On the importance of equatorial metal-centered excited states in the photophysics of cyclometallated Ir(III) complexes

Abstract

In the present contribution, the following three cyclometallated Ir(III) complexes were theoretically investigated using density functional theory calculations to explain their different photophysical properties: [Ir(ppy)₂(bpy)]⁺, where Hppy is 2-phenylpyridine and bpy is 2,2′-bipyridine, [Ir(ppy)₂(pbpy)]⁺, where pbpy is 6-phenyl-2,2′-bipyridine, and [Ir(ppy)₂(dpbpy)]⁺, where dpbpy is 6,6′-diphenyl-2,2′-bipyridine. Despite sharing the same molecular skeleton, with the only difference being the addition of one or two phenyl groups attached to the ancillary bpy ligand, the complexes show different emission quantum yields in CH₂Cl₂ solution (0.196, 0.049 and 0.036, respectively). Such a behavior was previously justified as a consequence of a different ability to non-radiatively decay through an axial metal-centered (MC) triplet state. In the present contribution, a new non-radiative decay path has been characterized to be mediated by the so-called equatorial MC states, in which an Ir–N_bpy bond is elongated instead of an Ir–N_ppy bond as observed in the axial MC states. The decay path involving the equatorial MC states is more favorable than that associated with the axial MC states, and the different ability to decay through the former better explains the photoemission properties exhibited by the three complexes.

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Introduction

Ionic transition-metal complexes (iTMCs) have been studied in recent years in relation to their use in light-emitting electrochemical cells (LECs).^1,2 In contrast to organic light-emitting diodes (OLEDs), LECs have a low production cost due to their simpler structure, which does not require a strict encapsulation.³ The most commonly employed iTMCs for LECs are based on Ru(II) or Ir(III) centers. In general terms, the former, a second-row transition metal, presents lower emission quantum yields and efficiencies than a third-row transition metal such as Ir. These differences are explained by the lower ligand-field splitting energies of Ru(II) complexes, which facilitate the population of the metal-centered (MC) excited triplet states.⁴ A high emission quantum yield is essential to obtain a good performance of the final LEC device. In addition to their use in LECs, Ir complexes also exhibit important applications in areas such as photocatalysis,⁵ biological imaging,⁶ luminescence sensitizers^7,8 and chemosensors.^9–11

Among Ir complexes for electroluminescence applications, the most studied are the cyclometallated complexes based on the general formula [Ir(C^N)₂(N^N)]⁺, the Ir[(ppy)₂(bpy)]⁺ complex, where Hppy is 2-phenylpyridine and bpy is 2,2′-bipyridine, being the archetype reference of such a family. The photophysical properties of Ir[(ppy)₂(bpy)]⁺ can be easily modified by the introduction of electronically active substituents. For example, the addition of fluoro and tert-butyl groups giving rise to the [Ir(diFppy)₂(dtb-bpy)]⁺ complex, where diFHppy is 2-(2,4-difluorophenyl)pyridine and dtb-bpy is 4,4′-di-tert-butyl-2,2′-bipyridine, determines a significant increase of the emission quantum yield with respect to Ir[(ppy)₂(bpy)]⁺ (from 0.196 to 0.71, respectively).¹² On the other hand, the addition of phenyl groups on the bpy ancillary ligand has the opposite effect. In fact, complexes [Ir(ppy)₂(pbpy)]⁺ and [Ir(ppy)₂(dpbpy)]⁺, where pbpy represents 6-phenyl-2,2′-bipyridine and dpbpy is 6,6′-diphenyl-2,2′-bipyridine, display significantly lower emission quantum yields of 0.049 and 0.036, respectively.¹³

It is generally accepted that, upon excitation, a common non-radiative decay path for iTMCs goes through the population of the triplet metal-centered states (³MC).^14–17 In particular, for the family of [Ir(C^N)₂(N^N)]⁺ complexes, such a state is associated with the so-called axial ³MC, hereafter ³MC_ax, which leads to a strong geometrical distortion resulting from the elongation of the Ir–N_C^N bonds due to the occupation of the Ir e_g* molecular orbital (MO). Such a deformation determines a drastic reduction of the energy gap with the ground state (S₀) at the corresponding ³MC_ax minimum and the presence of a nearby T₁/S₀ singlet–triplet crossing (STC) region, leading the system back to the ground state in a non-radiative way.¹² Additionally, in other complexes where one pyridine ring of the ancillary ligand is substituted by a five-membered ring, another MC state (the so-called equatorial ³MC, hereafter ³MC_eq), characterized by the elongation of the Ir–N_N^N bond of this ring and its rotation around the interring bond, has been localized. Consequently, in the ³MC_ax state, the Ir atom still exhibits a distorted octahedral geometry, whereas in the ³MC_eq state, the coordination of Ir decreases from 6 to 5 due to the Ir–N_N^N elongation and rotation, globally displaying a distorted trigonal bipyramidal geometry around the Ir atom. As for the ³MC_ax state minima, the strong geometrical distortion suffered by the system at the ³MC_eq minima also leads to a much smaller gap with the ground state and the presence of accessible T₁/S₀ STC regions. Regarding their energy positions, it is important to stress that in all the cases reported in the literature, the ³MC_eq state appears to be lower in energy than the ³MC_ax one, consequently making its involvement in principle more relevant than that of the ³MC_ax state.^18–24 As a final remark, similar MC states were also found while studying the photorelease of N^N ligands in some complexes of the [Ru(N^N)₃]²⁺ family.^25–29

