Complexes: An Integrated Computational Study of Radiative and

Mar 16, 2018 - the same kr value as 4, indicating the two extra −CH2 groups in the ancillary ligand do not exert any influence on the radiative deca...
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Cite This: Inorg. Chem. XXXX, XXX, XXX−XXX

Comprehensive Investigation into Luminescent Properties of Ir(III) Complexes: An Integrated Computational Study of Radiative and Nonradiative Decay Processes Yu Wang,† Peng Bao,*,‡ Jian Wang,† Ran Jia,† Fu-Quan Bai,*,† and Hong-Xing Zhang*,† †

International Joint Research Laboratory of Nano-Micro Architecture Chemistry, Laboratory of Theoretical and Computational Chemistry, Institute of Theoretical Chemistry, Jilin University, Changchun 130023, People’s Republic of China ‡ Beijing National Laboratory for Molecular Sciences (BNLMS), State Key Laboratory for Structural Chemistry of Unstable and Stable Species, Institute of Chemistry, Chinese Academy of Sciences, Zhongguancun, Beijing 100190, People’s Republic of China S Supporting Information *

ABSTRACT: A comprehensive and concrete exploration into the deactivation mechanisms of luminescent materials is imperative, with the improvement of simulating and computing technology. In this study, an integrated calculation scheme is employed on five Ir(III) complexes for thorough investigation of their photophysical properties, including radiative (kr) and nonradiative (knr) decay rates. As a most famous Ir(III) complex with superior quantum efficiency, facIr(ppy)3 herein serves as a reference relative to the other four β-diketonate complexes. Both temperature-independent and temperature-dependent knr are taken into account quantitatively for the first time, to unearth the role of different ancillary ligands in the determination of luminescent properties. Since the validated calculations of kr for the five complexes are of the same order of magnitude, the nonemissive peculiarity of 4 is caused by large knr. The newly designed compound 5, which simply has two more −CH2 groups than 4 in the ancillary ligand, further manifests that the reason for large knr in molecule 4 should be attributed to the ligand resonance caused by great π conjugation.

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INTRODUCTION Organic light-emitting diodes (OLEDs)1,2 are excellent candidates among highly efficient electroluminescent devices due to their wide applications in both soft and solid-state lighting realms.3−6 As the so-called second generation of OLEDs, phosphorescent-based OLEDs (phOLEDs) are the most widespread devices, owing to their attainable almost 100% internal electroluminescence quantum efficiencies,7 as well as their self-assembled characters.8 This scenario is known as “triplet harvesting” especially for heavy-transition-metal complexes,9 in virtue of the “heavy-atom effect” which gives rise to large spin−orbit coupling (SOC).10,11 It is demonstrated that, in addition to the “heavy-atom effect”, the rates of electronic transitions also rely on the energies, electronic configurations, and nuclear structures of triplet excited states.12 Several factors that can essentially determine the phosphorescent efficiency are summarized as follows: (i) the energy gap between singlet and triplet excited states,13 (ii) the oscillator strength, f (or the transition dipole moment μ), of the singlet excited states from which the triplet excited state borrows intensity,13 (iii) the energy gap between excited and ground states, abiding by the “energy gap law” (EGL),14 (iv) the structure distortion degree of the excited state relative to the ground state,15 and (v) the probability of transforming into a dark metal-centered (MC) excited triplet state from the emissive triplet excited state.16 © XXXX American Chemical Society

