Achieving Long‐Wavelength Electroluminescence Using Two‐Coordinate Gold(I) Complexes: Overcoming the Energy Gap Law

Abstract Two‐coordinate coinage metal complexes have emerged as promising emitters for highly efficient organic light‐emitting devices (OLEDs). However, achieving efficient long‐wavelength electroluminescence emission from these complexes remains as a daunting challenge. To address this challenge, molecular design strategies aimed at bolstering the photoluminescence quantum yield (Φ) of Au(I) complex emitters in low‐energy emission regions are investigated. By varying amido ligands, a series of two‐coordinate Au(I) complexes is developed that exhibit photoluminescence peak wavelengths over a broad range of 533−750 nm. These complexes, in particular, maintain Φ values up to 10% even in the near‐infrared emission region, overcoming the constraints imposed by an energy gap. Quantum chemical calculations and photophysical analyses reveal the action of radiative control, which serves to overcome the energy gap law, becomes more pronounced as the overlap between hole and electron distributions (S r(r)) in the excited state increases. It is further elucidated that S r(r) increases with the distance between the hole‐distribution centroid and the nitrogen atom in an amido ligand. Finally, multilayer OLEDs involving the Au(I) complex emitters exhibit performances beyond the borderline of the electroluminescence wavelength−external quantum efficiency space set by previous devices of coinage metal complexes.


