Article pubs.acs.org/IC
Comprehension of the Effect of a Hydroxyl Group in Ancillary Ligand on Phosphorescent Property for Heteroleptic Ir(III) Complexes: A Computational Study Using Quantitative Prediction Xiaolin Wang, Huiqing Yang, Yaping Wen, Li Wang,*,† Junfeng Li,*,‡ and Jinglai Zhang*,† †
College of Chemistry and Chemical Engineering, Henan University, Kaifeng, Henan 475004, P. R. China Division of Theoretical Chemistry and Biology, School of Biotechnology, Royal Institute of Technology, SE-106 91 Stockholm, Sweden
‡
S Supporting Information *
ABSTRACT: A new Ir(III) complex (dfpypya)2Ir(pic−OH) (2) is theoretically designed by introduction of a simple hydroxyl group into the ancillary ligand on the basis of (dfpypya)2Ir(pic) (1) with the aim to get the highefficiency and stable blue-emitting phosphors, where dfpypya is 3-methyl6-(2′,4′-difluoro-pyridinato)pyridazine, pic is picolinate, and pic−OH is 3-hydroxypicolinic acid. The other configuration (dfpypya)2Ir(pic−OH)′ (3) is also investigated to compare with 2. The difference between 2 and 3 is whether the intramolecular hydrogen bond is formed in the (dfpypya)2Ir(pic−OH). The quantum yield is determined by three different methods including the semiquantitative and quantitative methods. To quantitatively determine the quantum yield is still not an easy task to be completed. This work would provide some useful advices to select the suitable method to reliably evaluate the quantum yield. Complex 2 has larger quantum yield and more stability as compared with 1 and 3. The formation of intramolecular hydrogen bond would become a new method to design new phosphor with the desired properties. development of various ancillary ligands11,12 is an alternative express pathway to shift emissive wavelength. However, introduction of the substituent into ancillary ligand is rarely reported. Additionally, the phosphorescent efficiency and stability of blue phosphorescent dopant material are other two important items deserving of care in the real application of OLEDs. Yi et al. have reported that the formation of intramolecular hydrogen bonding in an ancillary ligand from a heteroleptic Ir(III) complex plays a vital role in improving the phosphorescent efficiency by introduction of a simple hydroxyl group in picolinate.13 Inspired by it, we would like to explore the influence of hydroxyl group incorporated into the ancillary ligand of (dfpypya)2Ir(pic) (see Figure 1) on the phosphorescent behavior and efficiency. It has been well-known that the detailed photophysical studies on structurally related complexes are essential to establish structure−property relationship. In the past decades, a great deal of theoretical studies were focused on the investigation of luminescence process for Ir(III) and Pt(II) complexes.14,15 However, the shortage of efficient method to evaluate the quantum efficiency is one of the key challenges in the field of theoretical research. Wu and co-workers employed the contribution of metal-to-ligand charge transfer (3MLCT)
1. INTRODUCTION As one of the potential candidates for next-generation flat-panel displays and solid-state lighting, organic light-emitting diodes (OLEDs) have attracted numerous attentions from both academic and industrial communities owing to the low fabrication cost, high intrinsic efficiency, and other special virtues.1,2 Among various promising phosphorescent emitters, Ir(III) complexes are of paramount importance, which is attributed to their high photoluminescence quantum yield (PLQY), short lifetime, and facile color tuning.3,4 To date, the scarcity of blue-emitting phosphorescent OLEDs (PhOLEDs) is the block stone to realize the full color display.5,6 Bis[2-(4,6-difluorophenyl)pyridinato-C 2 ,N](picolinato)iridium(III) (FIrpic) is a famous blue phosphor with the emitting wavelength of 468 nm.7 After that, numbers of Ir(III) complexes with general formula of Ir(C^NCH)2(L^X) are developed. Recently, Zhang et al. have synthesized two blueemitting Ir(III) complexes utilizing C^NN cyclometalated ligand as primary ligand with PLQY of 0.38 and 0.41, respectively.8 As compared to C^NCH ligand, the lack of H atom in vicinity N to the chelating N atom (i.e., pyridine vs pyridazine) results in the smaller steric hindrance between Ir and N atom. Finally, the stronger Ir−N bond would be expected, which is favorable to facilitating and refining the phosphorescent process. Besides alteration of the primary ligands,9 the incorporation of substituents into the primary ligand10 or © 2017 American Chemical Society
Received: April 17, 2017 Published: July 14, 2017 8986
DOI: 10.1021/acs.inorgchem.7b00946 Inorg. Chem. 2017, 56, 8986−8995
Article