Notably, cyclometalated iridium complexes are the most preferred phOLEDs due to their chemical stability, high phosphorescent efficiency, and attainable red to blue color emitting and have been extensively investigated in both experimental and theoretical fields.17−22 A widely known example is the green-emitting complex fac-Ir(ppy)3 (1; ppy = 2-phenylpyridine), which was reported by Watts and coworkers in 1991.23 From then on, vastly improved iridium complexes sprang up mainly based on the tris-cyclometalated fac-Ir(ppy)3. Through introduction of functional or bulky groups on cyclometalating ligands, tris-cyclometalated homoleptic iridium compounds have been synthesized with different specialties, such as various color emission and concentration quenching minimization.24−26 With consideration of the tradeoff between stability and reactivity in homoleptic complexes, heteroleptic complexes are growing to be the focus of investigations. Note that the ancillary ligands in heteroleptic complexes could make the synthetic approach more efficient and competitive.27 Additionally, heteroleptic iridium compounds, such as the representative Ir(ppy)2acac (2; acac = acetylacetonate) and Ir(ppy)2tmd (3; tmd = 2,2,6,6tetramethyl-3,5-heptanedionate), have a relatively high phosReceived: March 16, 2018

A

DOI: 10.1021/acs.inorgchem.8b00705 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry phorescent efficiency.28 It has been established that the phosphorescence of iridium complexes stems from the lowest triplet excited (T1) states, which is a metal-to-ligand charge transfer (MLCT) character mixed with a intraligand (IL) character.29 Experimental results revealed that heteroleptic complexes, such as the aforementioned complexes 2 and 3, exhibit room-temperature phosphorescence similar to those of the tris-cyclometalated complexes, which suggest a dominant role of cyclometalating ligands in the luminescence of these heteroleptic compounds.30 Accordingly, much attention has been paid to modify cyclometalating ligands, for the sake of improving the quality of charge transfer transitions.31,32 Nevertheless, under some circumstances, the ancillary ligands can also play a decisive role in phosphorescent efficiency. For example, Ir(ppy)2phen (phen = 1,10-phenanthroline)33 has a charge-transfer character centered on its ancillary phen ligand. However, the decisive role played by ancillary ligands in luminescence can also have side effects. The complex Ir(ppy)2dbm (4; dbm = 1,3-diphenyl-1,3-propanedione), which has ancillary-ligand-dominant charge-transfer character, is nonemissive, though it bears the same cyclometalating ligand as complexes 2 and 3.28 How do the subtle differences in ancillary ligands decide the final luminescent efficiency? Previous explanation of the nonemissive Ir(ppy)2dbm is that the emission from a lower triplet dbm-based excited state results in inefficient phosphorescence.28 However, such an obscure interpretation does not make it clear in which way the dbm-based excited state hinders phosphorescent emission. To present a more convincing explanation, the compound Ir(ppy)2dpd (5; dpd = 1,5-diphenylpentane-2,4-dione) has been constructed by appending two saturated methylene spacers in the dbm ancillary ligand of complex 4 as shown in Figure 1. Through analyzing and comparing among the five iridium complexes mentioned above, we probe the relationship between molecular structure and luminescent efficiency.

ular photophysical processes.34 Recently, ab initio and density functional theory (DFT) studies have provided concrete information regarding the deactivation mechanisms of kr and knr in target phosphors,35,36 which serve as powerful resources for us in the investigation of rthe elationship between molecular structure and photophysical properties. Herein, an integrated computational scheme is employed on the chosen five iridium complexes, to probe into the influence exerted by subtle changes of ancillary ligands on photophysical properties from a molecular level. Among the five complexes, fac-Ir(ppy)3 serves as a reference, since it has the highest quantum efficiency and has been the most intensely studied.37−39 Under the integrated calculation scheme, we have comprehensively and systematically investigated the deactivation mechanisms in both radiative and nonradiative processes of these five complexes. In particular, for the assessment of knr, for the first time both temperature-independent and temperature-dependent processes are taken into consideration quantitatively. With regard to temperature-independent knr, a quantitative convolution method is applied.40 In addition, for temperature-dependent knr(T), the quantitative estimation proposed by Escudero is employed.41

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COMPUTATIONAL DETAILS

It is known that the luminescent efficiency of a molecular material determines its application values. Hence, deteriming the issue of luminescent efficiency is necessary. Theoretically, phosphorescent luminescence quantum efficiency can be expressed as Φphos(T ) =

kr k r + k nr + k nr(T )

