Bond Fission and Non-Radiative Decay in Iridium(III) Complexes

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Bond Fission and Non-Radiative Decay in Iridium(III) Complexes Xiuwen Zhou,† Paul L. Burn,*,‡ and Benjamin J. Powell*,† †

School of Mathematics and Physics and ‡School of Chemistry and Molecular Biosciences, Centre for Organic Photonics & Electronics, The University of Queensland, Brisbane, Queensland 4072, Australia S Supporting Information *

ABSTRACT: We investigate the role of metal−ligand bond fission in the nonradiative decay of excited states in iridium(III) complexes with applications in blue organic light-emitting diodes (OLEDs). We report density functional theory (DFT) calculations of the potential energy surfaces upon lengthening an iridium−nitrogen (Ir−N) bond. In all cases we find that for bond lengths comparable to those of the ground state the lowest energy state is a triplet with significant metal-to-ligand change transfer character (3MLCT). But, as the Ir−N bond is lengthened there is a sudden transition to a regime where the lowest excited state is a triplet with significant metal centered character (3MC). Time-dependent DFT relativistic calculations including spin−orbit coupling perturbatively show that the radiative decay rate from the 3MC state is orders of magnitude slower than that from the 3MLCT state. The calculated barrier height between the 3MLCT and 3MC regimes is clearly correlated with previously measured nonradiative decay rates, suggesting that thermal population of the 3MC state is the dominant nonradiative decay process at ambient temperature. In particular, fluorination both drives the emission of these complexes to a deeper blue color and lowers the 3MLCT−3MC barrier. If the Ir−N bond is shortened in the 3MC state another N atom is pushed away from the Ir, resulting in the breaking of this bond, suggesting that once the Ir−N bond breaks the damage to the complex is permanentthis will have important implications for the lifetimes of devices using this type of complex as the active material. The consequences of these results for the design of more efficient blue phosphors for OLED applications are discussed.

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INTRODUCTION

Organic light-emitting diodes (OLEDs) based on iridium(III) [Ir(III)] complexes have attracted significant attentionfueled by the discovery of a near-unity photoluminescence quantum yield (PLQY) in fac-tris(2-phenylpyridyl)iridium(III) [Ir(ppy)3] and the demonstration of high-efficiency green OLEDs based on Ir(ppy)3.1 Highly efficient red OLEDs based on Ir(III) complexes have also been reported.2 However, blue Ir(III) phosphors with high PLQYs are limited to the sky blue region of the spectrum.2 Attempts to chemically tune these materials to the deep blue required for full color displays and white lighting applications have been made, but they often result in a dramatic drop in the PLQY.3−6 The decrease in the PLQY as phosphors are tuned to deeper blue results predominately from an increase in the nonradiative decay rates. For example, fac-tris(1-methyl-5-phenyl-3-n-propyl-[1,2,4]triazolyl)iridium(III) [Ir(ptz)3] (1) (shown in Figure 1) displays sky blue phosphorescence with a good ambient temperature PLQY (66%).3 Fluorination of Ir(ptz)3 can be used to tune the color from sky blue to deep blue. However, it also dramatically lowers the PLQY at room temperature.3,7 The radiative rates of all the complexes 1−4 (Figure 1) are found to be of the same order of magnitude, but the nonradiative rates vary significantly among the four complexes.3,7 © XXXX American Chemical Society

Figure 1. Structures of complexes 1−4 based on the parent fac-tris(1methyl-5-phenyl-3-n-propyl-[1,2,4]-triazolyl)iridium(III) (1). Fluorination on the ligand phenyl ring blue shifts the emission but results in a decrease in the measured PLQY (cf. Table 3).3,7

There has been a great deal of theoretical work aimed at understanding the nature of the low-energy excited states in Ir(III) complexes with applications in OLEDs.8 Two main strands of this work are relativistic (time-dependent) density functional theory (TD)DFT and model Hamiltonians. It has been demonstrated that density functional methods provide reasonable accuracy at relatively low computational cost7−15 and that model Hamiltonians provide significant insights into the trends observed across a broad range of materials.8,16−22 In Received: January 31, 2016