Inorganic Chemistry
theory (ΔSCF-DFT) calculation28,29 in which the solvent effect is considered by the polarized continuum model (PCM) in CH2Cl2 solvent.30 The vibrationally resolved electronic emissive spectra, based on Franck−Condon principle, were calculated by B3LYP method. The kr, singlet−triplet splitting energy ΔE(Sn−T1), and SOC matrix element ⟨T1|HSOC|Sn⟩ were computed by the quadratic response theory in the framework of TDDFT with the B3LYP functional31,32 on the respective optimized geometries of possible emissive triplet states, which is implemented in the Dalton code.33,34 Meanwhile, linear response TDDFT theory was employed to calculate the transition dipole moment μ(Sn). At the same level, the SOC matrix element between ground state and the lowest triplet state was computed by the linear response TDDFT approach on the basis of the lowest tripletstate geometry. The Huang−Rhys factors for normal modes were performed by Franck−Condon calculation. To estimate the temperature-dependent nonradiative decay rate constant (knr(T)), the triplet potential energy profiles for the thermal deactivation process were constructed by location of the 3 MLCT/π−π* state, 3MC d−d state, transition state between 3 MLCT/π−π* state and 3MC d−d state, and minimum energy crossing point (MECP) between 3MC d−d state and S0 state, which were all optimized by the UB3LYP method. All the frequency calculations were performed by the same method to confirm that each configuration was a minimum/transition state on the potential energy surface. The same mixed basis set was employed for all calculations, that is, the “double-ζ” quality basis set consisting of Hay and Wadt’s effective core potentials (LANL2DZ)35,36 for the Ir atom and 6-31G(d)37 for all other atoms. All electronic computations were performed by the Gaussian 09 program except for the special mentioned.38 The SOC splits the emissive triplet manifold (Tem) into three sublevels, which are separated in energy in the absence of an external magnetic field. The radiative decay rate constants of three sublevels can be computed by the following equation:39
Figure 1. Sketch structures of all the investigated Ir(III) complexes.
character, singlet−triplet splitting energy, and the transition dipole moment to estimate the radiative decay rate constant (kr) and the energy difference between the lowest triplet excited state (T1) and metal-centered (3MC d−d) state to evaluate the nonradiative decay rate constant (knr).16,17 It is no doubt that there are great deviations or even contradictory results between theoretical estimated quantum yield and experimental result, since both kr and knr are qualitatively determined. Later, Minaev and coauthors calculated the accurate value of kr by the quadratic response (QR) time-dependent density functional theory (TDDFT) including spin−orbit coupling (SOC) account.18,19 Additionally, the potential energy profiles for the thermal deactivation process via 3MC d−d state have been explored by Lam et al. for the first time.20 Nevertheless, the quantum yield could still not be quantitatively confirmed because of the complicated nonradiative decay process. Recently, significant progresses have been made to quantitatively determine the PLQY. One method is that Escudero first predicted the PLQY on the basis of kr and activation barriers related with temperaturedependent nonradiative decay channel.21 The other method is to calculate the PLQY by evaluation of kr and knr.22 However, they are not suitable for all blue-emitting phosphors. In this work, quantum yields of three Ir(III) complexes are estimated by one semiquantitative and two quantitative methods. Our central goals are to design the more stable blue-emitting Ir(III) phosphors with high efficiency, to evaluate the quantum yields precisely, and to testify the suitability of reported equation.
kri = kr(S0 , Tiem) =
4α03 ΔES0 − Tiem 3 3t0
|M ji|2
∑
(1)
j ∈ {x , y , z}
i where ΔES0−Tem is the transition energy, t0 = (4πε0)2ℏ3/mee4, (me stands for the quality of electron, e represents the charge of electron), α0 is the fine-structure constant, and Mij is the electric transition dipole moment between the ground state and the ith sublevel of the emissive triplet state Tem. According to the perturbation theory, Mij can be expressed as40 ∞
Μij
=
∑
∧
E(Sn) − E(Tem)
n=0