Introduction
The advances of organic light-emitting devices (OLEDs) have been driven by the development of emitting molecules capable of harvesting all the electrogenerated excitons.In particular, organic molecules exhibiting thermally activated delayed fluorescence (TADF) enable high-efficiency electroluminescence across a broad range of visible regions. [1]However, incorporating organic TADF emitters into OLEDs presents challenges such as the moderate operational stability and a decline in electroluminescence efficiencies at high brightness, primarily due to slow exciton conversion. [2]Recently, two-coordinate complexes involving coinage metals such as Cu(I), Ag(I), and Au(I) have emerged as promising alternatives to organic TADF emitters. [3]3v,w,4] Importantly, this exciton harvest does not compromise the quantum yield for photoluminescence (Φ), facilitating high-brightness emission.As a result, coinage metal complexes are capable of uniquely combining the advantages of both organic TADF molecules and phosphorescent complexes of late transition metals, such as Ir(III) and Pt(II).
3b-k] The two-coordinate coinage metal complexes typically involve an anionic amido ligand and a neutral carbene ligand.This structure permits the ligand-to-ligand charge-transfer (LLCT) transition that produces TADF emission.3o,7] Nevertheless, the importance of low-energy-emissive compounds persists, given their significant potential in diverse applications, including night vision devices, optical communication, and information security, thus driving a continued high demand for the development of narrow energy-gap coinage metal complexes.
To meet the demand, we embarked on our research to develop two-coordinate coinage metal complexes producing long-wavelength emission.3v,w,4] Our molecular strategy was based on using a carbene ligand with the deep lowest-unoccupied molecular orbital (LUMO) and an amido ligand with the shallow highestoccupied molecular orbital (HOMO).Our main focus was placed on facilitating a radiative process, because most low-energy emitters are inevitably subject to a high nonradiative decay rate (k nr ) as governed by the energy gap law (see below). [9]Given the relationship of Equation ( 1), one can improve Φ by maximizing the radiative decay rate (k r ) even at a large k nr : We aimed at identifying molecular factors that regulate k r in two-coordinate Au(I) complexes, thereby achieving high Φ values suitable for OLED applications with long-wavelength emissions.
In this research, we created a series of electroluminescent two-coordinate Au(I) complexes featuring various amido ligands.We investigated the steady-state and transient photoluminescence properties of these complexes, and analyzed them based on ground-(S 0 ) and excited-state geometries obtained from Xray single-crystallography and quantum chemical calculations.Our analyses led to a molecular strategy to overcome the tradeoff limitation between the Φ and an emission wavelength.Subsequently, we fabricated multi-layer OLEDs utilizing these Au(I) complexes as dopants, achieving long-wavelength electroluminescence with a maximum external quantum efficiency (EQE max ) of 7.0% and a peak wavelength ( EL ) of 680 nm that extended up to 706 nm at high doping ratios.The electroluminescence results expand the borderline of the EQE max − EL space of coinage metal complexes (see the bottom panel in Figure 1).
It is envisioned that the limitation imposed by the energy gap law can be surpassed through the radiative control exerted by amido ligands, which represents the second electronic effect.According to Fermi's golden rule, k r is predicted to increase in proportion to a cubic E 00 , as shown in Equation (3): [10] In Equation (3), c is the speed of light, ϕ S1 and ϕ S0 are wavefunctions of the S 1 and S 0 states, respectively, and μ is the electric transition dipole moment.Consequently, k r must be low in low-energy emission regions.We noted that k r is proportional not only to E 00 3 but also to the transition probability |⟨ S 1 || S 0 ⟩| 2 .Specifically, k r is enhanced through the overlap between the hole and electron distributions (S r (r)) in the S 1 state that is directly proportional to the transition probability (see below and the Supporting Information for more discussion).The structurally varied amido ligands would exhibit different S r (r) values in their Au(I) complexes, enabling us to elucidate the molecular factor governing k r .Therefore, our structural control provides a valuable opportunity to establish the molecular design strategy toward improving Φ of long-wavelength emissions from Au(I) complexes.
Six Au(I) complexes were prepared through the four-step synthesis established by Hamze et al. [3r] that involved a Pd-catalyzed C─N coupling reaction, a condensation reaction to form a pyrazinoimidazolium precursor, the Au(I) complexation reaction, and the substitution of a chloro ligand with an amido ligand in the presence of NaO t Bu.The details of the synthetic procedures and spectroscopic identification data are shown in the Supporting Information.All complexes were highly soluble in polar organic solvents, such as CH 2 Cl 2 .
Single crystals of the Au(I) complexes, excluding [Au( Dipp PZI)(PXZ)], could be obtained by layering pentane or hexane onto CH 2 Cl 2 or by diffusing diethyl ether vapor.Crystallographic data and the key geometric parameters of the Au(I) complexes are compiled in the, Tables S1−S11 (Supporting These structural parameters appear to align with the trend of the percent buried volume (%V bur ) that quantifies the degree of encapsulation of the Au(I) center by ligands (Figure S6, Supporting Information).Overall, our X-ray crystallographic studies indicate a loosening in the coordination geometry of Au(I) complexes upon the integration of an acyclic amido ligand and a cyclic amido ligand having a carbonyl unit.
Figure 3a depicts the UV−Vis absorption spectra of 10 μm Au(I) complexes recorded in toluene.The LLCT transitions, characterized with the broad spectral shape, are clearly observed across the 400−800 nm range.The structured bands near 400 nm of [Au( Dipp PZI)(ACD)] are due to the local excitation centered at the ACD ligand. [11]Peak wavelengths of the LLCT bands are distributed from 462 to 619 nm and their molar absorbance () are in the range 5.6−9.8 × 10 3 m −1 cm −1 (see Table 1).
3p-s,12] The Au(I) complexes exhibit fluorescence emission over the broad range of peak emission wavelengths ( em s) of 598−808 nm in toluene (Figure S7, Supporting Information).3o,7] We thus resorted to investigate emission behaviors for thin films of Zeonex doped with 5 wt.% Au(I) complexes.Photophysical parameters determined for thin films are compiled in Table 1.As shown in Figure 3b, thin films exhibit broad emissions with  em increasing from the 533 nm ([Au( Dipp PZI)(ACD)]) to 750 nm ([Au( Dipp PZI)(PXZ)]).The emission spectra of thin films are hypsochromically shifted relative to those of toluene, indicating rigidochromism.3d] The Au(I) complexes show absolutely determined Φ values ranging from 0.10 to 0.84, which decreases with an increase of  em .[Au( Dipp PZI)(PXZ)] did not produce a reliable Φ value, due to its low emission intensity.Evidently, there is an inverse relationship between Φ and  em .
To understand the  em control by the amido ligands, electrochemical analyses using cyclic and differential pulse voltammetry were employed.Anhydrous THF containing a 2.0 mm Au(I) complex and a 0.10 m tetrabutylammonium hexafluorophosphate (TBAPF 6 ) supporting electrolyte exhibits one-electron oxidation and reduction processes of Au(I) complexes (Figure 4).The oxidation potentials (E ox s) show a significant shift, depending on the amido ligand structure (1.05 to 0.25 V vs saturated calomel electrode (SCE)).On the other hand, the reduction potentials (E red s) remain relatively unperturbed, values ranging from −1.49 to −1.62 V vs SCE.3v] The corresponding electrochemical bandgap energy (E g elec ), which is calculated through  S12, Supporting Information).The ΔE S1−T1 values comparable to the thermal energy at 298 K (ca. 25 meV) suggest the TADF nature.This notion is also supported by thermal enhancements (Figure S12, Supporting Information) and O 2 -induced quenching (Figure S13, Supporting Information) of the photoluminescence intensity.Rate constants for intersystem crossing (k ISC ) and reverse intersystem crossing (k rISC ) could also be determined following the approach established by Ying et al., [3o] and are tabulated in Table 1.The k nr , which can be derived using the relationship k nr = (1 − Φ)/ obs , increases by an order of magnitude from the green-emissive [Au( Dipp PZI)(ACD)] (5.0 × 10 5 s −1 ) to the NIR-emissive [Au( Dipp PZI)(DMAC)] (5.6 × 10 6 s −1 ) (Table 1).At the same time, the rate constant for TADF (k r TADF ), which is calculated through the relationship k r TADF = Φ/ obs , decreases from 2.6 × 10 6 s −1 for [Au( Dipp PZI)(ACD)] to 6.3 × 10 5 s −1 for [Au( Dipp PZI)(DMAC)].The increase of k nr and the decrease of k r TADF indicate nonradiative and radiative control governed by E 00 following Equations ( 2) and (3), respectively.In particular, the linearity found between the logarithm of k nr and E 00 presents compelling evidence for the adherence to the energy gap law (Figure S14, Supporting Information).Meanwhile, the absence of a substantial correlation between k r TADF and the ratio of k rISC to k ISC indicates that the radiative process is not governed by a preequilibrium between the singlet and triplet excited states through ISC/rISC cycles (Figure S15, Supporting Information).
