Toward rational design of TADF two-coordinate coinage metal complexes: understanding the relationship between natural transition orbital overlap and photophysical properties

Abstract

A series of twelve two-coordinate coinage metal, Cu, Ag and Au, complexes with carbene-metal-amide structures were prepared. The complexes all display thermal assisted delayed fluorescence (TADF) emission at room temperature from interligand charge transfer (ICT) excited state with short lifetimes (less than 2 μs) and photoluminescent quantum yields that reach near unity. Owing to the involvement of the substituents in the emissive transitions and different metal ion volume, the natural transition orbital (NTO) overlap of the emissive state can be adjusted in a wide range from 0.21 to 0.41. Investigations on the relationship between the NTO overlap of the emissive state and key TADF photophysical properties demonstrated that both singlet–triplet energy gap and radiative decay rate of S₁ state increase along with the NTO overlap exponentially. Consequently, the overall TADF radiative decay rate leads to a maximum when plotted against the NTO overlap, giving the ideal zone from 0.25 to 0.30 for high TADF radiative decay rate in this class of two-coordinate coinage metal complex luminophores.

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Introduction

Thermally assisted delayed fluorescence (TADF), also known as E-type delayed fluorescence, has been investigated in a wide range of photophysical and photochemical applications.^1–11 The process involves the endothermic intersystem crossing (ISC) from the triplet excited state (T₁) to singlet (S₁) excited state followed by emission from the S₁ state (Scheme 1).¹² A recent promising application of TADF emitters is to replace heavy-metal (Ir, Pt and Rh etc.) phosphorescent complexes used as luminescent dopants in commercial organic light emitting- diodes (OLEDs).¹³ Both TADF and heavy-metal phosphors provide a means to achieve near 100% efficiency in these devices.^14–17 Organic TADF luminophores adopt donor-acceptor (D–A) structure with large dihedral angle between the D–A moieties.¹⁸ Such a twisted geometry leads to weak coupling between D and A, and thus a small energy gap between the S₁ and T₁ states (ΔE_ST), favoring thermal activation from the triplet to the singlet state at room temperature.

Scheme 1 The kinetic scheme for emission via TADF mechanism in two-coordinate coinage metal complex, where and k^TADF_r are radiative decay rates of S₁ state and TADF process, K_eq indicates the equilibrium constant between S₁ and T₁ states via ISC transitions.

Three- and four-coordinate Cu(I) complexes have also been reported that demonstrate TADF behavior, from largely metal to ligand charge transfer (MLCT) transitions.^19–24 Recently, a significant advance in Cu^(I)-based TADF materials was achieved using two-coordinate complexes with a carbene ligand to serve as an acceptor and an amide ligand as a donor.^25–36 In addition to the copper complexes, isoelectronic silver and gold based complexes have been shown to give highly efficient TADF.^31,36–38 Here we will refer to the (carbene)M(amide) family of complexes as cMa for M = Cu^(I), Ag^(I) and Au^(I). Early reports of complexes with cMa structures and their promising luminescent properties³⁹ led to further study^40–42 and successful application in OLEDs generated new enthusiasm for these types of emitters.^{25,28–30,37} Investigations have been carried out focusing on two-coordinate TADF complexes experimentally and theoretically, to develop structure–property relationships and strategies to achieve high radiative (k_r) and low non-radiative (k_nr) decay rates.^{29–31,38,43–48}

TADF molecules fall into two basic categories, depending on whether they have slow or fast rates for intersystem crossing (ISC).¹² Organic TADF materials generally have slow ISC rates (k_ISC = 10⁵–10⁸ s⁻¹) owing to weak spin-orbital coupling (SOC), which makes fluorescent radiative decay competitive with intersystem crossing.⁴⁹ Consequently, the radiative decay rate for TADF (k^TADF_r) is intimately tied to k_ISC (both S₁ → T₁ and T₁ → S₁) and the radiative rate of S₁. In contrast, cMa complexes have ISC rates that are markedly faster (k_ISC = 10¹⁰–10¹¹ s⁻¹) than owing to high SOC imparted by the central metal ion.³¹ Such rapid rates for k_ISC means the equilibrium between singlet and triplet excited states is established rapidly, well before the emission from S₁. Compounds where than ISC rate exceeds allow one to employ the pre-equilibrium approximation such that the equilibrium constant (K_eq) becomes a principal factor that determines k^TADF_r as shown in eqn (1):¹²