2. COMPUTATIONAL DETAILS The ground-state (S0) geometries were optimized by the Becke’s three-parameter hybrid exchange functional combined with the Lee−Yang−Parr correlation functional (B3LYP) method.23,24 The first five triplet excited states were optimized by means of TD-B3LYP level of theory, which are served as an initial guess for the final UB3LYP optimizations. For these calculations, UDFT is preferred over TDDFT, since the latter fails to provide a balanced description of excited states of different characters, especially for excited states with pronounced charge-transfer (CT) character.25−27 On the basis of the optimized triplet excited states, the phosphorescence emissive wavelengths were simulated by the delta-self-consistent field density-functional
∧
i ⟨S0|μj |Sn⟩⟨Sn|HSO|Tem ⟩
j ∈ {x , y , z}
∞
+
∑ m=1
∧
∧
⟨S0|HSO|Tm⟩⟨Tm|μj |Tiem⟩ E(Tm) − E(S0) (2)
On the basis of the linear response theory, the transition dipole moment from the ith sublevel of triplet excited states and ground state can be evaluated, and the Cartesian components j ∈ {x,y,z} are employed to represent spin eigenfunctions. The operators μ̂ j and Ĥ SO represent the electric dipole and spin−orbit Hamiltonian, respectively. At ambient temperature or in the so-called high-temperature limit, the kr of triplet emissive state is determined by the average of kir values: 1 kr = 3 8987
3
∑ kri i=1
(3) DOI: 10.1021/acs.inorgchem.7b00946 Inorg. Chem. 2017, 56, 8986−8995
Article
Inorganic Chemistry
3. RESULTS AND DISCUSSION 3.1. Ground-State and the Lowest Triplet Excited-State Geometries. The stick models of ground-state structures optimized at the B3LYP level are plotted in Figure S1. All Ir(III) complexes present a distorted octahedral symmetry with N1 and N2 atoms from two pyridazine rings located at the inverse direction bearing the N1−Ir−N2 angle in a range of 175.91°− 175.99° (see Table S1). Other three unstable conformers are neglected directly.41,42 It is worth noting that the CO2···H−O bond distance is 1.61 and 3.63 Å for complexes 2 and 3, respectively, indicating that the intramolecular hydrogen bond is formed in complex 2. It has been testified that the bond length would be overestimated by B3LYP method because of its less proportion of Hartree−Fock exchange than PBE0 method (hybrid-type Perdew−Burke−Ernzerhof exchange correlation functional).43 The ground-state geometries are also optimized by PBE0 method with the same basis set (see Table S2). The maximum deviations of geometries between two methods are within 0.04 Å and 0.83° indicating the reliability of B3LYP method. Moreover, the B3LYP functional would be employed to perform subsequent TDDFT quadratic response calculations of the phosphorescence rate with SOC account involved in Dalton program. Thus, the B3LYP is finally chosen in this work to keep the consistency. To explore the phosphorescent properties, the triplet-state geometry is a more important item that is required to be cared for. On the basis of respective optimized triplet-state geometries, the triplet states are finally distinguished by the different energy levels and named by the distinct spin density plots, which is shown in Figure 2. Three, two, and three different triplet states are located for 1, 2, and 3, respectively. The distortion between triplet-state and ground-state geometries is not large except that some Ir−ligand (L) bonds are contracted in the triplet state. Correspondingly, the spin density would distribute over the Ir center and ligand being the shorter distance with the metal center. 3.2. Emissive Spectrum. On the basis of optimized tripletstate geometries, the phosphorescent emissive wavelengths are computed by the ΔSCF-DFT method in CH2Cl2 solvent. To get a more reliable result, the vertical transition energy is calculated by three different methods on the basis of the same geometries optimized at the B3LYP level of theory. The corresponding wavelengths are also listed in Table 1. For complex 1, the emissive wavelengths of both 3MLCT/3LCdfpypya2 (ligandcentered) state (2.58 eV/481 nm) and 3MLCT/3LCdfpypya1 state (2.59 eV/478 nm) calculated by M062X44 method are close to experimental value (2.51 eV/494 nm) with the maximum deviation of 0.08 eV, while the emissive wavelengths evaluated by other two methods are far away from the experimental values and out of the blue region. Thus, the M062X method is finally determined to calculate the emissive wavelengths of other two complexes. Besides the wavelength, the shape of emissive spectrum should also be considered to confirm the accuracy of the lowest triplet state, which is important to estimate the quantum yield in the next discussion. As shown in Figure S2, the calculated phosphorescent spectrum (red line) of 3MLCT/3LCdfpypya2 state for complex 1 agrees well with the experimental result with the half width at half-maximum (HWHM) of 700 cm−1, while the phosphorescent spectra of other triplet states (green line and blue line) obviously deviate from the experimental result with the smaller HWHM.