To identify the molecular parameters governing the radiative control by the amido ligand, we conducted quantum   chemical calculations for the Au(I) complexes at the CAM-B3LYP level of theory.The optimized geometries of the S 0 state exhibited a co-planar structure, consistent with the single-crystal structures (Table S13, Supporting Information).The relaxed geometries of the S 1 and T 1 states were obtained at timedependent (TD) CAM-B3LYP level of theory, and the geometry parameters are summarized in the Tables S14−S19 and Figure S16 (Supporting Information).The T 1 state geometry is characterized with a coplanar conformation between the two ligands, whereas the S 1 state geometry has an orthogonal disposition between the two ligands.3a,13] The full calculation results for the TD-DFT calculations are summarized in the Tables S20−S25 (Supporting Information).3d,p,s,4] The transition character is consistent with the notion derived from our UV−Vis absorption and fluorescence spectra.Notably, the HOMO and LUMO isosurfaces exhibit partial delocalization onto the 5d-orbitals of Au, indicating a potential spin−orbit coupling exerted by Au.
Conventionally, natural transition orbitals (NTOs), which are obtained by transforming multiple molecular orbitals involved in the electronic transition into the most dominant contributing orbitals following Equation ( 4), are used to describe an electronic transition: [3v,4,14] In this equation, U′ is the occupied orbital matrix, T is the single particle transition density matrix, V is the virtual orbital matrix,  i is the associated eigenvalue, and  ij is a set of orbitals defined by unitary transformation.3v,4] Despite their utility, the limitation of NTOs is that they often represent only the most representative pair contributing to the electronic transition, as shown in Equation ( 4).This approach can lead to erroneous results because it may result in a partial loss of information about hole-electron transitions where there are multiple NTOs describing electronic transition. [14,15]o circumvent the limitation, we chose to employ densitybased hole ( hole (r)) and electron ( electron (r)) distributions and their overlap (S r (r)) that is defined as follows: We reasoned that S r (r) provides a more precise representation for analyzing an electronic transition because it does not rely on multiple pairs of molecular orbitals but instead focuses on a single pair of hole and electron density distributions. [16]Therefore, S r (r) is directly proportional to the term |⟨ S 1 || S 0 ⟩| 2 in Equation (3), thereby quantifying radiative control more accurately.The S r (r) value over an entire structure of an Au(I) complex (denoted as S r,total (r)) could be calculated for the singlet transition in the T 1 geometry, with the values ranging from 0.24 to 0.33 (Figure 5a).As anticipated, the k r TADF values typically exhibit an upward trend with increasing S r,total (r) until it reaches a value of 0.26.Beyond this threshold, k r TADF levels off (Figure S17, Supporting Information).Interestingly, despite the decrease in emission energy, we consistently observed high k r TADF values over 10 5 s −1 in the red to NIR regions, prompting us to delve deeper into the underlying factors in more detail by analyzing S r,total (r) values.To facilitate this investigation, S r,total (r) was fragmented into three components within the Au(I) complex: the carbene ligand (referred to as S r,carbene (r)), Au(I) (referred to as S r,Au (r)), and the amido ligand (referred to as S r,amido (r)).The S r,amido (r) values varied within the range of 0.12−0.16,whereas S r,carbene (r) and S r,Au (r) remained relatively unchanged at 0.09−0.10 and 0.05−0.06,respectively (Table S26, Supporting Information).These findings are especially intriguing because they defy the intuitive expectation of the hole-electron overlap being greatest at the Au(I), thereby adding an additional layer of interest to our investigation.Figure 5b demonstrates a rough proportionality relationship between S r,total (r) and S r,amido (r).This observation suggests that the radiative control exerted by the amido ligands is best represented by S r,amido (r).
We also discovered that S r,amido (r) is primarily governed by the distance between the centroid of the hole distribution and the N-atom in the amido ligand (d h−N , refer to Figure 5a).Notably, d h−N exhibits a substantial dependence on the structure of the amido ligand, with values from 0.74 to 1.19 Å.As depicted in Figure 5c, Au(I) complexes with larger d h−N values yield higher S r,amido (r) values.Additionally, both Φ and k r TADF values exhibit proportionality relationships with d h−N (Figure 5d).The deviation of Φ from linearity is likely attributable to additional nonradiative processes.Moreover, d h−N serves as a significant parameter intricately tied to radiative control due to its proportionality relationship with the transition dipole moment (μ) (Figure 5e).Note that this relationship is not limited to our Au(I) complexes, but is applicable to previous Au(I) complexes (Figure S18, Supporting Information).Therefore, d h−N can serve as a pivotal parameter, intimately connected to both S r,total (r) and μ, within the context of radiative control.These findings suggest that maximizing Φ should involve increasing d h−N , providing valuable guidelines for molecular design, including the utilization of conjugated cyclic amido ligands and electron-withdrawing substituents (Figure 5f).Ultimately, the incorporation of cyclic amido ligands in the investigated Au(I) complexes enables for the attainment of high k r TADF values, even under low-energy-emissive regions, effectively surpassing the constraints imposed by the energy gap law.
To further confirm the radiative control, we computed theoretical Φ curves using k nr and k r values based on Equations ( 2) and (3), respectively (Figure S19a, Supporting Information).It is predicted that k r increases with E 00 , whereas k nr decreases sharply with E 00 .However, contrary to k nr , k r depends on both E 00 and the transition dipole moment.The E 00 dependence of k r is mitigated by the transition dipole moment.Correspondingly, a larger Φ value is obtainable from an emitter with a greater transition dipole moment than that with a smaller transition dipole moment.Experimental Φ values of our Au(I) complexes are located close to the theoretical curves of Φ having large transition dipole moment (Figure S19b, Supporting Information).This observation demonstrates that judicious control of S r,total (r) through d h−N could overcome the constraints of E 00 toward improved Φ.
In  material, PBICT was the TADF host, DBTTP1 was the tripletexciton-guiding host, [17] TSPO1 was the hole-blocking layer, TPBi was the electron-transporting layer, and LiF was the electron injection layer.The emission layer consisted of mixed hosts of PBICT and DBTTP1 (7:3, w/w) that were doped with Au(I) complexes in the range of 1−10 wt.%. [Au( Dipp PZI)(PXZ)] was excluded from our device fabrication due to its very low Φ.The Au(I) complexes were thermally stable, as evidenced by high temperature of 5 wt.% decomposition greater than 269 °C (Figures S20 and S21, Supporting Information).Table 2 summarizes electroluminescence performances of OLEDs with our Au(I) complex emitters.
Figure 6b shows the electroluminescence spectra recorded for OLEDs containing 3 wt.% Au(I) complexes.Electroluminescence results for devices with 1, 5, and 10 wt.% Au(I) complex dopants are shown in the, Figures S22−S24 (Supporting Information).The  EL ranges 539−680 nm that is hypsochromically shifted with respect to each of the photoluminescence   The green-emissive [Au( Dipp PZI)(ACD)] device exhibits an EQE max of 24.4% at an  EL of 539 nm.The EQE max decreases as  EL increases, in the order of 23.3% for the [Au( Dipp PZI)(Cz)] device ( EL = 551 nm), 11.6% for the [Au( Dipp PZI)(DPAC)] device ( EL = 655 nm), 10.7% for the [Au( Dipp PZI)(DPA)] device ( EL = 650 nm), and 7.0% for the [Au( Dipp PZI)(DMAC)] device ( EL = 680 nm) (Figure 6e).A positive correlation is found between Φ and EQE max , which indicates that the hole trapping does not affect EQE values appreciably (Figure S25, Supporting Information).It should be emphasized that our Au(I) complexes set a new boundary in the EQE max − EL space shown in Figure 1.3o] OLEDs based on our Au(I) complexes exhibit maximum current efficiencies from 2.8 to 85.7 cd A −1 (Figure 6f).As shown in Figure 6g, the power efficiency exhibits an analogous trend.3h-j,m,p,r,s,7b,8a,12c] Overall, the  EL , the EQE, and the suppressed roll-off behaviors highlight the electroluminescence utility of our Au(I) complexes.