(1)

It can be seen that the quantum efficiency mainly depends on the radiative decay rate kr, the nonradiative temperature-independent decay rate knr, and the nonradiative temperature-dependent decay rate knr(T). In this work, a comprehensive calculation of these three dominating factors is implemented quantitatively. Radiative decay rate. The expression of kr embodies the transition rate constant. Under the premise of the Born−Oppenheimer approximation, the radiative decay rate constant from the T1 excited state to S0 ground state can be further simplified within perturbation theory. The final three main factors determined kr can be expressed as15,42

k rα(T1→S0)

1/2 ⎫2 ⎧ ⎪ ⟨T1α|HSOC|Sn⟩ ⎛ fn ⎞ ⎪ η2 3 = E(T) ⎜ ⎟ ⎬ ∑ 1 ⎨ ⎪ ⎪ 1.5 1 ⎝ E(Sn ) ⎠ ⎩ n E(Sn) − E(T) ⎭

=

⎧ ⎫2 ⟨T1α|HSOC|Sn⟩ 1/2 ⎪ η2 ⎪ ⎨ ⎬ f ∑ n ⎪ 1/2 1.5 ⎪ ⎩ n χn (χn − 1) ⎭

(2)

where ⟨Tα1 |HSOC|Sn⟩ is the SOC integral from three sublevels (α = x, y, z) of the T1 state and the coupled Sn state, η is the refractive index of the medium, f n represents the oscillator strength, and χn is the energy ratio between excited coupling states Sn and T1, namely E(Sn)/E(T1). The energy shift of spin sublevel α in the T1 state can be expressed as

Figure 1. Chemical structures of compounds 1−5.

At present, a thorough investigation of the fundamentals in photophysical properties from a theoretical perspective is essential and indispensable, especially upon evaluating novel material properties prior to synthesis. With the rapid development of the computational industry, theoretical methods have extended the application domains from qualitative assessment to quantitative interpretation of molec-

ΔE(T1α) =

∑ n

|⟨T1α|HSOC|Sn⟩|2 E(Sn) − E(T) 1

(3)

and the zero-field splitting (ZFS) parameter can be obtained as the difference in energy shifts between spin sublevels. For a system of three excited substates, the averaged radiative decay rate, with consideration of the ZFS, can be expressed as43 B

DOI: 10.1021/acs.inorgchem.8b00705 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry ΔE I,II

k r,av(T1→S0) =

DFT and TDDFT Calculations. Throughout this work, the hybrid functional B3LYP,51,52 which has been widely and credibly implemented in calculating iridium complexes,53−56 was employed for all calculations performed with the Gaussian 09 program.57 For the basis set, 6-31G* was adopted for all atoms, and LanL2DZ accompanied by a relativistic effective core potential (ECP) with 18 valence electrons proposed by Hay and Wadt58 was employed for the Ir atom. Geometry optimization for the S0 state was carried out using the restricted density functional theory (RDFT), and that for the T1 state as well as the transition state (TS) and MC state was carried out using unrestricted density functional theory (UDFT). The nature of stationary points was confirmed by vibrational frequency calculations at the same level of theory. The MECPs between the relevant potential energy surfaces were calculated using Gaussian09 together with the code developed by Harvey et al.59,60 All of the geometry optimizations took into account the solvent effect of dichloromethane (CH2Cl2), which was simulated by using the polarized continuum model (PCM).61 Time-dependent DFT (TDDFT) calculations were performed with the Amsterdam Density Functional (ADF) 2016.104 program62,63 based on the optimized structure using the B3LYP functional with a Slater type all-electron triple-ζ basis with polarizations (TZP).64,65 One-component zeroth-order regular approximation (ZORA)66,67 TDDFT calculations, with the perturbation of SOC included, were performed on the 10 lowest scalar relativistic singlet and triplet excitations. Including SOC as a perturbation can give essentially the same results, in comparison with the more expensive two-component method.68,69 Moreover, the conductor like screening model (COSMO) of solvent with CH2Cl2 was taken into account in TDDFT calculations.70 The reorganization energy and Huang−Rhys factors were obtained from a normal-mode analysis approach with the DUSHIN program.71