However, there is only one emissive wavelength reported in experiment for complex 1. Normally, most emissions are from the Kasha state. The emissions from non-Kasha state should be further confirmed.45 According to the following relationship46 D=
Φ(Tx) k (T ) = r x e[−ΔE(T1− Tx)/ kBT ] Φ(T) kr(T) 1 1
(4)
the emission would only come from the Kasha state when the D value is less than 1 × 10−2; the non-Kasha emission would be possible when the D value is more than 1 × 102; values between two limits would lead to the dual emission scenarios. In eq 4, Φ is the quantum yield; kr is the radiative decay rate constant; ΔE(T1−Tx) is the active energy between the higher-lying triplet state and the lowest triplet state; kB is the Boltzmann constant; and T is the room temperature. The kr is computed by the quadratic response TDDFT with B3LYP funtional on the optimized geometry of respective emissive triplet state, which is performed by the Dalton code.33,34 The D value of complex 1 is 0.14 for 3MLCT/3LCdfpypya1 state, which should follow the dual emission rule. In other words, the phosphorescent emissions from both 3MLCT/3LCdfpypya2 and 3MLCT/3LCdfpypya1 states are possible. However, the emission from 3MLCT/3LLCT (LLCT = ligand-to-ligand charge transfer) state of complex 1 is neglected by us, although its D value (0.09) is slightly larger than the lower limitation of 1 × 10−2. In this work, the ΔE(T1−Tx) is calculated by the energy difference between the higher-lying triplet state and the lowest triplet state, which is smaller than that of the actual active energy between them. If ΔE(T1−Tx) is further enhanced, D value is decreased correspondingly, which would be smaller than the limitation of 1 × 10−2. Additionally, the deviation between emissive wavelength of 3MLCT/3LLCT state and experimental result is much larger than that of other two states. Thus, only two triplet emissive states are considered for complex 1. They are almost degenerate states with the similar energy (2.58 vs 2.59 eV), which is difficult to be distinguished. It would be the reason that only one emissive wavelength is measured in experiment. On the basis of the same analogy, two emissions from 3MLCT/3LCdfpypya2 and 3MLCT/3LCdfpypya1 states (3MLCT/3LCdfpypya2 and 3MLCT/3LLCT states) are kept for complex 2 (3), respectively. The emission from 3 MLCT/3LCpic−OH state of complex 3 is not possible, because its D value is much smaller than 1 × 10−2. 3.3. Quantum Yields. The quantum yield is one of the most vital items to assess the performance of phosphors. The quantum yield is determined by the following relationship: ′ + k nr(T )) Φem = k r /(k r + k nr
(5)
where kr is radiative decay rate constant, knr(T) is temperaturedependent nonradiative decay rate constant, and k′nr is temperature-independent nonradiative decay rate constant. Considering different methods to determine the kr and knr, they are classified into the following three types. 3.3.1. Semiquantitative Determination of Quantum Yields. 3.3.1.1. Radiative Decay Rate Constant. The calculated triplet radiative decay rate constants were listed in Table 1. For the lowest triplet state, kr of complex 2 is the largest, which is favorable to improving the quantum yield. Since the phosphorescent emission follows the dual-emission scenarios, kr of the second-lowest triplet state should also be considered. The kr of 3 for 3MLCT/3LLCT state is larger than that of 1 and 2, while for the same triplet state the kr of 2 is comparable to that of 1. Considering that the lowest triplet state should play a more 8988
DOI: 10.1021/acs.inorgchem.7b00946 Inorg. Chem. 2017, 56, 8986−8995
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Inorganic Chemistry
Figure 2. Selected bond lengths (Å) in the optimized structures of S0, different triplet excited states, and 3MC d−d states of complexes 1 (a), 2 (b), and 3 (c). The computed spin density distributions at the B3LYP/6-31G(d)-LANL2DZ level are shown below each triplet state. Purple color represents the positive value that means α-electrons are more than β-electrons, and green color represents negative value. 8989
DOI: 10.1021/acs.inorgchem.7b00946 Inorg. Chem. 2017, 56, 8986−8995
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Inorganic Chemistry 3
MLCT/3LCdfpypya2 state. As to 1 and 3, the kr of 3 is larger than that of 1 owing to the comparable kr for 3MLCT/3LCdfpypya2 state and much larger kr for 3MLCT/3LLCT state. If the radiative decay rate constant is evaluated by qualitative means, the following items are taken into account, that is, the transition dipole moment μ(Sn), singlet−triplet splitting energy ΔE(Sn−T1), and SOC matrix element ⟨T1|HSOC|Sn⟩. On the basis of eq 2, the larger transition dipole moment and SOC matrix element associated with the smaller singlet−triplet splitting energy are beneficial for the relatively larger radiative decay rate constant. As shown in Table 2, the singlet−triplet splitting energy of S1 state for 2 is larger than that for 1 and 3. Moreover, it possesses the smaller transition dipole moment and SOC matrix element than 1 and 3. Combining all three factors, 2 has the smaller radiative decay rate constant than 1 and 3. Although the SOC matrix element of S1 state for 1 is larger than that for 3, 1 has the larger singlet−triplet splitting energy and the smaller transition dipole moment. Thus, it is difficult to determine the relative sequence of radiative decay rate constants for 1 and 3. Similarly, both transition dipole moment and SOC matrix element of S5 state for 2 are larger than those for 3, which is favorable to enhancing kr. However, the singlet−triplet splitting energy of S5 state for 2 is also larger than that for 3, which is detrimental for the radiative decay rate constant. In general, it is hard to determine the relative sequence of kr for three complexes, since no one has all advantageous items for every studied state. Certainly, the μ(Sn), ΔE(Sn−T1), and ⟨T1|HSOC|Sn⟩ of 1, 2, and 3 at the other optimized geometries of emissive state are also calculated, respectively, which are listed in Table S3. It is not an easy task to judge the one that has the larger radiative decay rate constant, because no one has the absolute superiority. The radiative decay rate constant determined by qualitative method is even difficult to provide a clear relative sequence. Thus, it is necessary to evaluate it by quantitative method. Certainly, the calculated radiative decay rate constant could not be directly compared with the experimental measured values. However, it could be expected that it would provide a reliable relative order for a series of similar complexes.