In this equation, k^TADF_r is dependent on and K_eq, the latter which is related to ΔE_ST. Thus, it is not necessary to know the exact ISC rates in these cMa emitters provided they are faster than . The pronounced differences in ISC rates of organic versus cMa TADF emitters result in characteristic transient decay behavior from the excited state. Luminescence decay traces from organic TADF emitters typically display a short lived “prompt” fluorescence (ns time scale) and a longer lived “delayed” fluorescence (usually >1 μs, even up to ms timescale).¹⁸ The prompt signal is a combination of radiative fluorescence from the S₁ state and nonradiative ISC to the triplet state, where the delayed k^TADF_r is controlled by ISC back to the S₁ state (T₁ → S₁). However, the absence of a “prompt” process is often manifested in the cMa emitters since equilibration between the S₁ and T₁ states is typically faster than the instrument response function of the detector (on the order of less than 200 ps).³¹ Consequently, the emissive decay traces of cMa molecules is usually observed as a single exponential signal on μs scale, similar to those seen in phosphorescent complexes.

According to the analysis above, predictions can be made regarding the TADF properties of cMa complexes without prior knowledge about ISC rates since only and ΔE_ST need to be determined to determine k^TADF_r. The values of can be obtained experimentally from absorption spectra according to the Strickler–Berg equation, whereas fits of temperature dependent luminescence data can be used to accurately derive ΔE_ST values. In this contribution, we explore the use of the spatial overlap between the hole and electron natural transition orbitals (NTOs) to predict k^TADF_r in cMa emitters. The value of the NTO overlap can range from zero—which indicates purely CT transitions with no spatial overlap—to unity where excitation is localized on the same molecular orbital. The use of NTO overlap to predict TADF properties has been reported; however, this analysis only considered the impact of NTO overlap on the magnitude of ΔE_ST.⁵⁰ Although a small ΔE_ST will give rise to more efficient ISC for T₁ → S₁, a small NTO overlap also results in a low oscillator strength for emission from the S₁ state, and thus a lower which is detrimental for k^TADF_r. As the value for NTO overlap influences both variables critical for k^TADF_r, but with countervailing effects, a question is raised: is there an optimal value of NTO overlap where the two parameters are ideal? Here, by investigating a large family of cMa complexes with NTO overlaps ranging from 0.2 to 0.4, together with insight into their photophysical parameters, an optimal region for high k^TADF_r in cMa complexes were identified to be from 0.25 to 0.30. Such analysis was also applied for organic TADF emitters, providing useful trends for these materials as well.

Results and discussion

The general synthetic route to the compounds studied here is presented in Fig. 1, detailed synthetic procedures and characterization are included in the (ESI†). The N-heterocyclic carbene (NHC) precursor triflate salts 2 were prepared according to a published Ag(I) catalyzed 6-endo-dig cyclization.⁵¹ The diisopropyl phenyl (dipp) substituents on the carbene nitrogen atoms hinder axial rotation around the metal–ligand bonds.^29,38 The preparation of the intermediate complex 3 varied depending on the metal ions. For Cu complexes, deprotonation of 2 with strong base provided the free carbene in situ, and the products were obtained by reacting it with CuCl. For Ag complexes, 2 was treated with Ag₂O and the triflate salt was isolated. The Au chloride complexes were synthesized via a metal exchange reaction with the Ag triflate salts using chloro-dimethylsulfide-gold^(I). The cMa complexes were then prepared by reacting 3 with deprotonated carbazole or 3-cyanocarbazole, in yields over 70%. All these complexes were obtained as light yellow to orange crystalline powders. No obvious decomposition is observed in the ¹H NMR spectra when the complexes are stored under ambient conditions. Acronyms to distinguish the complexes are given as R₁–M or R₁–M^CN, where R₁ is Me (methyl) or Ph (phenyl) according to the substituent group, M is Cu, Ag or Au and the superscript CN is shown when R₂ is CN.