A

DOI: 10.1021/acs.inorgchem.6b00219 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry particular, the combination of these two approaches has provided an excellent understanding of the radiative properties of Ir(III) complexesparticularly the zero-field splitting and radiative rates of the three triplet substrates that are crucial for OLED applications. For example, TDDFT calculations accurately predict these properties for complexes 1−4. Furthermore, it has been shown that geometry relaxation in the excited state is crucial for understanding the radiative properties of Ir(III) complexes.11−16 Nevertheless, understanding nonradiative processes in Ir(III) complexes remains a major challenge. But, if one aims to rationally design more efficient blue OLEDs it is the problem that needs to be solved. A number of possible processes inducing nonradiative decay in phosphorescent cyclometalated complexes have been discussed, including both intra- and intermolecular processes: (i) Quenching of excited states to the ground state by intramolecular vibronic coupling.23−29 Previous studies have suggested that the nonradiative rate, knr, of many phosphorescent organo-transition-metal compounds (including d6 metal complexes similar to those discussed here) can be described by the energy gap law (EGL) due to intramolecular vibronic coupling.23−28 This law predicts an exponential decrease in knr with the increasing of the energy gap between the excited state and the ground state.30,31 The EGL arises when the nonradiative decay rate is determined, largely, by the vibrational overlap between the excited and ground states and the geometry changes between the ground and excited states are small (in a sense that can be made precise).30,31 For both organic molecules and organometallic complexes, the frequencies of the relevant vibrational modes, ω, are large compared to ambient temperature (ℏω ≫ kBT). Therefore, intramolecular vibrations tend to lead to a temperature-independent nonradiative decay rate.25,30,31 (ii) Nonradiative decay via a thermal population of nonradiative states.6,32−42 The emissive state of cyclometalated Ir(III) complexes, that is, the lowest triplet (T1) state, displays significant metal-to-ligand-chargetransfer (MLCT) character and will henceforth be denoted as 3MLCT. When a metal-centered state of dd* character (3MC state) lies close to 3MLCT, it may be thermally populated if the activation energy is sufficiently small. A thermal population of 3MC states could result in nonradiative deactivation pathways via distorted excited-state geometries.6,32,33,35−39 It has been argued that this temperature-dependent nonradiative process accounts for a number of transition metal complexes displaying phosphorescence with high PLQY at low temperature but having very low PLQY or even becoming nonemissive at room temperature.6,32,33,35−39 Van Houten and Watts43 proposed that a 3MC states play an important role in the decay process of [Ru(bpy)3]2+ on the basis of their temperature-dependent emission lifetime data. Specifically, they proposed that 3MLCT states transfer to 3MC states, and then the 3 MC states decay subsequently via ligand loss. However, there was no direct spectroscopic evidence for the energy levels of the proposed 3MC states. Treboux et al.32 and Yang et al.33 showed theoretically that 3MC states become more relevant in specific Ir(III) complexes on

lengthening Ir−ligand bonds. In particular, Treboux et al. showed that the activation barriers between 3MLCT and 3 MC states in Ir(ppy)3 and Ir(ppz)3 (ppz = 1phenylpyrazolyl) differ by several kilocalories per mole. Sajoto et al.6 reported that, in a series of closely related Ir(III) complexes, there is a significant activated component in the nonradiative decay rate. They ascribed this to the breaking of the Ir−N bond and showed theoretically that the T1 state is 3MC when this bond is broken. However, they did not investigate the bondbreaking mechanism in detail, calculate the activation barriers, or calculate the radiative rates once the Ir−N bond was broken. (iii) Finally, it has been proposed that there are several intermolecular interactions that may quench the emissive states. These include triplet−triplet annihilation,44,45 selfquenching,46 and impurity quenching (e.g., molecular oxygen).47 However, we will not investigate intermolecular interactions in this paper. In this work, we investigate the reaction paths to nonradiative states of models of the four Ir(III) complexes shown in Figure 1. We show that on lengthening an Ir−N bond the 3MLCT state changes to a 3MC state. We demonstrate a clear correlation between the calculated activation barrier between these states and the previously measured nonradiative decay rates of the complexes. We argue that, at room temperature, the decay via the thermal population of 3MC states is the dominant nonradiative decay process. However, we expect that at lower temperatures other (temperature-independent) processes will come to dominate resulting in a significantly lower nonradiative decay rate for all complexes. Furthermore, we show that once the 3MC state is populated, nonradiative decay proceeds via the breaking of an Ir−N bond. Shortening the Ir−N bond in the 3 MC state weakens and eventually breaks another Ir−N bond. Thus, the damage to the complex and the resultant loss of the ability to emit light is likely to be permanent. Thus, bond fission not only dominates nonradiative decay but may also be a key determinant of device lifetime.