Table 1. Computed Adiabatic Relative Energies, Emission Wavelengths Calculated by Different Functions in CH2Cl2 Solvent, and Radiative Decay Rate Constant (kr) from the Possible Emissive States of Complexes 1, 2, and 3 Together with the Experimental Values8 1 3
MLCT/3LCdfpypya2
adiabatic relative energies [eV] ΔSCF-PBE0 [eV(nm)] ΔSCF-B3LYP [eV(nm)] ΔSCF-M062X [eV(nm)] kr (Tem → S0) [s−1] kr [s−1]a λexpt [eV(nm)]
3
MLCT/3LCdfpypya1
MLCT/3LLCT
3
0
0.076
0.126
2.29(542)
2.25(552)
2.63(472)
2.28(544)
2.24(554)
2.57(483)
2.58(481)
2.59(478)
2.94(421)
4.74 × 104 5.47 × 105 2.51(494)
1.26 × 105
5.47 × 105
2 3
MLCT/3LCdfpypya2
adiabatic relative energies [eV] ΔSCF-PBE0 [eV(nm)] ΔSCF-B3LYP [eV(nm)] ΔSCF-M062X [eV(nm)] kr (Tem → S0) [s−1] MLCT/3LCdfpypya2
a
MLCT/3LCdfpypya1
0 2.32(533) 2.32(535) 2.66(466) 7.35 × 104 3
3
adiabatic relative energies [eV] ΔSCF-PBE0 [eV(nm)] ΔSCF-B3LYP [eV(nm)] ΔSCF-M062X [eV(nm)] kr (Tem → S0) [s−1]
3
3
0.040 2.27(545) 2.27(547) 2.62(473) 9.91 × 104
MLCT/3LLCT
3
MLCT/3LCpic−OH
0
0.095
0.318
2.27(546)
2.58(480)
2.33(533)
2.26(547)
2.52(492)
2.39(519)
2.55(486)
2.89(428)
2.86(433)
4.22 × 104
4.46 × 105
4.28 × 102
kr stands for estimated value from experiment result.
crucial role in phosphorescent process, the kr of 2 is larger than that of the other two complexes due to the largest kr for
Table 2. Transition Dipole Moments μ(Sn) (Debye) for S0−Sn Transitions, Singlet−Triplet Splitting Energies ΔE(Sn−T1) (eV), and the SOC Matrix Elements ⟨T1|HSOC|Sn⟩ (cm−1) of 1, 2, and 3 at Their Respective T1 Optimized Geometries 1 S1 S2 S3 S4 S5 S6 S7 S8
μ(Sn)
ΔE(Sn−T1)
⟨T1|HSOC|Sn⟩
1.33 0.43 2.70 0.59 0.91 0.81 0.64 0.61
0.63 0.80 1.01 1.14 1.27 1.36 1.39 1.46
387.98 74.52 398.08 179.75 248.15 606.12 68.27 40.40
2 S1 S2 S3 S4 S5 S6 S7 S8
3
μ(Sn)
ΔE(Sn−T1)
⟨T1|HSOC|Sn⟩
1.04 0.35 2.63 0.81 1.48 0.45 0.61 0.94
0.64 0.87 1.06 1.18 1.27 1.43 1.47 1.56
373.37 95.53 379.34 302.90 474.35 227.66 25.38 24.81
S1 S2 S3 S4 S5 S6 S7 S8 8990
μ(Sn)
ΔE(Sn−T1)
⟨T1|HSOC|Sn⟩
1.46 0.46 2.22 1.17 1.45 0.35 0.49 0.50
0.60 0.75 0.96 1.10 1.15 1.27 1.30 1.35
375.19 107.07 361.20 117.28 312.70 14.23 87.19 88.15 DOI: 10.1021/acs.inorgchem.7b00946 Inorg. Chem. 2017, 56, 8986−8995
Article
Inorganic Chemistry 3.3.1.2. Nonradiative Decay Rate Constant. Case 1. The temperature-independent nonradiative decay rate constant k′nr is related with the deformation between S0 state and T1 excited state, which is expressed with the Huang−Rhys factor (Smax). As shown in Table 3, the Huang−Rhys factor decreases in the Table 3. SOC Matrix Elements ⟨T1|HSOC|S0⟩ (cm−1), Maximum Huang−Rhys Factor (Smax) of the Normal Modes, and Absolute Hardness η (eV) for All the Investigated Complexes 1 2 3 a
⟨T1|HSOC|S0⟩
η
Smax
knr (s−1)a
176.07 187.54 169.58
2.96 3.00 2.90
4.80 2.25 3.52
7.86 × 105
knr stands for calculated value from experiment result.8
order of 1 > 3 > 2. The Huang−Rhys factor plays a vital role in determining the k′nr, which would be mentioned several times. The accuracy of calculated Huang−Rhys factor for 1−3 is testified by the Duschinsky matrix, which is plotted in Figure S3. The smaller Duschinsky effect indicates the greater accuracy of Huang−Rhys factor. In addition, the intersystem crossing between T1 and S0 state accounts for the k′nr. The 3 has smaller SOC matrix element between S0 and T1 state than 1 and 2. Moreover, it has a smaller Huang−Rhys factor than 1. Consequently, the k′nr of 1 should be larger than that of 3. Although the SOC matrix element of 1 is smaller than that of 2, its Huang−Rhys factor is the largest. Thus, it is difficult to determine the relative sequence between 1 and 2. Similar result would also be suitable for 2 and 3. Besides the temperature-independent nonradiative decay process, the thermal deactivation of the emitting state via 3MC d−d excited state should also be discussed to deeply understand the nonradiative decay mechanism. Case 2. Temperature-dependent nonradiative decay rate constant knr(T). The triplet exciton has a possibility to convert from 3MLCT/π−π* state to 3MC d−d state, and then the 3MC d−d state would decay to the ground state by irreversible nonradiative decay process. The potential-energy profiles of the deactivation pathway from the 3MLCT/π−π* state to S0 state via the 3MC d−d state are constructed to deeply comprehend the nonradiative decay process, which is plotted in Figure 3. In the thermal viewpoint, the 3MC d−d state is not facile to be formed, because the transformation from 3MLCT/π−π* state