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

doi:10.21203/rs.3.rs-4984416/v1

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

https://doi.org/10.21203/rs.3.rs-4984416/v1

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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.

Organic light emitting diodes (OLEDs) are widely used in screen displays¹, medical devices², chemical sensors³, and other fields due to their advantages such as low power consumption⁴, fast response speed⁵, and high-resolution capability². 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 (S₁) to the lowest triplet state (T₁) and enhances the radiative transition from T₁ to the ground state (S₀). 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 interactions¹⁷ and self-interaction errors¹⁸. 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 S₀ 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 (S₀), 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)₃²⁹, fac-Ir(tpy)₃²⁹, mer-Ir(tpy)₃²⁹, fac-Ir(piq)₃³⁰, mer-Ir(piq)₃²⁹ and Ir(C^N)₂LX-type complexes^31–32: Ir(ppy)₂acac³³ and Ir(tpy)₂acac³³ 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 order³⁴ 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 ωB97X 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.

2.1 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:

$$J\left( \omega \right)=\hbox{min} \left\{ {\left| {{E_{HOMO}}(\omega ) - IP(N)} \right|+\left| {{E_{LUMO}}(\omega ) - IP(N+1)} \right|} \right\}$$

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 PBE0³⁹, B3LYP⁴⁰ and range-separated ωB97X⁴¹, CAM-B3LYP⁴² 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, ωB97X 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 ωB97X 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

3.1 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, ωB97X, 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 C₃ 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 C₃ symmetry. In contrast, for the meridional configuration with C₁ 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: ωB97X 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 ωB97X functional, as evidenced by its minimal deviations in bond lengths and angles, it is deemed the most suitable for further studies. The ωB97X 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 ωB97X 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.
		ωB97X	CAM-B3LYP	PBE0	B3LYP	exp.
mer-Ir(tpy)₃		Bond Lengths (Å)
	Ir-C1	2.176	2.102	2.090	2.115	2.151²⁹
	Ir-N1	2.080	2.167	2.152	2.187	2.044²⁹
	Ir-C2	2.065	2.087	2.076	2.098	2.065²⁹
	Ir-N2	2.103	2.073	2.057	2.084	2.076²⁹
	Ir-C3	2.086	2.109	2.008	2.026	2.086²⁹
	Ir-N3	2.106	2.058	2.042	2.066	2.010²⁹
fac-Ir(ppy)₃		Bond Lengths (Å)
	Ir-C	2.031	2.033	2.022	2.041	2.033⁴⁸
	Ir-N	2.155	2.146	2.130	2.162	2.158⁴⁸
fac-Ir(piq)₃		Bond Lengths (Å)
	Ir-N1	2.154	2.145	2.130	2.161	2.135³⁰
	Ir-C2	2.029	2.030	2.019	2.038	2.009³⁰
	N1-C1	1.375	1.372	1.370	1.376	1.374³⁰
	N1-C3	1.350	1.354	1.361	1.368	1.339³⁰
		Bond Angles (degree)
	N1-Ir-C2	78.4	78.3	78.5	78.2	78.5³⁰
	Ir-N1-C1	123.4	123.0	123.1	123.2	124.8³⁰
	Ir-N1-C3	115.3	115.7	115.9	115.7	115.1³⁰

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, ωB97X, 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 C₃ 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 C₃ symmetry.

Compared with the vertical IP values in Fig. 2, we can readily observe that the range-separated ωB97X 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 ωB97X 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, ωB97X 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 ^1/3MLCT

MLCT assignments

All-electron scalar relativistic DKH2 Hamiltonian combined with five DFT functionals (ωB97X, CAM-B3LYP, PBE0, B3LYP, and tuned ω*B97X) were applied to calculate the lowest excited triplet (T₁) and singlet (S₁) states. The electron-hole wavefunctions for the transition from S₁/T₁ to the ground state (S₀) were analyzed using Multwfn 3.8⁴⁹. 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 S₁ and T₁ states exhibit DFT functional-dependent characteristics. For example, the DFT functionals B3LYP and ω*B97X produce C₃ symmetric electron-hole wavefunctions, with the electron (green) and hole (blue) wavefunctions equally distributed on the three ppy ligands. The DFT functionals ωB97X and CAM-B3LYP slightly break the C₃ symmetry of the electron-hole wavefunctions, while PBE0 strongly breaks the C₃ 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 S₁ or T₁, 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 S₁ and T₁ 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 S₁ and T₁ states. Therefore, we assign the S₁ and T₁ states as the ¹MLCT and ³MLCT states, respectively.