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THEORETICAL CALCULATIONS Structure. Following our previous work,7 the structure of complex 1 was optimized taking the reported crystal structure3 as the starting point. The initial structures of complexes 2−4 were based on the optimized structure of complex 1 and then optimized with DFT.48,49 The n-propyl groups were removed for the following reasons: (i) This model has been used in the previous theoretical literature concerning these complexes and therefore facilitates easy comparison of our results with this body of work. (ii) Benchmarking calculations have shown that the effect of these groups on the photophysical properties of these complexes is small. (iii) The propyl groups are significantly more flexible than the rest of the complex. This makes the potential energy surface extremely soft but does not affect the features in the surface relevant to nonradiative decay. The 6-31G* basis set50 was used for hydrogen, carbon, nitrogen, and fluorine, and the LANL2DZ basis set51 with an effective core was used for iridium. The B3LYP functional52−54 was used throughout. Many of the low-energy excitations of the complexes studied here have significant MLCT character.8 It is well-known55−58 that the inclusion of Hartree−Fock exact exchange significantly improves the physical description of charge-transfer excited states of small molecules in B

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Table 1. Bond Lengths (Three Ir−N Bonds and Three Ir−C Bonds) and Orbital Energies of Complexesa 1−4 at Geometries Optimized for Ground State bond length (Å)

a

orbital energy (eV)

complex

Ir−N

Ir−C

HOMO

LUMO

LUMO+3

ΔEHOMO−LUMO

ΔELUMO−LUMO+3

knr[300 K] (s−1)3,7

1 2 3 4

2.15 2.18 2.16 2.16

2.05 2.03 2.04 2.03

−0.181 −0.192 −0.192 −0.203

−0.035 0.011 −0.040 −0.044

0.017 0.028 0.013 0.001

0.146 0.203 0.152 0.159

0.052 0.017 0.053 0.045

(3.1 ± 1.0) × 105 (5.8 ± 2.8) × 105 6.3 × 106 (6.5 ± 3.3) × 106

The measured room temperature non-radiative rate (knr) is also provided.

TDDFT59−61 calculations. Extensive benchmarking62 has shown that this is also true for Ir(III) complexes and that B3LYP accurately reproduces the energetics of these complexes.8 All calculations in this work were performed using the Gaussian 09 set of programs63 unless specified. Potential-Energy Surfaces. To find the activation barrier to thermally populated 3MC states, we first studied a selection of likely reaction paths. This survey indicated that lengthening the Ir−N bond was the most promising avenue for detailed investigation. This is consistent with the formally dative nature of these bonds, and the observations that the Ir−N bonds are longer than the Ir−C bonds in the ground state structures, and that the bonding energy of Ir−phenyl is greater than that of Ir− triazolyl. The idea that the Ir−N bond may be unstable is also consistent with previous reports.32,33,6 We therefore selected an Ir−N bond as the reaction coordinate for this study. We then performed a relaxed potential-energy surface (PES) scan for T1 state along the reaction coordinates. In the relaxed PES scan, the starting structure has the Ir−N bond length equal to that found in the optimized ground-state structure, and then a series of 0.1 Å increments were made in the Ir−N bond length. The geometry at each scan point is optimized subject to the constraint of this single bond length. The initial geometry for each optimization after increasing the Ir−N bond length took the position of the remaining atoms to be those found in optimized structure for the previous Ir−N bond length. The energy of the T1 state was then calculated with unrestricted DFT, since T1 contains open-shells of unpaired electrons. Unrestricted DFT is known to be quite good at modeling the properties of open-shell molecular systems: including spin polarization (in contrast the unrestricted Hartree−Fock approximation overestimates polarization) and energetics.64 In determining the triplet PES a quadratically convergent selfconsistent field (SCF) procedure65 was used, which is slower than regular SCF but is more reliable. In interpreting such PES curves, one should take careful note of how they are really calculatedin particular, one should recall that the self-consistent optimization of a molecular geometry only generates a local minimum and that the initial geometry in the optimization process affects which minima is found. This accounts for the history dependence of the optimized geometries that will be discussed below. However, chemistry is local and hence strongly history-dependent. We will argue below that these calculations capture important aspects of the nonradiative decay processes in these complexes. The energy of the lowest singlet (S0) state was also calculated with restricted DFT, both along the T1-PES described above and along the equivalent PES with the geometry calculated in the S0 electronic state. Radiative Rates. Relativistic calculations were performed for selected structures to obtain the radiative rate and more accurate information on electron excitations. In these