ΔE I,III

( ) + k exp(− ) 1 + exp(− ) + exp(− )

kI + kII exp −

III

kBT

kBT

ΔE I,II

ΔE I,II

kBT

kBT

(4)

where kI, kII, and kIII present the individual decay rates of the triplet sublevels I−III, which are ordered by energy, ΔEI,II, ΔEI,III are the energy intervals between the substates, and kB is the Boltzmann constant. At room temperature, the expression can be approximated to the averaged triplet radiative decay, due to the usual small ZFS for heavy-metal complexes:40 RT k r,av (T1→S0) =

1 3

∑ krα

(5)

α

Nonradiative Decay Rate. The temperature-independent nonradiative decay rate knr is related to factors including SOC integral, energy gap, and the degree of structural deformation between T1 and S0 states, which can be calculated under Fermi’s golden rule with Condon approximation.44 The convolution method40,45 employed in this study for the assessment of knr can serve as an improvement of the traditional EGL method.46 This convolution approach takes more consideration of the low-frequency region in electron transitions from excited states to the ground state, and thereby more temperaturedependent factors are taken into account. Such a convolution method can be formulated as

2π ⟨T1|HSOC|S0⟩2 [2π ℏ2(D12 + P 2)]−1/2 ℏ ⎡ (ΔE − n ℏω − λ − μ)2 ⎤ S nM 00 M M 1 ⎥ exp(− SM) M exp⎢ − 2 2 2 nM! 2π ℏ (D1 + P ) ⎣ ⎦ knr(T1→S0) =

μ=

1 2

ℏ2D12 =

∑ ℏωjS j ∈ lf

bj

coth

■

ℏωjT

RESULTS AND DISCUSSION Electronic Transition Properties. The energy levels of selected frontier molecular orbitals (FMOs) of compounds 1− 5 are depicted in Figure 2. Detailed profiles of selected FMOs

2kBT

⎛ ℏωS ⎞2 ℏωjT j ⎟ coth ⎟ 2kBT ⎝ bj ⎠

∑ Sj⎜⎜ j ∈ lf

1 ℏP = 2 2 2

where Sj =

1 − bj2

1 2

2 ⎡ (1 − bj2) ℏωjT ⎤ S ⎥ ⎢ coth ∑ ⎢ℏωj 2kBT ⎥⎦ bj j ∈ lf ⎣ mjωj

( )ΔQ ℏ

j

(6)

is the Huang−Rhys factor of the jth normal

mode, SM = ∑j∈hf Sj, λM = ∑j∈hf Sjℏωj is the reorganization energy in the high-frequency region, λ1 = ∑j ∈ lf energy in the low-frequency region, bj =

SjℏωjS bj ωjT ωjS

is the reorganization

; ℏωM =

∑j ∈ hf Sjℏωj ∑j ∈ hf Sj

, hf and

−1

lf represent the high-frequency region (1000 < ωhf < 1700 cm ), and the low-frequency region (ωlf ≤ 1000 cm−1), respectively, E00 is the zero-point energy difference between T1 and S0 states, and nM is the number of vibrational quanta of ℏωM, where the value is corrected to the smaller integer. Other items in the equation can be referred to ref 40. The main improvements in the adopted methods in comparison with EGL are the general consideration of the frequency deflection between T1 and S0 states and the Huang−Rhys factors are treated in the strong coupling limit at the low-frequency region. When it comes to the nonradiative temperature-dependent decay constant knr(T), the kinetic factor, namely the energy barrier between the T1 state and the MC state, as well as the energy gap between MC state and the minimum energy crossing point (MECP) should be taken into consideration. Accordingly, a simplified formula put forward by Escudero was carried out (vide infra). In addition, the transition rate constants from the T1 state to the MC state are also computed using conventional transition state theory (TST),47,48 with the consideration of one-dimensional Wigner tunneling (WT),49 as implemented in the KiSThelP program.50