Conclusion
Achieving long-wavelength luminescence from two-coordinate coinage metal complexes remains as a formidable challenge due to the significant decline in the luminescence efficiency.This limitation hampers the utilization of two-coordinate metal complexes in full-color OLEDs.In this research, we investigated the effects of the amido ligand structure on  em and Φ of twocoordinate Au(I) complexes.It was found that the  em showed a correlation with E ox influenced by the amido ligand, in accordance with the LLCT transition nature.Φ decreased rapidly as  em increased, indicating nonradiative control governed by the energy gap law.Remarkably, our quantum chemical calculations and photophysical analyses unveiled a radiative control mechanism capable of circumventing the limitation imposed by the energy gap law.Specifically, k r TADF increases with S r,amido (r) that is directly proportional to d h−N .These findings offer insights into a molecular design strategy for maximizing Φ in two-coordinate metal complexes.Finally, OLEDs based on one of our Au(I) complexes produced an EQE max of 7.0% at an  EL of 680 nm that extended up to 706 nm at high concentrations.This represents the lowest-energy electroluminescence achieved to date for twocoordinate coinage metal complexes.It is envisioned that our research will guide the future molecular design strategies for developing high-efficiency OLEDs that emit long-wavelength emissions.

Figure 1 .
Figure 1.Ligand control strategy toward the development of two-coordinate Au(I) complexes with low-energy emissions.Top structures show the chemical structures of the Au(I) complexes with varied amido ligands.Bottom images illustrate the electronic effects exerted by the amido ligands, and comparisons of maximum external quantum efficiencies and peak electroluminescence wavelengths of devices with previous (empty circles) and our (red stars) coinage metal complexes.Refer to the main text for definitions of symbols.
E g elec = −e⋅(E red − E ox ) where e is the elementary charge, shows a linear correlation with the LLCT transition energy obtained from the UV−Vis absorption spectra (Figure S8, Supporting Information).Since our Au(I) complexes exhibit LLCT fluorescence, the emission energy of Au(I) complexes is governed primarily by the electron-donating capability of amido ligands.The Au(I) complexes exhibit short fluorescence lifetime ( obs ) in the range 0.019−0.32μs at 298 K (Table1; FigureS9, Supporting Information).Applying the two-level Boltzmann model to the temperature-dependent  obs values, we could deduce the energy difference between the singlet and triplet states (ΔE S1−T1 ) to be in the range 40−64 meV(Figures S10 and S11; Table