calculations, spin−orbit coupling (SOC) was included perturbatively to the results of one-component TDDFT calculations66 utilizing the one-component zeroth order regular approximation (ZORA).67−69 A total of 40 spin-mixed excitations were calculated. The calculations were performed with ADF (2013.01 version),70 using Slater-type TZP basis sets,71,72 and a frozen core approximation for the iridium [1s 2s 2p 3s 3p 3d 4s 4p 4d 4f], fluorine [1s], nitrogen [1s], and carbon [1s] shells.

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RESULTS AND DISCUSSION Correlation of Nonradiative Decay Rates with Ground-State Geometry/Electronic Structure. To understand the impact of fluorination on the ground-state geometry and electronic structure, key geometric parameters and orbital energy values are collated in Table 1. We note that there is no obvious correlation between the ground-state structure and the nonradiative rates. It has previously been shown7 that the lowest excitation is predominately a highest occupied molecular orbital (HOMO) to lowest unoccupied molecular orbital (LUMO) transition (∼70% weight). The T1 states of all four complexes have strong (∼50%) MLCT character, consistent with other organotransition-metal phosphors−this can be understood as the HOMO has strong mixed metal−ligand character, whereas the LUMO has negligible weight on the iridium.16 Given previous suggestions of the key role of 3MC states in nonradiative decay, the energy level of the d* orbitals of Ir are of significant interest. Indeed, pushing up the relative energy of the d* orbitals by ligand modification has previously been invoked as a design criterion for blue phosphorescent emitters.73−76 We can roughly analyze the energy of the d* orbitals by considering the lowest unoccupied orbital with significant orbital coefficients from the Ir. In their ground state geometries, we find that in all four complexes the fourth lowest unoccupied molecular orbital (LUMO+3) is the lowest energy unoccupied molecular orbital with significant orbital coefficients contributed from the Ir (cf. Figure 2). (Note that to a very good approximation the LUMO

Figure 2. Key molecular orbitals (HOMO, LUMO, and LUMO+3) of complex 4 at the geometry optimized for the ground state. The equivalent orbitals for the other complexes show the same trend, i.e., a significant metallic contribution to the HOMO and LUMO+3, but not to the LUMO (or LUMO+1 and LUMO+2). C

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Figure 3. PESs for complexes 1−4 as the Ir−N1 bonds is lengthened and the remaining atomic positions are optimized self-consistently. The curves labeled S0(S0) [black circles] show the energy of the S0 state when the geometry is optimized for the S0 state. The T1(T1) curves [large red diamonds] show the energy of the T1 state when the geometry is optimized for the T1 state. For both of these curves the geometry optimization took the optimized S0(S0) structure (without any bond length constraints) as the initial structure, cf. Table 1, and then increased the Ir−N1 bond length, relaxing the rest of the structure at each stage. The S0(T1) curves [black diamonds] show the lowest energy singlet state in the geometry optimized for the T1 state. The label MC above the T1(T1) curves indicate where the character of the T1 state changes (discontinuously) from predominately 3 MLCT to 3MC. The observed jumps in the energies suggest that there are multiple stable minima in the geometry relaxation. This is confirmed by performing a geometry relaxation in the T1 state starting from the first 3MC state and then shortening the Ir−N1 bond length and optimizing the structure in the T1 state at each point. We label the resultant PESs r-T1(T1) [small blue diamonds]. We will see below (cf., e.g., Figure. 5) that these lower energy states result from the breaking of a different Ir−N bond. Arrows indicate the scan direction of the curves.