Figure 2. Energy levels of selected frontier molecular orbitals and natural transition orbital analysis of the S0 → T1 transition for complexes 1-5 at their optimized ground states. The dotted arrow represents the largest T1 transition.

are presented in Figures S1−S5. It can be seen that all complexes have a similar electron density distribution of the highest occupied molecular orbitals (HOMOs). For the lowest unoccupied molecular orbitals (LUMOs), complex 4 has the electron density residing in its dbm ancillary ligand, which is consistent with previous studies,72 while others have the electron density located on ppy cyclometalated ligands. C

DOI: 10.1021/acs.inorgchem.8b00705 Inorg. Chem. XXXX, XXX, XXX−XXX

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complex 4 has a different transition character from the others of 1 MLCT/1LLCT (where LLCT means ligand to ligand charge transfer). The unique property of complex 4 is due to the lower energy of its ancillary ligand that renders its nonemissive character at room temperature. Radiative Decay. The phosphorescent properties of the five complexes have been theoretically evaluated via eq 2, on the basis of the optimized structures of their emissive states. Tables S7−S12 give the major singlet−singlet and singlet− triplet transitions of 1−5 for the assessment of radiative decay constants. In this study, the first 10 singlet excited states are considered in the SOC formalism. The calculated radiative rate constants kr are shown in Table 2. All five compounds have the same order of magnitude in calculated kr and compare satisfactorily with those found in experiments (kr,exp = ϕem/ τem), which fully demonstrated the feasibility of the current computational protocol. According to eq 2, three main factors govern the radiative rate constant. They respectively are SOC matrix elements ⟨Sn| HSOC|T1⟩, the energy ratio χn between the coupling Sn and T1 states, and the oscillator strength f n of the Sn → S0 transition. Herein, the SOC integrals between excited T1 and Sn states are computed through one-component scalar relativistic ZORA TDDFT calculations. Since the one-electron SOC constant for the Ir(III) 5d electron (ξc = 4430 cm−1)75 is significantly larger than that of other atoms in complexes 1−5, the SOC strength may be approximated considering only the d electrons in the iridium atom. Therefore, an increased portion of iridium d in the molecular orbitals associated with the T1 state may enhance the SOC integrals. Under the simplified SOC elements, the electronic configuration [(d)1(π*)1]3 of the T1 state can only effectively couple with those Sn states possessing specific [(d)1(π*)1]1 configurations involving different d orbitals and a common π* orbital.35 To further illustrate the radiative decay process, three main factors that govern kr mentioned above of selected singlet excited states coupled with the T1 state for the five complexes are displayed in Table 2. It is noted that the strongest SOC of each complex occurs mostly between T1 and S2 or between T1 and S3 states; the reasons rely not only on the greater d orbital constituent involved in coupling states (see Tables S13−S17) but also on the larger CI coefficient in comparison to other coupling excited states. In addition, the T1 and S1 states have

Moreover, detailed FMOs reveal that, for complexes 2, 3, and 5, their ancillary ligand electron density distributions appear on LUMO+2 or LUMO+3 orbitals. From the same type of π* orbitals of these compounds, the energy of the dbm ancillary ligand dominating the unoccupied orbital is the lowest, as can be seen in Figure 2. On comparison of complexes 4 and 5, when the great π conjugation in the ancillary ligand of 4 is broken through adding two −CH2 groups, the energy of the ancillary ligand dominating orbital in 5 improved greatly. Natural transition orbital (NTO) analysis of essential transition characters from S0 to T1 state is depicted in Figure 2. Table 1 gives important transitions for the emissive T1 states Table 1. Major Transitions of the Emissive T1 States for Complexes 1−5 at Their Optimized Ground-State Geometries complex

excitationa

contribution (%)