In the present work, the photophysical properties of [Ir(ppy)₂(bpy)]⁺, [Ir(ppy)₂(pbpy)]⁺ and [Ir(ppy)₂(dpbpy)]⁺ (hereafter complexes 1, 2 and 3, respectively, see Fig. 1) were studied theoretically through density functional theory (DFT) and time-dependent DFT (TD-DFT) calculations. The main aim is to explain the different emission quantum yields exhibited by these complexes in CH₂Cl₂ solution (0.196, 0.049 and 0.036 for 1, 2 and 3, respectively).^12,13 In a previous study, Accorsi, Ortí and coworkers concluded that the different quantum yields could be explained by the reduction of the adiabatic energy difference between the minimum-energy geometries of the non-emitting ³MC_ax state and the emitting metal-to-ligand charge transfer (³MLCT) state, which indeed decreased along the series.¹³ By performing thorough characterization of the potential energy surface (PES) involving the lowest-energy excited triplet states, we now conclude that the ³MC_eq states, which were not considered previously, play a fundamental role in the non-radiative decay of this family of Ir complexes.

Fig. 1 Chemical structures of the Ir(III) complexes studied in this work, [Ir(ppy)₂(bpy)]⁺ (1), [Ir(ppy)₂(pbpy)]⁺ (2) and [Ir(ppy)₂(dpbpy)]⁺ (3).

Computational details

The energy minima of all the triplet and singlet states of complexes 1–3 were calculated at the DFT level of theory by optimizing the molecular geometry without imposing any symmetry constraints. Becke's three-parameter exchange–correlation B3LYP functional^30,31 was selected, which was previously employed, successfully, for these and other Ir cationic complexes.^12,13 As a basis set, the DEF2-SVP basis was used for all the atoms in the systems.^32–34 All calculations were carried out employing the Orca software (in its 5.0.1 version).³⁵ The inner core electrons of Ir were substituted by the Stuttgart–Dresden effective core potential while explicitly treating the outer core [(5s)²(5p)⁶] and the (5d)⁶ valence electrons. For the calculations implying triplet states, the unrestricted UDFT approximation was used, checking that the spin contamination was, always, between 1.95 and 2.05. Frequency calculations were carried out to guarantee that all the optimized geometries have no imaginary frequency and therefore correspond to true minima. Solvent (CH₂Cl₂) effects were included in all the calculations using the conductor-like polarizable continuum model (CPCM).³⁶ To assign the nature of the different excited triplet states, TD-DFT calculations, at the same level of theory, were carried out as implemented in Orca 5. To facilitate this assignment, natural transition orbitals (NTOs)³⁷ were obtained at the B3LYP/DEF2-SVP level for the minima computed with Orca 5 for the different excited states using the Gaussian 16 software (Rev. A.03)³⁸ and the polarized continuum model (PCM) to simulate the solvent effects.³⁹ The climbing image nudged elastic band (CI-NEB)⁴⁰ method was employed, as implemented in Orca, to find the minimum energy paths (MEPs) connecting the minima of the different excited states and also the climbing image (CI) along them (Fig. S28†). Starting from these structures, the corresponding transition states (TSs) were optimized (Fig. S29†). The Orca software was also employed for the optimization of the minimum-energy crossing points (MECPs) for singlet/triplet crossings (STC-MECPs).

Results and discussion

Radiative decay of complexes 1–3

The electronic ground-state minima, hereafter (S₀)_min, of complexes 1–3 were localized by optimizing the geometry of the complexes at the DFT/B3LYP-DEF2-SVP level of theory including solvent effects using the CPCM method. The optimized bond distances defining the coordination sphere of Ir in (S₀)_min, together with those obtained for the different excited states discussed below, are summarized in Table 1, and appear to be in agreement with previous theoretical (Table S1, ESI†) and experimental data.¹³ The three complexes present a near octahedral coordination of the Ir atom in S₀ (Fig. S1, ESI†), although the symmetry of the (S₀)_min structure decreases on passing from 1 to complexes 2 and 3. Whereas for complex 1, the two Ir–N_bpy distances are equal, significant differences appear between them for the corresponding minima of 2 and 3 (Table 1). Smaller differences are found for the two Ir–N_ppy and two Ir–C_ppy bonds. In addition, the attachment of phenyl rings to the bpy ligand in complex 2 or 3 induces an internal twisting around the interring bond of the bpy of 15.13° and 35.30° for complexes 2 and 3, respectively (dihedral angle N₁–C₇–C₈–N₂ in Fig. 1). Instead, for complex 1, the bpy ligand remains mostly planar (N₁–C₇–C₈–N₂ = 1.74°).

Table 1 DFT B3LYP/DEF2-SVP-CPCM(CH₂Cl₂) optimized bond lengths (in Å) computed for the energy minima of the different electronic states characterized for complexes 1, 2 and 3