Complex 4 with fluorine atoms located on the phenyl ring ortho and para to the triazole of each ligand presents the simplest case. The geometry found for the T1 state at the equilibrium bond length is similar to that found in the S0 state, with some relaxation.11−15 As the Ir−N1 bond is lengthened there is a single discontinuous change in the energy when it is 0.2−0.3 Å longer than at equilibrium. This is followed by a simple monotonically decreasing T1 PES until a soft minimum is reached at a bond length of ∼3.5 Å. Presumably, the suddenness of the drop is a consequence of the onedimensional PESs plotted. Below we give a more detailed analysis of this, which suggests that the calculations do reveal important aspects of the photophysics of these compounds. At this stage, we note that it is very natural for one-dimensional PESs (with all other coordinated optimized) to display the type of large drop we find if there is significant relaxation in the other coordinates between neighboring points on the PES. This change could either proceed continuously or be driven by the existence of multiple local minima in higher-dimensional PESs. We will show below that there are significant changes of other internal coordinates at this point, consistent with this scenario. Thus, one must be careful not to overinterpret the discontinuities in the one-dimensional PESs. Nevertheless, it is interesting to note that the curves closely resemble the free energy curves associated with spinodal lines77 near first order

+1 and LUMO+2 are the E analogues of the LUMO, which has A symmetry, when the complexes have C3 symmetry−as they do at equilibrium.) The relative energy of the LUMO+3 orbital to LUMO orbital is reported in Table 1. However, there is no clear correlation between the relative level of the d* orbitals (as measured by the ground state LUMO − LUMO+3 gap) and the nonradiative rates. Therefore, at least at this simplistic level, such analysis based on Kohn−Sham molecular orbitals does not provide a good design criterion and as such it is important to develop a more sophisticated understanding of the 3MC states in these complexes. Potential Energy Surfaces. The calculated PESs for Ir−N bond elongation are shown in Figure 3 (henceforth we denote the N that we control the bond length for as N1 and the equivalent N atoms on the other ligands as N2 and N3). In all four complexes we observe an initial, approximately quadratic, rise in the energy of both S0 and T1 as the Ir−N1 bond-length is increased and eventually a sudden drop in the energy of the T1 state concomitant with a sudden increase in the S0 energy is observed. However, the details of the PESs are importantly different in the different complexes. For sufficiently large Ir−N1 separation the energy of each complex decreases slowly with increasing Ir−N1 separation demonstrating that the Ir−N1 bond is broken. D

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the localization of the excitation to a single ligand−this is entirely consistent with the localization observed when the geometry of the T1 state in related complexes is optimized free of constraints.11 The first structure after the first transition state has clear dd* character−we therefore identify it as the 3MC state. Using the same strategy, we can identify the first structure after the first transition state on the T1 PESs of complexes 1 and 3 as 3MC states. For complex 2, the 3MC state is not found until after the second transition state. To analyze whether the 3MC states can decay radiatively, we performed the relativistic TDDFT calculations with spin− orbital coupling included perturbatively. We found that the lowest three electronic excitations are from the lowest triplet. The results in Table 2 show that for the 3MC geometries all three substates have very low excitation energies (∼1 eV) and small oscillator strengths (∼10−5). Moreover, the radiative rates (∼103 s−1) from the 3MC states are 2 orders of magnitude less than that of the 3MLCT states (∼105 s−1).7 Thus, the 3MC states have little possibility decaying to ground state radiatively. Activation Barriers, knr, and Photoluminescence Quantum Yield. Given the results above we postulate that the first activation barrier on the T1 PES is the key energy barrier between the emissive and dark states in complexes 1-4; the values of these barriers are given in Table 3. There is a simple relation between the activation barrier and the nonradiative rate of the four complexes: the larger the calculated barrier, the higher the measured nonradiative rate. Clearly this is consistent with decay via a 3MC state being the dominant nonradiative decay pathway at room temperature. To investigate this more deeply, we briefly discuss the quantitative relation of these two values. Neglecting intermolecular quenching, the quantum efficiency can be expressed as a function of radiative and nonradiative rates by43