1

H→L H-1 → L+2 H-2 → L+1 H→L H-2 → L+1 H→L H-2 → L+1 H-1 → L H→L H-2 → L+1

48 12 12 73 15 76 13 92 73 15

2 3 4 5

character 3

MLCT/3IL 3 MLCT/3LLCT 3 MLCT/3LLCT 3 MLCT/3IL 3 MLCT/3LLCT 3 MLCT/3IL 3 MLCT/3LLCT 3 MLCT/3IL 3 MLCT/3IL 3 MLCT/3LLCT

a

Orbitals involved in the major trnasitions (H = HOMO and L = LUMO).

of complexes 1−5. The major transitions are all HOMO → LUMO with 3MLCT/3IL character focused on ppy ligands, except for complex 4, for which the main transition is HOMO− 1 → LUMO that also has 3MLCT/3IL character, but focused on its dbm ligand. In consideration of long-range separation of charge transfer in molecule 4, the hybrid functional CAMYB3LYP73 is also used to judge the rationality of functional B3LYP. The result shows that the major transition of the T1 state in complex 4 has the same property as the results reported by B3LYP (see Table S1). Selected singlet−singlet transitions are given in Tables S2−S6. It can be seen that the S1 state corresponds to the HOMO → LUMO transition for 1−5, yet

Table 2. Energy Ratios between Coupling Sn and T1 States, Oscillator Strengths of Transitions from Sn to S0 State, SOC Matrix Elements ⟨T1|HSOC|Sn⟩ (cm−1) of Complexes 1−5 and Their Calculated Radiative Decay Rates kr (×105 s−1) at 298 and 77 K, Respectively,a as well as the ZFS Parameters (cm−1) 1 2 3 4

5

Sn

χn

fn

⟨T1|HSOC|Sn⟩b

kr(298 K)

kr(77 K)c

ZFS

S2 S3 S3 S7 S3 S6 S2 S4 S5 S3 S7

1.30 1.32 1.39 1.55 1.36 1.55 1.50 1.62 1.65 1.39 1.55

0.0338 0.1818 0.0298 0.0699 0.0202 0.1044 0.0347 0.0175 0.1308 0.0261 0.1267

424 388 530 318 526 456 516 303 460 521 444

4.87 (5.63d)

2.33 (2.43e)

96.58

1.16 (2.13f)

1.12 (1.06f)

20.62

1.38

0.75

86.83

1.59

0.29

171.79

1.57

0.98

73.08

Data in parentheses are the available experimental values. bThe SOC matrix elements ⟨T1|HSOC|Sn⟩ that are less than or equal to the absolute value of 300 cm−1 are not given. ckr(77 K) is calculated using eq 4 dFrom ref 38, in CH2Cl2. eFrom ref 74, in 2-MeTHF. fFrom ref 28, in 2-MeTHF.

a

D

DOI: 10.1021/acs.inorgchem.8b00705 Inorg. Chem. XXXX, XXX, XXX−XXX

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Table 3. Values of ΔE00, ⟨T1|HSOC|S0⟩, λ1, and μ (cm−1), ℏ2D21 and ℏ2P2 (105 cm−2), nM, and knr (105 s−1) Calculated via Eq 6 at 298 and 77 K for Complexes 1−5a 1298K 177K 2298K 277K 3298K 377K 4298K 477K 5298K 577K a

ΔE00

⟨T1|HSOC|S0⟩

λ1

μ

ℏ2D21

ℏ2P2

nM

19864

336

372

514

403

19079

540

601

17480

627

2370

19153

520

418

2.57 2.19 2.57 2.32 3.50 2.39 9.19 4.15 2.66 2.05

12.8 0.75 10.1 0.67 9.39 0.54 8.67 0.38 7.46 0.41

13

19184

1292 1032 1407 1080 1412 1040 316 436 1432 1044

12 12 8 12

knr 0.474 0.422 0.863 0.577 0.190 0.036 142 187 0.834 0.177

(0.626b) (0.075c) (4.135d) (2.058d)

The available experimental values are given in parentheses. bFrom ref 38, in CH2Cl2. cFrom ref 74, in 2-MeTHF. dFrom ref 28, in 2-MeTHF.