to 3 MC d−d state is endothermic with the energy of 8.06, 8.25, and 7.52 kcal/mol for 1, 2, and 3, respectively. Moreover, the energy difference of 2 is larger than that of 3 indicating the more difficult formation of 3MC d−d state. Similarly, 2 has the largest energy barrier between 3MLCT/π−π* state and 3MC d−d state and between MECP and 3MC d−d state, which are both favorable to decreasing its knr(T). The structure of MECP is optimized using Gaussian 09 together with the code developed by Lu, which is a modified version of Harvey’s MECP program.47,48 The relevant structures are listed in Figure S4 together with the selected bond lengths. Combining three items, 2 has the smaller knr(T) than the other two complexes because of all three favorable items, that is, the largest energy differences between 3MLCT/π−π* state and 3 MC d−d state, between 3MLCT/π−π* state and transition state, and between MECP and 3MC d−d state. The knr(T) of 1 should be the largest due to the smallest barrier height between 3MLCT/π−π* state and 3MC d−d state and the smallest energy difference between MECP and 3MC d−d state. Combining temperature-independent nonradiative decay rate constant and temperature-dependent
Figure 3. Schematic potential-energy profiles of the deactivation pathway via the 3MC d−d state for complexes 1 (a), 2 (b), and 3 (c).
nonradiative decay rate constant (k′nr and knr(T)), the nonradiative decay rate constant of 2 is the smallest. In contrast, 1 has the largest nonradiative decay rate constant. Considering both kr and knr, the quantum yield of 2 is the largest owing to the larger kr and smaller knr. In contrast, complex 8991
DOI: 10.1021/acs.inorgchem.7b00946 Inorg. Chem. 2017, 56, 8986−8995
Article
Inorganic Chemistry 1 has the smallest quantum yield due to the smallest kr and the largest knr. Although the relative sequence of quantum yield is determined, its reliability is deserved to be considered. The final decision is reluctant to be made because of two reasons. One is that no complex has the absolute superiority for several items employed to determine the kr or knr. The other one is that the difference among various items is too small to distinguish them. Some differences are even in the acceptable computational error limitation. It is necessary to develop the quantitative method to make the more credible conclusion. Complex 2 has larger quantum yield than the other two complexes, which is mainly attributed to its smallest knr(T). The formation of intramolecular hydrogen bond would increase the rigidity of ancillary ligand, which could disturb the formation of trigonal bipyramid geometry. Sajoto et al. have stated that employment of rigid ligand that limits the degrees of freedom is one of the effective methods to inhibit the formation of 3MC d−d state.49 The population of 3MC d−d state is regarded as a crucial factor to determine the degree of knr(T), which predominates the nonradiative decay in blue-to-green phosphors especially in room temperature.49,50 In three investigated Ir(III) phosphors, the formation of 3MC d−d state for 2 is the most difficult because of the existence of intramolecular hydrogen bond. In contrast, the emissive lifetime would be greatly decreased if the intramolecular hydrogen bond is broken. Yi et al. have testified that if the intermolecular hydrogen bond is formed between Ir(III) complex and solvent, the emissive lifetime is greatly decreased.13 In addition, the intermolecular hydrogen bond would promote the dissipative process. The corresponding conclusion has also been testified in previous literature, such as in Ru(II) complex that is taken as the DNA probing, [Ru(phen)2dppz]2+, and [Ru(bpy)2dppz]2+.51,52 3.3.2. Quantitative Determination of Quantum Yields by Two Methods. 3.3.2.1. One Method. Recently, Escudero has reported the following simplified equation to compute the relative phosphorescent quantum yields at 298 K:21
Table 4. Activation Barriers (kcal/mol) for the TemperatureDependent Nonradiative Decay Channels, Prefactor x, Radiative Decay Rate Constant (s−1), and Calculated Quantum Yield 1 2 3
r1
lim1
Ebb
Ecc
Elimd
x
kr
Φcal
9.06 10.40 9.32
1.00 2.15 1.80
2.38 2.78 2.51
10.44 11.03 10.03
0.87 0.92 0.84
4.74 × 104 7.35 × 104 4.22 × 104
0.67 0.76 0.63
a
Ea stands for the difference between the T1 state and transition state. Eb corresponds to the difference between transition state and 3MC d−d state. cEc is the barrier height between 3MC d−d state and MECP. dElim value usually corresponds to Ea or Ec value, depending on the kinetic scenario. If the MECP barrier is above the transition state barrier, Elim is obtained according to Elim = Ea + Ec − Eb. b