phase transitions, which suggests that the discontinuities could be indicative of related physics in these finite (but large) systems. For the other complexes the T1 PESs are more complex showing additional activation barriers and multiple structural minima along the reaction coordinate. The discontinuous change in the optimized structure on the T1 PES is found after an Ir−N1 bond elongation of 0.5−0.6 Å, 0.4−0.5 Å, 0.2−0.3 Å, and 0.2−0.3 Å in complexes 1, 2, 3, and 4, respectively. Thus, this distance correlates with the measured nonradiative decay rate. For sufficiently large distortions in all four complexes the T1 state becomes lower in energy than the S0 state in the T1 optimized geometry (although not the S0 state in the S0 optimized geometry). Thus, there is no vertical transition at these geometries. This already suggests that in the bond broken state the radiative T1 to S0 transition will be strongly suppressed. Change in the Character of the T1 State from 3MLCT to 3MC. To investigate whether this reaction path is a nonradiative deactivation path, we analyzed the character of the T1 state along the reaction path. Since the lowest excited state is mainly composed of the HOMO−LUMO transition,8 analysis of the HOMO and LUMO provide key insights into the nature of the T1 excitation. Figure 4 shows the HOMO and LUMO

ΦPL(T ) =

k r(T ) k r(T ) + k nr1 + k nr2(T )

(1)

where ΦPL(T) is the temperature-dependent PLQY, kr(T) is the average temperature-dependent radiative rate, knr1 is the temperature-independent nonradiative rate, for example, due to vibronic coupling, and knr2(T) is the temperature-dependent nonradiative rate, that is, the rate of thermal population to an upper level (e.g., the 3MC state) that cannot decay radiatively. knr2(T) can be expressed in terms of the Arrhenius equation:37

Figure 4. Molecular orbitals of complex 4. first column: ground-state (GS) structure, 2nd column: 1st transition state (TS) on the T1(T1) PES in Figure 3, 3rd column: 3MC state found on the T1(T1) PES in Figure 3. Similar results are found for the other complexes.

k nr2(T ) = kae−ΔE / kBT

for three different geometries of complex 4: the ground state, the last 3MLCT state before the discontinuous change to a 3 MC state (which we henceforth refer to as the first transition state for brevity) and the first structure after the first transition state. The initial distortion to the first transition state results in

(2)

where ka is the rate constant, ΔE is the activation energy to the upper level, and kB is the Boltzmann constant. The exponential decrease in knr2(T) as ΔE increases implies that the differences in the activation energies of the four complexes changes the

Table 2. Calculated Excitation Energies (ε), Oscillator Strengths (f), and Radiative Rates (kr) of the Lowest Three Electronic Excitationsa of the 3MC States Found for Complexes 1−4 excitation 1 complex 1 2 3 4 a

ε (eV) 0.72 0.42 0.80 0.70

f 3 9 5 1

× × × ×

excitation 2 −1

kr (s ) −6

10 10−5 10−6 10−5

67 6.5 × 102 1.3 × 102 2.1 × 102

ε (eV)

f

0.72 1.24 0.80 0.71

2 4 1 9

× × × ×

excitation 3 −1

ε (eV)

kr (s ) −5

10 10−6 10−5 10−6

3.4 2.4 3.7 1.9

× × × ×

2

10 102 102 102

0.77 1.25 0.85 0.75

kr (s−1)

f 2 7 2 6

× × × ×

−4

10 10−6 10−4 10−5

5.2 4.4 5.7 1.4

× × × ×

103 102 103 103

That is, the three substates of T1. E

DOI: 10.1021/acs.inorgchem.6b00219 Inorg. Chem. XXXX, XXX, XXX−XXX

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Table 3. Calculated Activation Energy (ΔEactivation) to the 3MC States, Nonradiative Rate (knr) at 77 and 300 K Divided by Rate Constanta (ka), and the Measured Room-Temperature Nonradiative Rates (knr), Radiative Rates (kr), and Photoluminescent Quantum Yields (ΦPL) for Complexes 1−4 experimental3,7

calculated complex 1 2 3 4 a

ΔEactivation (eV) 0.375 0.384 0.066 0.065

knr[77K]/ka 2.7 7.3 4.7 5.4

× × × ×

−25

10 10−26 10−5 10−5

knr[300 K] (s−1)

knr[300 K]/ka 4.9 3.5 7.7 5.4

× × × ×

−7

(3.1 ± 1.0) × 10 (5.8 ± 2.8) × 105 6.3 × 106 (6.5 ± 3.3) × 106 5

10 10−7 10−2 10−2

kr[300 K] (s−1)