	Bond^a	(S0)min	(^3MLCT)min	(^3MCax 1)min	(^3MCax 2)min	(^3MCeq 1)min	(^3MCeq 2)min
a Atomic numbering follows that given in Fig. 1.
Complex 1	Ir–N1-bpy	2.218	2.203	2.229	2.232	3.272	—
	Ir–N2-bpy	2.218	2.203	2.260	2.232	2.312	—
	Ir–N3-ppy	2.090	2.090	2.292	2.493	2.081	—
	Ir–N6-ppy	2.090	2.090	2.610	2.493	2.084	—
	Ir–C4-ppy	2.029	2.007	2.044	2.028	2.065	—
	Ir–C5-ppy	2.029	2.007	2.040	2.028	2.041	—
Complex 2	Ir–N1-bpy	2.358	2.236	2.297	2.464	3.642	2.399
	Ir–N2-bpy	2.214	2.232	2.247	2.233	2.294	3.534
	Ir–N3-ppy	2.099	2.095	2.295	2.582	2.082	2.094
	Ir–N6-ppy	2.083	2.084	2.646	2.233	2.085	2.080
	Ir–C4-ppy	2.018	2.027	2.036	2.047	2.066	2.048
	Ir–C5-ppy	2.034	1.992	2.049	2.043	2.045	2.045
Complex 3	Ir–N1-bpy	2.369	2.305	2.303	—	3.674	—
	Ir–N2-bpy	2.346	2.238	2.456	—	2.402	—
	Ir–N3-ppy	2.085	2.083	2.225	—	2.079	—
	Ir–N6-ppy	2.089	2.100	2.623	—	2.094	—
	Ir–C4-ppy	2.022	1.996	2.036	—	2.045	—
	Ir–C5-ppy	2.026	2.020	2.054	—	2.049	—

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Regarding the electronic structure of these complexes, Fig. 2 shows the frontier MOs calculated for complex 1 at the ground state (S₀)_min geometry, which are relevant for the description of the lowest triplet excited states listed in Table 2. The e_g* MO (LUMO+10), whose population is responsible for the strong distortion of the Ir–N_ppy bonds leading to the MC_ax excited states, is also included in Fig. 2. The frontier MOs of complexes 2 and 3 display similar topologies to those calculated for 1, but now the e_g* MO corresponds to the LUMO+12 and LUMO+14, respectively (Fig. S2 and S3, ESI†). At the (S₀)_min minima, no e_g* MO that could be associated with the MC_eq state was found. The HOMO in the three complexes is composed of the d orbitals of Ir and the π orbitals from the ppy ligands, mostly from the phenyl rings. In contrast, the LUMO is localized on the auxiliary N^N ligand and corresponds in the three cases to the π* LUMO of bpy, as expected for these cyclometallated Ir complexes. The energy gap between the HOMO and LUMO increases along the series (3.21, 3.26 and 3.42 eV for 1, 2 and 3, respectively). This increment is mainly produced by the destabilization of the LUMO (−2.64, −2.60 and −2.45 eV, respectively) as a consequence of the attachment of phenyls rings to the ancillary ligand, which induces a rotation of the ligand around the interring bond, thus reducing the conjugation between the pyridine rings.

Fig. 2 Isosurface contour plots (±0.03 a.u.) computed for the molecular orbitals of complex 1 at DFT B3LYP/DEF2-SVP-CPCM(CH₂Cl₂). See Fig. S2 and S3 in the ESI† for the molecular orbitals of complexes 2 and 3.

Table 2 TDDFT B3LYP/DEF2-SVP-CPCM(CH₂Cl₂) low-lying triplet excited states calculated at the (S₀)_min geometries for complexes 1–3. H and L denote the HOMO and LUMO, respectively

	State	E (eV)	Monoexcitation (%)	Nature
Complex 1	T1 (^3MLCT)	2.50	H → L (98)	MLCT/LLCT
	T2	2.74	H → L+1 (66)	LCppy/MLCT
			H−1 → L+2 (16)
	T3	2.78	H → L+2 (54)	LCppy/MLCT
			H−1 → L+1 (25)
	T4	2.93	H−2 → L (40)	LCbpy/MLCT/LLCT
			H−6 → L (34)
			H−4 → L (11)
	T5	3.08	H−3 → L (54)	MLCT/LLCT
			H−1 → L (31)
	T6	3.18	H → L+1 (27)	LCppy/MLCT/LLCT
			H−2 → L+1 (20)
			H−1 → L+1 (15)
Complex 2	T1 (^3MLCT)	2.54	H → L (95)	MLCT/LLCT
	T2	2.71	H → L+1 (53)	LCppy/MLCT
			H−1 → L+2 (11)
			H → L+2 (11)
	T3	2.77	H → L+2 (34)	LCppy/MLCT
			H−1 → L+1 (26)
	T4	2.91	H−2 → L (36)	LCbpy/MLCT/LLCT
			H−8 → L (16)
			H−6 → L (15)
	T5	3.13	H−3 → L (42)	MLCT/LLCT
			H−1 → L (35)
	T6	3.14	H−2 → L+1 (19)	LCppy/MLCT/LLCT
			H → L+1 (17)
Complex 3	T1 (^3MLCT)	2.58	H → L (66)	MLCT/LLCT
			H → L+1 (15)
	T2	2.74	H → L+1 (17)	LCppy/MLCT
			H → L+2 (15)
			H−1 → L+1 (15)
			H → L+3 (13)
	T3	2.79	H → L (25)	LCppy/MLCT
			H → L+2 (22)
			H → L+1 (19)
	T4	3.03	H−2 → L (21)	LCbpy/MLCT/LLCT
			H−6 → L (11)
	T5	3.15	H−2 → L (22)	MLCT/LLCT
			H → L+2 (22)
			H−2 → L+2 (11)
	T6	3.16	H−5 → L (14)	MLCT/LLCT/LLCT
			H−4 → L (10)