Fig. 1 General synthetic route for the coinage metal complexes, note, the counter ion for 3 is triflate in Ag complex.

Molecular structures for five of the complexes were determined using single crystal X-ray analysis. Critical crystallographic data and molecular structures of Me–Cu and Ph–Au^C are shown in Fig. 2. As revealed by the diffraction results, the molecules present linear two-coordination geometry with near coplanar orientation of NHC and carbazole ligands in agreement with data from analogous cMa derivatives.^29–31,48 The dihedral angles between the two ligands planes range from 0.3° to 12.7°. The C_NHC–M bond is longer than the M–N_Cz bond in Me–Cu, but they become near equal in Me–Ag. In Au complexes, the C_NHC–Au is shorter than the M–N_Cz. The C_NHC⋯N_Cz distances in these complexes agree with our previous observations in related (carbene)M(amide) complexes Cu (∼3.7 Å) < Au (∼4.0 Å) < Ag (∼4.1 Å).³¹ Metal–metal contacts are all >8 Å and π–π contacts are well outside of van der Waals contacts in the packing of these complexes in the solid state. Packing diagrams are given in the ESI.†

Fig. 2 Critical crystallographic data from X-ray single crystal diffraction measurements, C_NHC denotes the carbene carbon and N_Cz is the carbazolyl nitrogen. Thermal ellipsoid figures of Me–Cu (top) and Ph–Au^CN (bottom).

The electrochemical properties of the complexes were investigated using cyclic voltammetry (CV) and differential pulsed voltammetry (DPV) methods (see ESI† for the electrochemical traces and data). All the complexes undergo irreversible oxidation in DMF solution. For complexes with same ligands, the metal ion influenced E_ox in a sequence of Ag < Cu < Au in steps of 0.1 V. Upon introduction of CN on the Cz ligand, the oxidation potential (E_ox) positively shifted by 0.24–0.29 V. A single reversible reduction (E_red = −2.25 to −2.37 V) is observed for complexes with methyl substituted carbenes within the measurable solvent window. Complexes with phenyl substituted carbenes show two reversible reductions, a reversible reduction near −2.0 V and an irreversible reduction at roughly −2.6 V. It is noteworthy that variations in E_red between complexes with the same ligands and different metal ions are relatively small, i.e., the range for Cu, Ag and Au complexes is 0.07 V.

The photophysical properties of the two-coordinate complexes were studied in fluid solution and in doped polystyrene (PS) films. The absorption and emission spectra in the two media are very similar, however, determining an extinction coefficient in a polymer thin film is problematic, so here we show toluene solutions for absorbance. Polystyrene is the preferred medium for photoluminescence as it prevents ligand rotation that can lead to nonradiative decay. Other than a difference in extinction coefficients between the three metals (vide infra) the absorption and emission spectra for Cu, Ag and Au complexes with identical ligands show very similar profiles. Representative spectra for the Cu derivatives are shown in Fig. 3, spectra for the Ag and Au derivatives are given in the ESI† and data for all complexes is tabulated in Table 1. UV-visible absorption spectra for the copper-based complexes (Fig. 3(a)) show π–π* transitions of the carbene ligands below 300 nm, transitions on the Cz ligands appear as well-structured bands from 300 to 375 nm and the broad, featureless bands at lowest energy are assigned to ICT transitions (Cz → carbene). Introduction of the CN substituent on Cz ligand stabilizes the HOMO and leads to a blue shift of 20 nm in the ICT absorption band. Replacing the methyl group with phenyl in the carbene ligand destabilizes the LUMO and leads to a further blue shift of roughly 15 nm. The effect of both substituents increases the energy of the ICT transition, resulting in blue shifted S₀ → S₁ absorption bands. The principal difference between the complexes imparted by the three metal ions is that the extinction coefficients for the ICT transitions fall in the order Au > Cu > Ag. This trend can be rationalized as reflecting the effects of an extensive polarizability of the Au complexes and the large separation between the donor (carbazolyl) and acceptor (carbene) ligands in Ag complexes, with the Cu derivative falling between those two extremes.