ΦPL [300 K]

(6.1 ± 0.8) × 105 (2.2 ± 0.9) × 105 4.0 × 105 (2.0 ± 1.6) × 105

0.66 ± 0.07 0.27 ± 0.05 0.06 0.03 ± 0.01

See eq 2.

Figure 5. Ir−N2 bond length relative to that of ground-state structure along the reaction path, for (a) lengthening and (b) shortening the Ir−N1 bond for complexes 1−4.

value of knr2(T) dramatically, as ka is expected to be of a similar magnitude in all four complexes. Comparison with the literature also suggests that thermal population of the 3MC state is the dominant nonradiative decay pathway at room temperature. Smith et al.7 predicted that kr(T) is of the same order of magnitude (∼5 × 105 s−1) in all four complexes for temperatures in the range of 70−300 K. The temperature-independent nonradiative rate knr1 of blue phosphors has been investigated by Sajoto et al.,6 who found that in their complexes knr1 < 4.0 × 104 s−1. If this carries over to complexes 1−4 it would imply that knr1 is an order-ofmagnitude smaller than kr(T) for temperatures in the range of 70−300 K. Hence, it appears that knr2(T) dominates the ambient temperature nonradiative decay for the four Ir(III) complexes investigated in the present work. Thus, it should be possible to predict, at least qualitatively, the room-temperature PLQY for new complexes based on Ir(ptz)3 via a calculation of the activation barrier to the 3MC states. (It has been demonstrated that kr can be predicted to an accuracy of better than a factor of 2.7,8) Our calculations, combined with previous results,7 lead to the prediction that ΦPL(T) at low temperature is much larger than that at room temperature for all four complexes. knr2 at 77 K is at least 3 magnitudes smaller than knr2 at 300 K for complexes 1−4 (Table 3). This suggests that knr1 becomes the dominant nonradiative process at low temperature; ΦPL(77 K) is predicted to have a value above 0.9 for all four complexes in marked contrast to their very different measured ΦPL(300 K), cf. Table 3. Of course, as we have only studied a single reaction coordinate in detail, our calculations represent an upper bound on the activation energy, which may modify this

prediction quantitatively. Nevertheless, the dramatic qualitative prediction is likely to be robust. Geometry, Electronic Structure, and Stability of 3MC States. To obtain important information about the geometry changes in the 3MC state relative to the ground-state structure, we monitored the length of the other five Ir−ligand bonds and the dihedral angle between the phenyl ring and triazolyl ring in each ligand, as one Ir−N bond is increasing (see Figures S1 and S2 of the Supporting Information). We note that the most significant changes occur in bond length between the Ir and the chelating N atom on another ligand (which we henceforth refer to as N2); see Figure 5a. The changes in the Ir−N2 bond lengths in 3MC state of complex 1−2 are less than that of complex 3−4. We note that the greater the structural distortion in 3MC state, the less the calculated activation barrier. This suggests the elongation of the Ir−N2 bond in the 3MC states plays an important cooperative role in the transition from the 3 MLCT state to the 3MC state. Our results also explain why some phosphorescent compounds exhibit higher PLQY in rigid host matrices than in fluid solutions.78 The rigid host environment may restrict the structural distortions and therefore lift the activation barrier to the 3MC states, resulting in a higher PLQY. We also note that the distortion in the structure in the 3MC state has subsequent effects on the electronic structure of the 3 MC state (cf. Figure 4). In particular, the π* orbitals of the ligands are no longer orthogonal with the Ir d-σ* orbitals as they are in ground state. And the electron density is transferred from the π* orbitals to the d-σ* orbital resulting the formation of a lowest triplet state with significant dd* character. F