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The excited triplet states of the three complexes were first investigated by performing TD-DFT calculations (50 roots) at the ground state minimum-energy (S₀)_min geometries (Table 2). The electronic nature of the lowest-lying triplet states at (S₀)_min was first determined by analyzing the monoelectronic excitations contributing to the wave function of the state with a weight higher than 10%, and confirmed by NTO analysis (see Fig. S4–S6† to visualize the NTOs calculated for states T₁, T₂ and T₃ of complexes 1, 2 and 3, respectively). As expected, the lowest triplet state (T₁) results in the three complexes from the HOMO → LUMO excitation, which implies an electron transfer from the Ir atom and the phenyl rings of the ppy ligands to the ancillary bpy ligand. The T₁ state thus exhibits a mixed metal-to-ligand/ligand-to-ligand charge transfer (³MLCT/³LLCT) nature and will be hereafter named ³MLCT. The T₂ and T₃ states possess a ligand-centered (³LC_ppy) character, and result from the HOMO−1, HOMO → LUMO+1, LUMO+2 excitations (Table 2) that mainly involve the ppy ligand with little contribution from the metal (Fig. 2 and Fig. S2–S3, ESI†). These states are around 0.2 eV higher in energy than the T₁ state (Table 2). The T₄ state shows a ligand-centered character involving the bpy ligand (³LC_bpy) combined with the ³MLCT/³LLCT character and is located for all complexes around 0.4 eV above the T₁ state. The T₅ state shows a ³MLCT/³LLCT nature, and T₆ has a ³LC_ppy character combined with ³MLCT/³LLCT.

The energy minima of the ³MLCT T₁ state of complexes 1–3, hereafter (³MLCT)_min, were characterized by optimizing the geometry of the complex at the UDFT B3LYP/DEF2-SVP-CPCM(CH₂Cl₂) level of theory using a spin multiplicity value of 3. The spin density plots shown in Fig. S7† and the NTO in Fig. S8,† with one unpaired electron residing on the phenyl rings and the Ir atom and the other unpaired electron on the bpy ligand, confirm the ³MLCT/³LLCT nature of the T₁ state of the three complexes. The equilibrium (³MLCT)_min structures are similar to those obtained for the (S₀)_min minima, maintaining the near octahedral coordination of Ir (see Table 1 and Fig. S1, ESI†). The geometrical parameters calculated for (³MLCT)_min also show lower symmetry for complexes 2 and 3 compared to those of 1. Due to the population of the LUMO, spreading over the N^N ligand as mentioned before, the bpy ligand becomes more planar in the ³MLCT state than that in S₀, with the N₁–C₇–C₈–N₂ dihedral structure having values of 0.98°, 8.72° and 1.59° for 1, 2 and 3, respectively. Compared to S₀, for which the N₁–C₇–C₈–N₂ angle has values of 1.74°, 15.13° and 35.30°, respectively, the planarization of the bpy ligand in complex 3 is nearly complete and much more relevant than that for complex 2. In addition, the dihedral angle Ir–N₁–N₂–C₈, defining the bending of the bpy ligand with respect to the equatorial plane of the complex, also increases along the series 1 (0.26°), 2 (17.07°) and 3 (26.98°), showing the distortion from the octahedral structure (Fig. 3).

Fig. 3 B3LYP/DEF2-SVP-CPCM(CH₂Cl₂)-optimized geometries for the ³MLCT, ³MC_ax and ³MC_eq states of complexes 1 (a), 2 (b and c) and 3 (d). Differences in selected bond lengths (dashed red lines) with respect to the (³MLCT)_min minima, highlighting the main geometrical deformations characterizing the ³MC_ax and ³MC_eq minima, are reported in Å.

The energy gap between the T₁ and S₀ states was vertically computed at the optimized (³MLCT)_min geometry to estimate the emission energy. Similar energy gaps of 2.06, 2.00 and 2.02 eV were obtained for complexes 1, 2 and 3, respectively. These values are in good agreement with the experimental emission energy maxima (2.08, 2.02 and 2.09 eV),¹³ thus supporting the computational approach employed in this work and the assignment of the ³MLCT T₁ state as the emissive state. Based on these results, it is possible to conclude that the same radiative decay path involving the ³MLCT state is in operation for the three complexes. The differences observed in the emission quantum yields reported experimentally for complexes 1–3 should be the result of different efficiencies in the non-radiative decay paths.

Non-radiative decay of complexes 1–3

According to the previous work of Accorsi, Ortí and coworkers,¹³ it was proposed that the difference in the emission quantum yield of complexes 1 (0.196), 2 (0.049) and 3 (0.036) was due to the difference in their ability to reach the ³MC_ax state from (³MLCT)_min, evaluated as the energy difference between the ³MLCT and ³MC_ax minima. In fact, according to the Frank–Condon principle and the strong spin–orbit coupling characterizing Ir complexes, most of the excited population is supposed to decay to the ³MLCT minimum, which can be considered as the starting point for all the decay processes. We can now map the PES between the ³MLCT and ³MC_ax minima and to localize the MECP between the S₀ and ³MC states, for evaluating the non-radiative decay process through ³MC_ax and its barriers.