Functional-dependent energies of ^1/3MLCT

According to the energies of S₁ and T₁ obtained from various DFT functionals, we compared them with their respective observed ³MLCT and ¹MLCT absorption peaks. The deviations (ΔE) of the calculated values from the experimental data are shown in Fig. 4 (a for ³MLCT, b for ¹MLCT). For the same DFT functional, ΔE for ³MLCT and ¹MLCT exhibits ligand-dependent characteristics.

Examining the ΔE results from the range-separated ωB97X functional, we find that for ³MLCT, Ir(ppy)₂acac has the largest ΔE (~ 0.31 eV) and Ir(bzq)₂acac has the smallest ΔE (~ 0.03 eV). For ¹MLCT, fac-Ir(piq)₃ has the largest ΔE (~ 1.2 eV) and fac-Ir(tpy)₃ has the smallest ΔE (~ 0.90 eV). Generally speaking, the range-separated functionals ωB97X and CAM-B3LYP overestimate the transition energies of ^1/3MLCT, 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 ΔE 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 ωB97X and CAM-B3LYP overestimate the transition energies of ^1/3MLCT, 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 C₃ symmetric fac-Ir(ppy)₃ notably breaks the C₃ symmetry.

Considering the transition energies of ¹/³MLCT and the symmetry of the electron-hole wavefunction, we conclude that the tuned range-separated ωB97X 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 ωB97X functional.

3.4 Evaluation of Higher-Energy Absorption Peaks Using the ω*B97X Functional

We have demonstrated that the ωB97X functional can accurately identify the ¹MLCT and ³MLCT energies in the absorption spectra of Ir(III) complexes. Next, we explore whether the ωB97X 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 ωB97X 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)₂acac, while the minimum MAD is 2.0 nm for mer-Ir(ppy)₃. These small average discrepancies demonstrate the precision of the ωB97X 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
		³MLCT	¹MLCT	Higher MLCT				MAD
fac-Ir(ppy)₃	exp.²⁹	488	455	405	377	341	283
fac-Ir(ppy)₃	cal.	484	460	403	368	343	288	4.5
mer-Ir(ppy)₃	exp.²⁹	488	457	410	382	339
mer-Ir(ppy)₃	cal.	486	458	410	383	333		2.0
fac-Ir(piq)₃	exp.³⁰	600	550	483	430	354	333
fac-Ir(piq)₃	cal.	611	560	482	444	344	332	7.8
fac-Ir(tpy)₃	exp.²⁹	485	450	410	374	347
fac-Ir(tpy)₃	cal.	484	459	403	366	344		5.6
mer-Ir(tpy)₃	exp.²⁹	485	451	420	383	336
mer-Ir(tpy)₃	cal.	487	459	416	384	336		3.0
fac-Ir(46dfppy)₃	exp.²⁹	456	428	388	353	312
fac-Ir(46dfppy)₃	cal.	460	424	378	340	304		7.8
Ir(bzq)₂acac	exp.³³	500	470	360
Ir(bzq)₂acac	cal.	511	483	368				10.7
Ir(ppy)₂acac	exp.³³	497	460	412	345
Ir(ppy)₂acac	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 S₀ to T₁ 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 ¹MLCT 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.

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, ωB97X 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 S₁ and T₁ 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.

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.

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No competing interests reported.

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You are reading this latest preprint version

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

Status:

Version 1

Abstract

Figures

1.Introduction

2.Theory and computational details

2.1 Optimally Tuned Range-Separated Functionals

2.2 Computational details

3.Results and Discussion

3.1 Ground State Geometry

3.2 Effects of functionals on Frontier Molecular Orbitals (FMO)

3.3 Effects of DFT functionals on ^1/3MLCT

3.4 Evaluation of Higher-Energy Absorption Peaks Using the ω*B97X Functional

3.5 Relativistic Effects of Ir Complexes

4.Conclusions

Declarations

Author Contribution

References

Additional Declarations

Supplementary Files

Status:

Version 1

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

Status:

Version 1

Abstract

Figures

1.Introduction

2.Theory and computational details

2.1 Optimally Tuned Range-Separated Functionals

2.2 Computational details

3.Results and Discussion

3.1 Ground State Geometry

3.2 Effects of functionals on Frontier Molecular Orbitals (FMO)

3.3 Effects of DFT functionals on 1/3MLCT

3.4 Evaluation of Higher-Energy Absorption Peaks Using the ω*B97X Functional

3.5 Relativistic Effects of Ir Complexes

4.Conclusions

Declarations

Author Contribution

References

Additional Declarations

Supplementary Files

Status:

Version 1

3.3 Effects of DFT functionals on ^1/3MLCT