independent nonradiative decay rate constant is neglected; (2) only the barrier height of rate-determining step is taken into account. 3.3.2.2. The Other Method. It is better to compute the kr and knr to directly determine the PLQY according to eq 5. In this work, we apply convolution method to obtain the nonradiative decay rates by considering that (1) the MLCT transition should cause a change in electron density on both the metal ion and ligand and the assumption of no frequency change between the T1 and S0 states should be removed; and (2) the Huang−Rhys factor for the low-frequency modes, Slf, are greater than 1, which means that the lf modes should be treated in the strong coupling limit. The lf modes are treated in the strong coupling limit, and the high-frequency (hf) modes are treated in the weak coupling limit. The knr is defined by the following relationship:55,56 2π ⟨T1|HSOC|S0⟩2 [2π ℏ2(D12 + P 2)]−1/2 ℏ ⎡ (ΔE − n ℏω − λ − μ)2 ⎤ Sn 00 M M 1 ⎥ × exp( − SM) M × exp⎢ − 2 2 2 nM! 2π ℏ (D1 + P ) ⎣ ⎦
k nr =
1 ⎛⎜ mjωj ⎞⎟ ΔQ j2 2⎝ ℏ ⎠
Sj =
k
x krx Φx (298 K) r1 = k E Φ1(298 K) x krx + (1 − x) Elimx
Eaa
∑ Sj
SM =
j ∈ hf
0≤x≤1
∑ Sjℏωj
λM =
(6)
j ∈ hf
where kr is radiative decay rate constant, x is prefactor, and Elim is the activation energy for the limiting step. The knr(T) is defined by the following expression: k nr(T ) = A exp( −E lim /kBoltzT )
λM SM
ℏωM =
(7)
λ1 =
SjℏωjS
∑
bj
j ∈ lf
Since the temperature-independent nonradiative decay rate constant is neglected, the expression (6) is equal to relationship (5). The Φ1 is the quantum yield for a specified complex, which has the highest PLQY and the largest Elim in all the investigated complexes. The Φx is the PLQY of unknown complex relative to that of the specified complex. In this work, (dfmppy)2Ir(pytz) (see Figure S5) is selected as the specified complex, while (dfpypy)2Ir(pic) is employed to obtain the correlation model between Elim and x (see Table S4) (where pytz is (1H-tetrazol-5-yl)pyridine, dfmppy is 2-(2,4-difluorophenyl)4-methylpyridine, pic is picolinate, and dfpypy is 4-methyl-2′,6′difluoro-2,3′-bipyridine).53,54 The fitting curve is plotted in Figure S6, in which the PLQY of (dfmppy)2Ir(pytz) is regarded as unit. On the basis of fitting model, the quantum yields of 1, 2, and 3 are 0.67, 0.76, and 0.63 (see Table 4). Although the PLQY is quantitatively determined by eq 6, there are two major disadvantages in this method to induce the mistakes: (1) the temperature-
μ=
1 2
∑ ℏωjS j ∈ lf
ℏ2D12 =
bj = nM =
bj
coth
ℏωjT 2kBT
⎛ ℏωS ⎞2 ℏωjT j S ∑ j⎜⎜ ⎟⎟ coth 2kBT bj ⎠ j ∈ lf ⎝
1 ℏP = 2 2 2
1 − bj2
2 ⎡ (1 − bj2) ℏωjT ⎤ S ⎢ ⎥ coth ∑ ⎢ℏωj 2kBT ⎥⎦ bj j ∈ lf ⎣
ωjT ωjS ΔE00 − λ1 − μ ℏωM
(8) 8992
DOI: 10.1021/acs.inorgchem.7b00946 Inorg. Chem. 2017, 56, 8986−8995
Article
Inorganic Chemistry in which ωjS(T) is the frequency of the jth normal mode of the S0 (T1) state; mj is the reduced mass of the jth normal mode; ΔQj represents the equilibrium displacement along the jth normal mode coordinate; ΔE00 is the zero-point energy difference between the T1 excited state and the S0 ground state; the frequency shift of the low-frequency modes between the T1 and S0 states, which could be quantified as bj = ωjT/ωjS; nM is corrected to the smaller integer due to it being the number of vibrational quanta of ℏωM; and σlf2 = ℏ2(D12 + P2) is the variance of the Gaussian approximation invoked in obtaining eq 8. On the basis of eq 8, the knr is calculated and listed in Table 5, with
complex. The PLQY is evaluated by three models, one semiquantitative and two quantitative methods. A number of parameters related to the kr calculation are reported, such as transition dipole moment, singlet−triplet splitting energy, and SOC matrix element. The temperature-independent k′nr is considered by Huang−Rhys factor and SOC matrix element between S0 state and T1 excited state. The temperaturedependent knr(T) is estimated by construction of the potential energy profiles for the thermal deactivation channel. The PLQY of complex 2 determined by three different models is higher than that of the other two complexes. Construction a hydrogen bond is a method to improve the PLQY, which paves a new avenue to build blue emissive phosphor. Moreover, the intramolecular hydrogen bond is also helpful to enhance the stability.
