u003cp\u003eIn summary, both SOC and scalar relativistic effects are crucial for accurately modeling the electronic structure and absorption spectra of Ir(III) complexes. Ignoring these effects can lead to significant deviations from experimental results, underscoring the importance of including relativistic corrections in computational studies of transition metal complexes.\u003c/p\u003e \u003c/div\u003e"},{"header":"4.Conclusions","content":"\u003cp\u003eIn this study, we systematically evaluated the electronic structures and photophysical properties of eight Ir(III) complexes using a variety of DFT functionals, with a particular focus on the tuned range-separated \u003cem\u003eω\u003c/em\u003e*B97X functional. Our primary objectives were to assess the accuracy of these functionals in predicting the lowest excited singlet (\u0026sup1;MLCT) and triplet (\u0026sup3;MLCT) states, as well as to explore the effects of relativistic corrections and spin-orbit coupling (SOC) on these electronic transitions.\u003c/p\u003e \u003cp\u003eThe optimized ground-state geometries obtained using different DFT functionals (PBE0, B3LYP, \u003cem\u003eω\u003c/em\u003eB97X and CAM-B3LYP) showed good agreement with experimental X-ray crystallography data, with minor variations confirming the reliability of these methods for modeling such complexes.\u003c/p\u003e \u003cp\u003eOur analysis of the electron-hole wavefunctions for the S\u003csub\u003e1\u003c/sub\u003e and T\u003csub\u003e1\u003c/sub\u003e states reaffirmed the metal-to-ligand charge transfer (MLCT) nature of these transitions. The results demonstrated that the \u003cem\u003eω\u003c/em\u003e*B97X functional, due to its optimal tuning, provided the most accurate predictions for both \u0026sup1;MLCT and \u0026sup3;MLCT states. This was further supported by the comparison of calculated absorption spectra with experimental data, where the \u003cem\u003eω\u003c/em\u003e*B97X functional not only accurately identified the MLCT states but also effectively modeled higher-energy absorption peaks.\u003c/p\u003e \u003cp\u003eThe inclusion of relativistic effects, specifically scalar relativistic Douglas-Kroll-Hess (DKH2) Hamiltonian and SOC, proved essential in aligning computational simulations with experimental observations. The results underscored the significance of these effects in accurately describing the electronic transitions in Ir(III) complexes, given the substantial relativistic effects inherent to heavy transition metals like iridium.\u003c/p\u003e \u003cp\u003eIn conclusion, the \u003cem\u003eω\u003c/em\u003e*B97X functional, coupled with appropriate relativistic corrections, emerged as a robust and reliable computational approach for studying the photophysical properties of Ir(III) complexes. This study highlights the importance of carefully selecting and tuning DFT functionals to achieve accurate predictions of electronic transitions in phosphorescent materials. The insights gained here not only advance our understanding of Ir(III) complexes but also pave the way for the design and synthesis of new phosphorescent materials with optimized properties for various applications in display technologies, medical devices, and chemical sensors.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eAssociated Content\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eSupporting information\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThese materials are available free of charge via the Internet.\u003c/p\u003e\n\u003cp\u003eIsosurfaces of electron-hole wave functions for the Ir(III)\u0026nbsp;complexes calculated using different DFT functionals, where green represents electron density and blue represents hole density are shown in Figure S1.\u003c/p\u003e\n\u003cp\u003eThe effect of spin-orbital coupling (SOC) on absorption spectrum Ir(III)\u0026nbsp;complexes are shown in Figure S2.\u003c/p\u003e\n\u003cp\u003eThe impact of scalar relativistic effects on the absorption spectra of Ir(III) complexes are shown in Figure S3.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAuthor Information\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCorresponding Author\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e*E-mail: [email protected]\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAcknowledges\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eSW Yin thanks National Science Foundation of China (Grant No. 22273054) for the financial supporting.\u003c/p\u003e\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\u003cp\u003eXinqin Ren did ORCA calculations and prepared the all the figures and Shiwei Yin wrote the manuscript text. All authors reviewed the manuscript.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eKang, K.; Byeon, I.; Kim, Y. G.; Choi, J.-r.; Kim, D., Nanostructures in Organic Light-Emitting Diodes: Principles and Recent Advances in the Light Extraction Strategy. Laser \u0026amp; Photonics Reviews 2024, 2400547.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eHong, G.; Gan, X.; Leonhardt, C.; Zhang, Z.; Seibert, J.; Busch, J. M.; Br\u0026auml;se, S., A Brief History of OLEDs\u0026mdash;Emitter Development and Industry Milestones. Adv. Mater. (Weinheim, Fed. Repub. Ger.) 2021, \u003cem\u003e33\u003c/em\u003e (9), 2005630.