Fig. 3 (a) Absorption and (b) emission spectra of Cu-based complexes. Absorption spectra recorded in toluene solution at room temperature and emission spectra in doped PS (1 wt%) films at room temperature (solid) and 77 K (dash).

Table 1 Photophysical properties of the cMa complexes at room temperature^a

Complex	λ ^absmax (nm)	ε (M^−1 cm^−1)	λ ^emmax (nm)	Φ PL	τ (μs)	k r (× 10^6 s^−1)	k nr (× 10^6 s^−1)
a Absorption data recorded in toluene solution, luminescence data in doped PS (1 wt%) films.
Me–Cu^CN	413	6300	482	0.77	1.4	0.55	0.16
Ph–Cu^CN	427	5460	500	0.83	1.1	0.75	0.15
Me–Cu	449	5470	534	0.58	1.5	0.39	0.28
Ph–Cu	468	4820	556	0.70	0.97	0.72	0.31
Me–Ag^CN	398	1990	476	0.83	0.41	2.0	0.41
Ph–Ag^CN	412	2120	498	0.88	0.60	1.5	0.20
Me–Ag	438	1960	530	0.77	0.41	1.9	0.56
Ph–Ag	456	2070	558	0.56	0.53	1.1	0.83
Me–Au^CN	409	8670	484	0.50	0.81	0.62	0.62
Ph–Au^CN	421	8330	504	1.00	0.82	1.2	<0.01
Me–Au	442	8180	528	0.50	1.1	0.45	0.45
Ph–Au	459	7550	554	0.77	0.80	0.96	0.29

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The cMa complexes all display a broad visible ICT emission band when doped in a PS film at room temperature (Fig. 3(b)). The emission energies are principally controlled by substituents on the ligands; changes in the metal ion lead to only minor shifts in energy. The introduction of the CN substituent on Cz ligand induces a hypsochromic shift of around 50 nm. Complexes with the phenyl substituted carbene are red shifted by 25 nm from the methyl substituted analogs. These shifts can be explained by stabilization of the HOMO and LUMO, respectively, in analogy to shifts in the corresponding ICT absorption transitions. The complexes are all highly efficient luminophores (Φ_PL ≥ 0.5) with short emission lifetimes. The high Φ_PL values are a consequence of radiative decay rates on the order of 10⁵ to 10⁶ s⁻¹. The radiative decay rates for complexes with CN substituted Cz are faster than the analogues with Cz ligand, consistent with their blue shifted emission. Nearly all the complexes retain broad ICT emission profiles at 77 K in PS film (Me–Ag^CN is the only one that gives structured emission at 77 K). The luminescence lifetimes become substantially longer upon cooling, with larger changes observed for the Cu (τ = 93–256 μs) and Au (τ = 47–82 μs) derivatives than for the Ag complexes (τ = 2.7–7.2 μs). The large increase in decay lifetimes is comparable to changes found in related two-coordinated cMa derivatives and consistent with TADF phenomenon being responsible for luminescence in these compounds.