Starting from the (³MLCT)_min geometries, the ³MC_ax energy minima, hereafter (³MC_{ax 1})_min, were localized by geometry optimization at the DFT level (Fig. S9†). The obtained minima are non-symmetric since they mainly involve the elongation of one Ir–N_ppy bond, which lengthens with respect to the (³MLCT)_min geometry by 0.520, 0.562 and 0.523 Å in complexes 1, 2 and 3, respectively (Table 1 and Fig. 3). By comparing the obtained structures with those published by Accorsi, Ortí and coworkers,¹³ both similarities and significant differences have been noted (see Table S1†). The most important point is that in their work, the ³MC minimum of complex 1 presents a symmetric structure characterized by the same elongation of both Ir–N_ppy bonds (leading to 2.505 Å bond distances). In contrast, in the here-optimized (³MC_{ax 1})_min structure, although again both Ir–N_ppy bonds are significantly enlarged, one displays a much higher value (2.610 Å) than the other (2.292 Å). In order to verify if that could be a consequence of the different computational details employed in the two studies, the ³MC structure reported by Accorsi, Ortí and coworkers was here re-optimized leading to a symmetric ³MC minimum, hereafter (³MC_{ax 2})_min, characterized by equal Ir–N_ppy bond distances of 2.493 Å. Regarding complexes 2 and 3, our calculations provide asymmetric structures similar to those previously reported (Table S1†),¹³ in which both Ir–N_ppy bonds are elongated, but one much more than the other (Table 1 and Fig. S9†). Some differences can however be noticed regarding the Ir–N_bpy distances, particularly in complex 2, where one Ir–N_bpy bond is 0.051 Å shorter than the value previously calculated (Table S1†). Any attempt to optimize in complexes 2 and 3 a ³MC_ax structure having equal Ir–N_ppy bond distances failed. An additional factor affecting complex 2 is that, due to its lower symmetry, two non-equivalent ³MC_ax minima, (³MC_{ax 1})_min and (³MC_{ax 2})_min, are possible, depending on which of the two Ir–N_ppy bonds is elongated (Table 1, Fig. 3 and Fig. S9†).

Altogether, we have characterized the following ³MC_ax minima in our three complexes (Fig. S9†). Two minima are observed for complex 1: (³MC_{ax 1})_min, having one Ir–N_ppy much longer than the other, and (³MC_{ax 2})_min, having equal Ir–N_ppy bonds. Two minima are observed for complex 2, (³MC_{ax 1})_min and (³MC_{ax 2})_min, depending on which Ir–N_ppy bond is the one most significantly lengthened. One minimum is observed for complex 3, again characterized by one Ir–N_ppy bond distance remarkably longer than the other. The nature of the ³MC states of all these minima was confirmed by computing the corresponding spin densities (Fig. S10†) and NTOs (Fig. S11†).

Once the ³MC_ax structures were optimized, their energies were computed to evaluate their importance in the photophysics of complexes 1–3. Table 3 summarizes the relative energies of all the triplet structures characterized for the three complexes, whereas Fig. 4 (right side) shows the MEPs connecting the triplet states most relevant for the decay along the ³MC_ax. The adiabatic energy differences between the ³MC_ax and ³MLCT minima are 0.61/0.67 (³MC_{ax 1} and ³MC_{ax 2}), 0.48/0.55 (³MC_{ax 1} and ³MC_{ax 2}) and 0.28 eV for complexes 1, 2 and 3, respectively. Despite the mentioned geometrical differences, these relative energies are in agreement with those previously reported by Accorsi, Ortí and coworkers (0.60, 0.50 and 0.20 eV, respectively) and, in principle, justify the hypothesis of relating the decrease in the emission quantum yield to an increase in the accessibility of the ³MC_ax-mediated non-radiative decay path. It is however important to notice that, although the trend in the energies is consistent with such an interpretation, the so-computed energy difference for complex 2 is much more similar to that obtained for complex 1 than to the one characterizing complex 3. This indeed is in contrast to the fact that complexes 2 and 3 have much similar emission quantum yields (0049 and 0.036, respectively) significantly lower than that of complex 1 (0.196). This might be an indication of the limitation of evaluating the viability of the process by just computing the energy difference between the final and initial points, which does not account for any possible barriers along the path.

Fig. 4 Schematic representation of the characterized photophysics of complexes 1 (a), 2 (b and c) and 3 (d). The left side (in orange box) shows the non-radiative decay path through the MC_eq states. The right side (in green box) shows the non-radiative decay path through the MC_ax states. All the reported energies are in eV and have been computed at the DFT B3LYP/DEF2-SVP-CPCM(CH₂Cl₂) level.

Table 3 DFT B3LYP/DEF2-SVP-CPCM(CH₂Cl₂) relative energies (in eV) computed for the S₀ and T₁ states at all the critical points characterized for complexes 1, 2 and 3^a

	Geometry	S0	T1
a All reported energies are referred with respect to the S0 energy computed at the (S0)min of the corresponding complex. It is worth noting that T1 refers to the lowest-energy triplet state at the respective geometry (Fig. 4).
Complex 1	(S0)min	0.00	2.59
	(^3MLCT)min	0.27	2.34
	(^3MLCT/^3MCax 1)ts	1.35	3.10
	(^3MCax 1)min	2.43	2.95
	(^3MCax 1/S0)stc-mecp	2.99	2.99
	(^3MCax 2)min	1.52	3.01
	(^3MCax 2/S0)stc-mecp	3.28	3.28
	(^3MLCT/^3MCeq 1)ts	2.40	2.95
	(^3MCeq 1)min	2.44	2.95
	(^3MCeq 1/S0)stc-mecp	2.96	2.97
Complex 2	(S0)min	0.00	2.63
	(^3MLCT)min	0.32	2.32
	(^3MLCT/^3MCax 1)ts	1.24	2.99
	(^3MCax 1)min	2.80	2.80
	(^3MCax 1/S0)stc-mecp	2.81	2.81
	(^3MLCT/^3MCeq 1)ts	0.54	2.62
	(^3MCeq 1)min	2.21	2.45
	(^3MCeq 1/S0)stc-mecp	2.45	2.45
	(^3MLCT/^3MCax 2)ts	1.13	3.02
	(^3MCax 2)min	2.35	2.87
	(^3MCax 1/S0)stc-mecp	2.90	2.90
	(^3MLCT/^3MCeq 2)CI-NEB	1.04	2.94
	(^3MCeq 2)min	2.27	2.78
	(^3MCeq. 2/S0)stc-mecp	2.82	2.82
Complex 3	(S0)min	0.00	2.68
	(^3MLCT)min	0.37	2.40
	(^3MLCT/^3MCax 1)ts	0.99	2.86
	(^3MCax 1)min	2.42	2.68
	(^3MCax 1/S0)stc-mecp	2.69	2.69
	(^3MLCT/^3MCeq 1)ts	0.38	2.56
	(^3MCeq 1)min	1.75	2.21
	(^3MCeq 1/S0)stc-mecp	2.25	2.25