DOI: 10.1021/acs.inorgchem.6b00219 Inorg. Chem. XXXX, XXX, XXX−XXX

Inorganic Chemistry

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To provide some insight into the fate of molecules in the MC state we investigated how the electronic and molecular structures change if one shortens the Ir−N1 bond starting from the 3MC state (the reverse process; Figures 3 and 5b). Surprisingly, we find that this procedure allows us to find a local structural minimum in the T1 states with strong MC character (Figure. 3). Indeed, at the equilibrium Ir−N1 bond length the 3MC state is lower in energy than the 3MLCT state! A first sight this result seems to be strongly contradicted by the large body of experimental evidence indicating that the lowlying excitations in this type of Ir(III) complex have significant 3 MLCT character.2,8 However, on comparing the molecular geometries of the 3MC and S0 states for the equilibrium Ir−N1 bond length it becomes clear that the calculations and experiment are not in contradiction; the relaxed 3MC geometry is very different from the relaxed S0 geometry and therefore optical excitation to the 3MC state is strongly Franck−Condon forbidden. Closer examination of the 3MC state geometry shows that, as the Ir−N1 bond is shortened, the Ir−N2 bond elongates (Figure 5b). That is, as one pushes one nitrogen atom closer to the Ir, another moves further away. There is no stable 3MC state close to the equilibrium geometry. This suggests that once the 3MC state is formed and an Ir−N bond is broken the complex will not be able to return to its equilibrium geometry without first relaxing to ground electronic state. Thus, we conclude that formation of the 3MC states will lead both to nonradiative decay and, most likely, permanent damage of any device based on the Ir(III) complex. 3

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Article

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.inorgchem.6b00219. Figures showing the most significant changes to the geometry of the complex as the Ir−N1 bond length varies, and listings of the Cartesian coordinates of the optimized ground-state geometry of complexes 1−4. (PDF)

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. (P.L.B.) *E-mail: [email protected]. (B.J.P) Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank M. Casida, E. Krenske, S. Olsen, and E. Moore for helpful discussions. X.Z. is supported by Swiss National Science F o u n d a t i o n ( Ea r l y P o st d o c M o bi l it y f e l lo w s h ip P2GEP2_155709). P.L.B. is supported by a Univ. of Queensland Vice-Chancellor’s Research Focused Fellowship. B.J.P. is supported by an Australian Research Council (ARC) Future Fellowship (FT130100161). This research was undertaken with the assistance of resources provided at the NCI National Facility systems at the Australian National Univ. through the National Computational Merit Allocation Scheme supported by the Australian Government, including Grant No. LE120100181.

CONCLUSIONS

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We have shown that increasing an Ir−N bond length of each of the four complexes studied here changes the nature of the lowest excited state from 3MLCT to 3MC. Adding SOC to our calculations shows that the radiative rate of the 3MC state is much weaker than that of the 3MCLT state. The calculated activation barrier to the 3MC state shows a clear correlation with the measured nonradiative decay rate. Given that previous work has established that TDDFT provides accurate predictions of the nonradiative process in these and related materialsthis discovery is an important step toward understanding, predicting, and engineering the PLQY of deep blue Ir(III) phosphors. We found that a simple calculation of the lowest molecular orbital with significant 3MC character at ground-state geometry does not predict, even qualitatively, knr. Our later results give a simple explanation for this. The 3MC state is stabilized by a significant geometry change, that is, from a sixfold coordinated Ir to a fivefold coordinated Ir. The energy of the 3MC state in the sixfold coordinated geometry is not relevant for understanding the energetics of the 3MC state that is the dark state responsible for nonradiative decay. Finally, a straightforward corollary of our results is that devices made from active materials with high PLQYs should have much longer (device) lifetimes than similar devices made from active materials with low PLQYs. Our results provide a simple explanation for this observation: the nonradiative decay process via the 3MC state requires the breaking of an Ir−N bond, which can lead to irreversible chemical decomposition.

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DOI: 10.1021/acs.inorgchem.6b00219 Inorg. Chem. XXXX, XXX, XXX−XXX