Figure 3. Calculated reorganization energies versus the normal-mode frequencies for the five complexes.

identical electronic transitions for all five complexes, as shown in Tables S7−S12, so as to weaken the strength of SOC between them. However, the SOC value alone cannot determine the final kr. As shown in Table 2, complex 1 has a kr value almost 3 times larger than the others, even though its SOC integral is not the largest. It is found that 1 has the smallest energy ratio, namely the smallest energy gap between Sn and T1 states, and also that a relatively larger oscillator strength belongs to 1, through a comparison in Table 2. Therefore, relatively small χn and large f n also play crucial roles in the measurement of kr. It is noteworthy that 4 has a radiative decay rate comparable with those of other complexes, even higher than 2 and 3, though it is nonemissive at room temperature as observed in experiment. Complex 5 has almost the same kr value as 4, indicating the two extra −CH2 groups in the ancillary ligand do not exert any influence on the radiative decay rate. Additionally, kr calculated at 77 K using eq 4 is

slightly slower than that at 298 K, which is in accordance with the experimental observations. Nonradiative Decay. The radiative decay rate alone cannot determine the phosphorescent efficiency of iridium complexes; thereby an investigation of the nonradiative decay rate is imperative. Herein, both temperature-independent and temperature-dependent nonradiative rates are explored. To begin with, the temperature-independent knr is first calculated and Table 3 gives parameters involved in eq 6, at 298 and 77 K, respectively. Data show that simply ΔE00 or the overlap between T1 and S0 cannot fully evaluate knr, which is in conflict with traditional EGL. This is because the convolution method adopted herein takes more consideration of the lowfrequency modes, and thereby far more temperature-dependent factors are taken into account in comparison to the EGL method.40 For the five compounds, the effective energy gap (ΔE00−λ1−μ) is in the order 4 (14794 cm−1) < 3 (17066 cm−1) < 5 (17303 cm−1) < 2 (17374 cm−1) < 1 (18200 cm−1). E

DOI: 10.1021/acs.inorgchem.8b00705 Inorg. Chem. XXXX, XXX, XXX−XXX

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is much smaller than for 4. (iii) For 4, the main component of vibration is the dihedral angle, which is associated with the phenyl ring out-of-plane motions, as shown in the normal mode displacement vectors depicted in Figure 5.

In addition, the SOCs between T1 and S0 increased in the order 1 < 2 < 5 < 3 < 4. However, the calculated knr reveals that 4 has the largest value and 3 has the smallest value, which demonstrates that other parameters such as ℏ2P2, ℏ2D21, SM, and nM are also playing vital roles in the determination of knr. The general tendency of knr is consistent with experiment that complex 1 has a value (0.474 × 105 s−1) comparable with that of experiment (0.626 × 105 s−1). In addition, complex 4 has a 3 orders of magnitude higher knr value in comparison to the other four complexes, revealing its nonemissive peculiarity at ambient temperature. Moreover, the knr values calculated at 77 K have no obvious decrease with respect to those at 298 K. In order to make clear the nonemissive character of 4, the relationship between reorganization energies, namely the energy shift caused by structure relaxation when electrons transition from the T1 to S0 state, and normal-mode frequencies is depicted in Figure 3. It can be seen that the reorganization energies of 4 are much larger than those for the others, especially for the low-frequency region (