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To properly evaluate the energy barriers leading to the ³MC_ax minima, the corresponding TSs between the (³MLCT)_min and (³MC_ax)_min structures, hereafter (³MLCT/³MC_ax)_ts (see Fig. S12†), were optimized using as a starting geometry the so-called climbing image (hereafter (³MLCT/³MC_ax)_CI-NEB, Fig. S13†) obtained from the CI-NEB calculations between the two mentioned minima. All obtained TSs display a single imaginary frequency describing the corresponding geometrical deformation connecting the two minima (see Fig. S14–S17†). For complex 3, the corresponding TS is also characterized by an imaginary frequency displaying the expected elongation of one Ir–N_ppy bond, but the structure shows an unexpected significant elongation of one Ir–N_bpy bond, significantly larger than that in the (³MC_{ax 1})_min structure. Using such TSs, but keeping in mind the limitations reported for the TS of complex 3, the barriers from (³MLCT)_min to (³MC_ax)_min are equal to 0.76, 0.67/0.70 and 0.46 eV for complexes 1, 2 and 3, respectively (Fig. 4, right). These values confirm the increasing ability of reaching the ³MC_ax minima along the present series of complexes, in agreement with the decrease of the emission quantum yield along the series. However, as for the adiabatic energy differences, the barrier computed for complex 2 is much more similar to that of complex 1 than to the one computed for complex 3.

The second step in the non-radiative decay path mediated by the ³MC_ax state is the passage from the (³MC_ax)_min minima to the ³MC_ax/S₀ MECP, hereafter (³MC_ax/S₀)_stc-mecp, leading back to the ground state. From the characterized ³MC_ax minima, geometrically close ³MC_ax/S₀ MECPs (Fig. S18†) were localized at 0.04 (³MC_{ax 1})/0.27 (³MC_{ax 2}), 0.01 (³MC_{ax 1})/0.03 (³MC_{ax 2}), and 0.01 eV for complexes 1, 2 and 3, respectively (Fig. 4, right). Then, complex 1 has to surmount the non-negligible barrier of 0.27 eV to reach the ³MC_ax/S₀ MECP closer to the (³MC_{ax 2})_min geometry, whereas all other ³MC_ax minima are almost degenerate with their corresponding (³MC_ax/S₀)_stc-mecp. These results are in agreement with the recent work of Luo et al. on a different family of Ir complexes,⁴¹ where it was also concluded that the (³MC_ax)_min minima are almost degenerate (<2 kcal mol⁻¹) with their (³MC_ax/S₀)_stc-mecp structures. The higher difference from the (³MC_{ax 2})_min structure is in line with the much higher S₀/T₁ energy gap characterizing complex 1 at such a geometry (1.49 eV, Table 3) with respect to the remaining ³MC_ax minima, displaying a S₀/T₁ gap of no more than 0.6 eV. With that in mind and taking into account that the more symmetric (³MC_{ax 2})_min structure is 0.06 eV higher in energy than the (³MC_{ax 1})_min structure, we consider that the latter plays a much prominent role in the photophysics of complex 1 than the former, which will not be further discussed here.

Having localized the different ³MC/S₀ MECPs, it is feasible to evaluate the accessibility of the non-radiative decay process by computing both what we call the global energy barrier (the sum of the barrier to reach the ³MC_ax minimum from the (³MLCT)_min and the barrier to the corresponding T₁/S₀ MECP) and the energy difference between the (³MLCT)_min and (³MC_ax/S₀)_stc-mecp structures. Due to the negligible energy separation between the ³MC_ax minima and the T₁/S₀ MECPs, in the present case, the computation of this separation is not very informative, so we can base our evaluation of the ³MC_ax-mediated non-radiative decay process using the previously stated barriers from the (³MLCT)_min to the (³MC_ax)_min.