As discussed in the Introduction, the rate of emission is controlled by and ΔE_ST in TADF luminophores that have fast ISC rates (where S₁ is the ¹ICT state for cMa complexes discussed in this paper). In a study of related cMa complexes it was shown that both parameters could be accurately determined from fits to the temperature dependent luminescent decay rates between 200 and 300 °C. The kinetic scheme employed to fit the temperature dependent lifetime data uses a modified Arrhenius type equation (eqn (2)).³¹ The slope of this fit gives ΔE_ST whereas the intercept provides . For this fit to be valid the zero-field splitting of the triplet sublevels (ZFS) must be ≪ ΔE_ST to ensure that the emission in the 200–300 °C range is due solely to TADF and that temperature dependent phosphorescence is not contributing to the decay rate. This is a valid assumption for cMa complexes.³⁴ Fits for the methyl-substituted carbene complexes are shown in Fig. 4 (fits for the phenyl-substituted carbazole complexes are given in the ESI†) and the values for ΔE_ST are given in Table 2.

Fig. 4 Fits to the temperature dependent TADF radiative decay rate from 210 to 310 K according to the full kinetic dynamic scheme.

Table 2 TADF related photophysical data and calculated NTO overlap values

Complex	Cpd. no.	k ^TADFr (10^6 s^−1)	k ^TADFr/E^3 (10^4 s^−1 eV^−3)	ΔEST (meV)	(10^6 s^−1)	(10^6 s^−1)	NTO overlap (S1)	NTO overlap (T1)
Me–Cu^CN	1	0.55	3.1	83	38	34	0.361	0.456
Ph–Cu^CN	2	0.75	4.8	55	19	25	0.301	0.433
Me–Cu	3	0.39	3.0	64	13	24	0.377	0.450
Ph–Cu	4	0.72	6.5	55	19	18	0.311	0.418
Me–Ag^CN	5	2.0	11	16	13	14	0.272	0.360
Ph–Ag^CN	6	1.5	9.5	10	6.7	15	0.211	0.309
Me–Ag	7	1.9	15	14	9.5	11	0.268	0.343
Ph–Ag	8	1.1	9.6	14	5.5	11	0.212	0.289
Me–Au^CN	9	0.62	3.6	78	37	46	0.391	0.509
Ph–Au^CN	10	1.2	8.2	61	38	39	0.364	0.498
Me–Au	11	0.45	3.6	75	25	37	0.411	0.500
Ph–Au	12	0.96	8.6	59	28	29	0.342	0.477

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In our previous studies of related cMa complexes values for were determined from the intercept of linear fits to eqn (3); however, this approach was for samples where nonradiative decay was slow and temperature independent (Φ_PL ∼ 1).³¹ Although some of the samples here have Φ_PL ∼ 1, others are markedly below this value. Therefore, to correct for any temperature dependence of , k^TADF_r was calculated from the PL efficiency determined at each temperature (see ESI†) and those values were used to estimate from fits to eqn (2). Alternately, a method for estimating described by Strickler and Berg can be used based on the absorption spectra.^52,53 This analysis uses the integrated extinction spectrum for the ¹ICT band to estimate the oscillator strength and Einstein equation to give the radiative rate (see ESI† for details). To evaluate both methods for determining , radiative rates from the temperature dependent studies were compared to estimates for from a Strickler–Berg analysis of the absorption spectra in toluene solution . The relationship between the two values was plotted (Fig. S25, ESI†) and a linear correlation was established, with Pearson correlation coefficient of 0.93. A good agreement is found between the values derived from fitting eqn (2) and the Strickler–Berg analysis in cases where Φ_PL ∼ 1. However, the correspondence between values from the two methods shows pronounced divergence for compounds that have the lowest Φ_PL (Table 2). This leads us to consider that the correction made for Φ_PL < 1 is inadequate to fully account for the temperature dependence of nonradiative decay. For this reason, values for from the Strickler–Berg analysis were used to obtain correlations with the NTO overlap in the subsequent plots.