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eMiyamoto, K.-i.; Kaneko, K.; Matsuo, A.; Wagner, T.; Kanoh, S. i.; Sch\u0026ouml;ning, M. J.; Yoshinobu, T., Miniaturized chemical imaging sensor system using an OLED display panel. 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J., Theories of phosphorescence in organo-transition metal complexes \u0026ndash; From relativistic effects to simple models and design principles for organic light-emitting diodes. Coord. Chem. Rev. 2015, \u003cem\u003e295\u003c/em\u003e, 46\u0026ndash;79.\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"theoretical-chemistry-accounts","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"tcac","sideBox":"Learn more about [Theoretical Chemistry Accounts](http://link.springer.com/journal/214)","snPcode":"214","submissionUrl":"https://submission.nature.com/new-submission/214/3","title":"Theoretical Chemistry Accounts","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"","lastPublishedDoi":"10.21203/rs.3.rs-4984416/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4984416/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eOrganic light-emitting diodes (OLEDs) are prominent in various applications, including screen displays, medical devices, and chemical sensors, due to their low power consumption, fast response speed, and high-resolution capability. Phosphorescent emitters, especially cyclometalated Ir(III) complexes, are particularly significant in OLEDs because they enable internal quantum efficiencies of up to 100% through strong spin-orbit coupling (SOC). This study focuses on the accurate characterization of singlet and triplet metal-to-ligand charge transfer (MLCT) states in Ir(III) complexes, which is essential for optimizing their performance. Using a combination of quantum mechanical methods, particularly time-dependent density functional theory (TDDFT) with optimally tuned range-separated functionals and the full-electron scalar relativistic Douglas-Kroll-Hess (DKH2) Hamiltonian, we evaluate the electronic structures and MLCT states of eight Ir(III) complexes. Our results highlight the efficacy of the tuned \u003cem\u003eω\u003c/em\u003e*B97X functional in predicting MLCT energies and higher-energy absorption peaks, demonstrating its superiority over conventional functionals like PBE0 and B3LYP. The inclusion of relativistic effects and SOC in our models ensures alignment with experimental absorption spectra, providing reliable benchmarks for computational approaches. This comprehensive analysis not only advances the understanding of MLCT transitions in phosphorescent materials but also aids in the design of new Ir(III) complexes with enhanced photophysical properties.\u003c/p\u003e","manuscriptTitle":"Exploring the Photophysical Properties of Iridium (III) Complexes Using TD-DFT: A Comprehensive Study","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-10-01 15:18:11","doi":"10.21203/rs.3.rs-4984416/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2024-10-22T10:36:19+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2024-10-17T18:16:57+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"2207072307678354394430887522749272655","date":"2024-09-27T13:08:24+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"1560363602349212411804628891621948281","date":"2024-09-13T16:19:07+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2024-09-13T15:09:39+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2024-08-27T14:44:14+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2024-08-27T14:42:37+00:00","index":"","fulltext":""},{"type":"submitted","content":"Theoretical Chemistry Accounts","date":"2024-08-27T12:12:54+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"theoretical-chemistry-accounts","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"tcac","sideBox":"Learn more about [Theoretical Chemistry Accounts](http://link.springer.com/journal/214)","snPcode":"214","submissionUrl":"https://submission.nature.com/new-submission/214/3","title":"Theoretical Chemistry Accounts","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"d1238cbf-3471-4956-80a6-62bacd62f3a0","owner":[],"postedDate":"October 1st, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[],"tags":[],"updatedAt":"2024-12-16T16:01:41+00:00","versionOfRecord":{"articleIdentity":"rs-4984416","link":"https://doi.org/10.1007/s00214-024-03169-y","journal":{"identity":"theoretical-chemistry-accounts","isVorOnly":false,"title":"Theoretical Chemistry Accounts"},"publishedOn":"2024-12-12 15:57:36","publishedOnDateReadable":"December 12th, 2024"},"versionCreatedAt":"2024-10-01 15:18:11","video":"","vorDoi":"10.1007/s00214-024-03169-y","vorDoiUrl":"https://doi.org/10.1007/s00214-024-03169-y","workflowStages":[]},"version":"v1","identity":"rs-4984416","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-4984416","identity":"rs-4984416","version":["v1"]},"buildId":"qtupq5eGEP_6zYnWcrvyt","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}