Since the different ability to evolve along the non-radiative decay mediated by the ³MC_ax states can only partially explain the experimental differences in the emission quantum yields of complexes 1–3, we also studied the existence of ³MC_eq states and their importance in the photophysical properties. To optimize the corresponding minima, hereafter (³MC_eq)_min, one Ir–N_bpy bond was elongated and, in some cases, the dihedral angle (N₁–C₇–C₈–N₂) defining the coplanarity of the two pyridine rings in the bpy ligand was rotated to reduce the coordination of the Ir atom from six to five. In all cases, even in those in which the starting geometry has an Ir coordination of six, the obtained (³MC_eq)_min minima display a distorted trigonal bipyramidal geometry around the Ir atom, in which one Ir–N_bpy bond distance is around 2.3–2.4 Å and the other Ir–N_bpy distance is much longer (3.3–3.7 Å) due to the internal rotation of the pyridine ring (see Table 1, Fig. S19† and Fig. 3). As for the ³MC_ax state, two (³MC_eq)_min minima are found for complex 2, each one associated with the elongation of one of the two non-equivalent Ir–N_bpy bonds. The (³MC_{eq 1})_min structure implies the elongation of the Ir–N_bpy bond involving the pyridine ring substituted with the phenyl ring, and the (³MC_{eq 2})_min results from the elongation of the Ir–N_bpy bond of the unsubstituted pyridine ring. The structure and electronic nature of the (³MC_eq)_min minima found for complexes 1–3 are similar to those previously reported, for a different [Ir(C^N)₃] family of complexes, by Treboux and coworkers and by Djurovich, Thomson and coworkers.^42,43

Altogether, we have characterized the following ³MC_eq minima in our three complexes (Fig. S19†). One minimum for complex 1, (³MC_{eq 1})_min, having one Ir–N_bpy much longer than the other. Two minima for complex 2, (³MC_{eq 1})_min and (³MC_{eq 2})_min, depending on which Ir–N_bpy bond is the one most significantly lengthened. One minimum for complex 3, again characterized by one Ir–N_bpy bond distance remarkably longer than the other. The ³MC nature of the triplet state in all these minima was confirmed by computing the corresponding spin-densities (Fig. S20†) and NTOs (Fig. S21†).

Once the ³MC_eq structures were optimized, the ability to decay through them was evaluated as we did for the ³MC_ax geometries. The relative energies of all the triplet structures characterized for the three complexes are summarized in Table 3, whereas the left side of Fig. 4 shows the MEPs connecting the triplet states for the decay through the ³MC_eq states. The adiabatic energy difference between the (³MC_eq)_min and the (³MLCT)_min optimized structures is computed to be 0.61 eV for complex 1, 0.13/0.46 (³MC_{eq 1} and ³MC_{eq 2}) for 2 and −0.18 eV for 3, with the ³MC_eq state being more stable than the (³MLCT)_min in complex 3.

TS optimizations were performed starting from the climbing images (hereafter (³MLCT/³MC_eq)_CI-NEB, Fig. S22†) obtained from CI-NEB calculations. The TSs connecting the (³MLCT)_min and (³MC_eq)_min minima, hereafter (³MLCT/³MC_eq)_ts, were found for the three complexes but for the (³MC_{eq 2})_min structure of complex 2 (Fig. S23†). The latter was then approximated as the obtained climbing image. The TSs were characterized by a small imaginary frequency, whose associated displacement vectors define the rotation of one pyridine ring of the bpy ligand leading to the dissociation of the Ir–N_bpy bond and to the geometrical change from a six-coordinated octahedral structure to a five-coordinated trigonal–bipyramidal structure (Fig. S24–26†). Using such TSs (and the climbing image structure as an approximation of the TS connecting the (³MC_{eq 2})_min in complex 2), the barriers from (³MLCT)_min to (³MC_eq)_min are equal to 0.61, 0.30/0.58 and 0.17 eV for complexes 1, 2 and 3, respectively. These values justify a decrease in the quantum yield along the series, even predicting a lower value for complex 3 than that for complex 2.

Similar to the ³MC_ax minima, almost degenerate ³MC/S₀ MECPs, hereafter (³MC_eq/S₀)_stc-mecp, were characterized geometrically near the ³MC_eq minima (Fig. S27†). These MECPs are indeed localized 0.02, 0.00/0.04 (³MC_{eq 1} and ³MC_{eq 2}) and 0.04 eV higher than the ³MC_eq minima of complexes 1, 2 and 3, respectively. Consequently, as for the ³MC_ax-mediated non-radiative decay, also in this case, the efficiency of the process can be evaluated only on the basis of the ability to reach the ³MC_eq minima through the respective TS.

At this point, we are in the position to compare the non-radiative decay path mediated by the ³MC_ax states and the one passing through the ³MC_eq states. Table 4 summarizes the barriers characterizing the ³MC_ax and ³MC_eq non-radiative decay paths for complexes 1–3, evaluated according to the obtained TSs between the ³MLCT and ³MC_ax and ³MC_eq minima, with the latter being almost degenerate with the corresponding ³MC/S₀ crossing.

Table 4 DFT B3LYP/DEF2-SVP-CPCM(CH₂Cl₂) energy barriers (eV) for evolving from the (MLCT)_min minimum to the (³MC_ax)_min and (³MC_eq)_min minima for complexes 1, 2 and 3

	Complex	TS^a
a Energy difference between the (MLCT)min and the TS connecting the two minima. b The climbing image structure is used as an approximation of the TS.
(^3MCax 1)min	1	0.76
(^3MCax 1)min	2	0.67
(^3MCax 2)min	2	0.70
(^3MCax 1)min	3	0.46
(^3MCeq 1)min	1	0.61
(^3MCeq 1)min	2	0.30
(^3MCeq 2)min	2	0.58^b
(^3MCeq 1)min	3	0.16