Table 5. Radiative Decay Rate Constant kr (s−1), Zero-Point Energy Difference between the T1 Excited State and the S0 Ground State E00 (cm−1), Nonradiative Decay Rate Constant knr (s−1), and Calculated Quantum Yields for the Studied Complexes as well as the Available Experimental Quantum Yield8 1 2 3
kr
E00
knr(298 K)
Φcal
Φexp
4.74 × 104 7.35 × 104 4.22 × 104
19 874.96 20 241.27 19 599.74
2.01 × 104 1.49 × 104 1.26 × 104
0.70 0.83 0.77
0.41
■
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.inorgchem.7b00946. The stick model of optimized ground state and MECP, phosphorescent spectra, Duschinsky matrix, molecular structures, and related data associated with model of predicting quantum yield, main optimized geometric parameters, and some important data related to calculation of knr (PDF)
relevant data enumerated Tables S5−S7. Some important parameters associated with the computation of knr are shown in Table S8. Combined with the kr of the lowest triplet state, the PLQY of each Ir(III) complex is quantitatively determined (see Table 5). The calculated PLQY of complex 1 is 0.70, which is slightly larger than the experimental measured result (0.41). The PLQY decreases in the order of 2 > 3 > 1. The PLQY of 2 is the highest from both the qualitative and quantitative viewpoints. Although the quantitative determination would provide the more direct and reliable result, it is not suitable for all investigated complexes. The eq 6 could only be applied to the blue-to-green phosphors, in which the temperature-independent nonradiative decay rate constant is regarded to be negligible, while the eq 8 would work well when a strong temperature dependence on knr could be observed. When using the convolution method, the temperature dependence could be a result of frequency shifts in the low-frequency modes, because they could be easily excited at room temperature. Thus, the qualitative determination is still an indispensable method to estimate the PLQY. Besides the high PLQY, the stability of blue emissive phosphor is also a key item to be cared for. The hardness is expressed by the relationship57,58
η = (IPa − EA a)/2
ASSOCIATED CONTENT
S Supporting Information *
■
AUTHOR INFORMATION
Corresponding Authors
*E-mail:
[email protected]. (L.W.) *E-mail: jfl
[email protected]. (J.-F.L.) *E-mail:
[email protected]. (J.Z.) ORCID
Li Wang: 0000-0001-6861-5982 Jinglai Zhang: 0000-0002-2728-0511 Notes
The authors declare no competing financial interest.
■
ACKNOWLEDGMENTS We thank the National Supercomputing Center in Shenzhen (Shenzhen Cloud Computing Center) for providing computational resources and software. We thank Dr. X. Tian (Chemical Engineering, Zhejiang Univ.) for providing an easy-to-use program written by himself to render Duschinsky Matrix. This work was supported by the National Natural Science Foundation of China (21376063, 21476061, 21503069, 21676071), Program for He’nan Innovative Research Team in University (15IRTSTHN005).
(9)
in which IPa is adiabatic ionization potential, and EAa is adiabatic electron affinity. The hardness of 2 is larger than that of 3 (see Table 3), indicating more stability. The formation of intramolecular hydrogen bond would not only improve the PLQY but also enhance the stability of phosphor. It provides a new pathway to design new complexes by a simple method rather than development of complicated ancillary ligand.
■
REFERENCES
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DOI: 10.1021/acs.inorgchem.7b00946 Inorg. Chem. 2017, 56, 8986−8995
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