Figure 4 .
Figure 4. Cyclic (CV, upper panel) and differential pulse (DPV, lower panel) voltammograms of the Au(I) complexes.Conditions: Ar-saturated, anhydrous THF containing a 2.0 mm Au(I) complex and a 0.10 m tetrabutylammonium hexafluorophosphate (TBAPF 6 ) supporting electrolyte; a Pt disk and a Pt wire for the working and counter electrodes, respectively; an Ag/AgNO 3 pseudo reference electrode; scan rate = 0.1 V s −1 (CV) and 0.004 V s −1 (DPV).The grey dotted line is the background signal of the blank solution containing only 0.10 m TBAPF 6 .

Figure 5 .
Figure 5. a) S r,total (r) isosurfaces of the singlet transition (green; isovalue = 0.001) for the Au(I) complexes.S r,amido (r) denotes S r (r) of the amido ligand fragment (yellow regions).d h−N refers to the distance between the centroid of the hole distribution (dark-orange sphere) and the N-atom in the amido ligand.b) Correlation between S r,total (r) and S r,amido (r).c) Correlation between S r,amido (r) and d h−N .d) Correlations of d h−N with Φ (black circles) and k r TADF (red circles).e) Correlation between transition dipole moment (μ) and d h−N .f) Graphical description for the amido ligand structural effect on μ.

Figure 6 .
Figure 6.a) The configuration of the electroluminescence devices tested, and the chemical structures of constituent materials.b) Normalized electroluminescence spectra.The shoulder band marked with a red asterisk is due to the host emission.c) Current density−voltage curves.d) Luminance−current density curves.e) External quantum efficiency−current density curves.f) Current efficiency−current density curves.g) Power efficiency−current density curves.

Table 1 .
Photophysical and electrochemical parameters for Au(I) complexes.

Table 2 .
Summary of the electroluminescence characteristics of devices containing 3 wt.% Au(I) complexes.