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On the basis of the computed TSs, both the ³MC_ax and ³MC_eq non-radiative decay paths display a trend in their energy barriers, diminishing on passing from 1 to 2 and to 3, which is in agreement with the experimentally observed decrease in the emission quantum yield. However, it is important to notice that in all cases, the energy barrier to reach the ³MC_eq minimum is significantly lower than the one for reaching the ³MC_ax state, being 0.15, 0.37 and 0.30 eV smaller for complexes 1, 2, and 3, respectively. In addition, it should be recalled that complexes 2 and 3 display very similar emission quantum yields (0.049 and 0.036), one order of magnitude lower than that of complex 1 (0.196). Therefore, similar decay barriers should be expected for complexes 2 and 3, significantly lower than that for complex 1. Looking at the ³MC_ax-mediated decays, the barrier for complex 2 is however much more similar to that of complex 1 (0.09 eV difference) than to the barrier for complex 3 (0.21 eV difference). Looking instead at the ³MC_eq-mediated decays, the barrier for complex 2 is much lower than that of complex 1 (0.31 eV lower), while the difference from complex 3 is not particularly pronounced (0.14 eV). Considering the higher accessibility of the ³MC_eq minima and the better agreement that their corresponding energy barriers display with respect to the experimental emission quantum yields, we can then assume that the ³MC_eq states will play a more prominent role in the photophysics of the here-studied complexes than the ³MC_ax structures.

As a final point, we found it instructive to evaluate the mentioned barrier on the basis of the obtained climbing image structures and the adiabatic energy differences (see Table S2†). Using the climbing image geometries, we obtained the same decreasing trend as that obtained employing the TSs, but, compared to the latter, the differences between the barriers of the different decay paths appeared much reduced. For instance, the energy difference between the ³MC_ax-mediated decay paths in complexes 1 and 3 (0.16 eV) is smaller than that obtained using the corresponding TSs (0.30 eV). A significant decrease is also observed between the ³MC_eq-mediated decay paths in complexes 1 and 3, although in this case, a clear difference is still appreciable (0.32 eV). Using the adiabatic energy differences between the ³MLCT and ³MC minima, again the same decreasing trend is obtained, but again significant differences with respect to the TS data emerged. For example, the same energy barrier now results in decaying along the ³MC_ax and ³MC_eq paths of complex 1, while for complex 3 the ³MC_eq decays will be very probable, with the ³MC_eq minimum being even lower than the ³MLCT structure. The comparison between the three different ways of evaluating the plausibility of a decay path highlights the importance of employing that through the characterization of the corresponding TSs, because even if the main feature (i.e., the decreasing trend) can be observed even when using the less accurate strategies, significant differences will however emerge.

Conclusions

In the present contribution, the main radiative and nonradiative decay paths for three Ir complexes, [Ir(ppy)₂(bpy)]⁺, [Ir(ppy)₂(pbpy)]⁺ and [Ir(ppy)₂(dpbpy)]⁺, have been theoretically studied by performing DFT-based calculations.

Despite their chemical similarities, complexes 2 and 3 show emission quantum yields one order of magnitude lower than that of complex 1 in CH₂Cl₂ solution. This has been previously explained as a consequence of the different abilities to decay non-radiatively through the so-called ³MC_ax states, characterized by a strong elongation of one Ir–N_ppy bond. On evaluating the barrier associated with this process by the characterization of the PES leading to the ³MC_ax minima, it has here emerged that a different ability to reach the ³MC_ax state is most probably not the main cause that determines the reported different emission yields. Instead, a non-radiative decay mediated by the so-called ³MC_eq states, characterized by a strong elongation of one Ir–N_bpy bond and the rotation of the respective pyridine ring leading to a five-coordinated trigonal–bipyramidal structure, appears to be more important in the photophysics of the studied complexes, in particular for complexes 2 and 3. In fact, the non-radiative decay path mediated by the ³MC_eq states is energetically more favorable than the one passing through the ³MC_ax states.

The present contribution is a clear example of the importance of MC states in the photophysics of cyclometallated Ir(III) complexes. Even more importantly, the study evidences the prominent role that equatorial MC states can play in the non-radiative decay of cyclometallated Ir(III) complexes, a role that, in the present case, appears to be more relevant than that of the axial MC states, despite the latter type of MC states being much more studied in the literature than the equatorial MC states. Knowing the importance of the non-radiative decay mediated by ³MC_eq states is fundamental information, since the formulation of complexes which do not favor the population of such states will in principle lead to better emission properties.

Author contributions

I. S.-D.: investigation, visualization, writing – original draft, writing – review & editing, formal analysis, and data curation; E. O.: methodology, project administration, resources, supervision, writing – review & editing, funding acquisition, formal analysis, and conceptualization; and A. G.: methodology, supervision, validation, writing – review & editing, formal analysis, and conceptualization.

Conflicts of interest

All the authors declare no conflict of interest.

Acknowledgements

The financial support by the MCIN/AEI of Spain (projects PID2021-128569NB-I00 and CEX2019-000919-M, funded by MCIN/AEI/10.13039/501100011033 and by “ERDF A way of making Europe”) and the Generalitat Valenciana (PROMETEO/2020/077 and MFA/2022/017) is acknowledged. The MFA/2022/017 project is a part of the Advanced Materials programme supported by the MCIN with funding from the European Union NextGenerationEU (PRTR-C17.I1) and by Generalitat Valenciana. A. G. is thankful to the MCIN/AEI for his Juan de la Cierva (IJC2018-035123-I) fellowship funded by MCIN/AEI/10.13039/501100011033 and by the “European Union NextGenerationEU/PRTR”. I. S.-D. also thanks Generalitat Valenciana for his predoctoral grant CIACIF/2021/438.

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Footnote

† Electronic supplementary information (ESI) available. See DOI: https://doi.org/10.1039/d3dt01404e

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