The radiative decay rate for TADF (k^TADF_r) for systems with fast ISC is determined principally by and ΔE_ST, i.e.. It is inferred that these two parameters are closely related to the change of electron density distribution between the initial and final states in the ¹ICT (S₁) transition, which can be quantified by the overlap between the h-NTO and e-NTO for the emissive ¹ICT state. In other words, greater overlap between these NTOs will increase the oscillator strength (and ) as well as the ΔE_ST owing to an increase in the exchange energy.^53,54 Since a large and small ΔE_ST is preferred when aiming for a rapid k^TADF_r, optimizing these two conflicting effects should lead to an ideal value for the NTO overlap to achieve the fastest k^TADF_r. The spatial NTO overlap integral between the electron and hole associated with the electronic transitions from ground state to both S₁ and T₁ state can be computed according to the following expression:

where are the electron and hole orbital pairs and σ_k is the amplitude of a given orbital pair that contributes to the total NTO. The overlap value was numerically evaluated as described previously.⁵⁵Table 2 gives the NTO overlap values for the S₁ and T₁ (ICT) states, ¹ICT and ³ICT, respectively. As observed previously,⁵⁶ the NTO overlap is larger for the triplet state than the singlet state, however the trends are the same as a function of metal, i.e.³ICT NTO overlaps fall in the order Au > Cu > Ag. These twelve complexes present ideal candidates to examine the dependence of and ΔE_ST on NTO overlap, since the different metal ions and substituents involved in the electronic transitions lead to a wide range of NTO overlap values (¹ICT NTO overlap from 0.21 to 0.41). The role of NTO overlap on these parameters was first investigated using values for ΔE_ST and oscillator strength obtained from TD-DFT calculations for the ¹ICT state. Plots of the two parameters versus¹ICT NTO overlap are shown in Fig. 5a and b. It is evident that ΔE_ST will be zero and will be vanishingly small when the NTO overlap is zero. Thus, these parameters were fit to the following exponential growth function: y = A(e^R₀x − 1), where R₀ is referred to as the growth rate. The values for both parameters obtained from TD-DFT calculations (R₀ = 4.7 and 4.9 for ΔE_ST and the oscillator strength, respectively) are proportional to the ¹ICT NTO overlap.

Fig. 5 Relationship between ¹ICT NTO overlap value versus theoretically calculated (a) ΔE_ST and (b) oscillator strength of the S₁ state by the TD-DFT method; fits to the data are obtained using the exponential growth function: y = A(e^R₀x − 1).

Experimental values for ΔE_ST and are plotted versus the ¹ICT NTO overlap in Fig. 6. These plots can also be fit to an exponential growth function with an R₀ of 6.6 and 5.5, respectively. It is interesting to note that the exponential fits to both theoretical and experimental results give similar values. Thus, the theoretical studies and temperature dependent photophysical investigations support the hypothesis that the NTO overlap of the emissive ¹ICT state is indeed a key parameter controlling ΔE_ST and , which consequently determines k^TADF_r.

Fig. 6 Relationship between ¹ICT NTO overlap value versus (a) ΔE_ST and (b) radiative decay rate of the ¹ICT state according to the Strickler–Berg equation; fits to the data are obtained from on the twelve complexes in this work using the exponential growth function: y = A(e^R₀x − 1).

According to the Einstein radiation law, the radiative decay rate is proportional to the cube of the emission energy. The reduced k^TADF_r (k^TADF_r/E³, where E is the emission energy derived from the emission maximum) for complexes in this work, as well as other monometallic and bimetallic (carbene)M(N-carbazolyl) complexes previously reported, was plotted as a function of the NTO overlap values calculated for ¹ICT state (Fig. 7). Note here, only those cMa complexes that emit from ICT states were selected to eliminate discrepancies caused by influence from the higher lying ³Cz state. From this data, rates for k^TADF_r are found to be fastest for complexes with NTO overlaps of 0.27–0.30 and decrease with higher and lower NTO overlap values.

Fig. 7 Relationship between the reduced TADF radiative decay rate versus NTO overlap of the ¹ICT state. The closed symbols are from this work and the open symbols are for previously reported (carbene)M(carbazolyl) complexes. See the ESI† for the identities of the literature complexes.

A similar analysis of NTO overlap was carried out for selected organic TADF molecules to evaluate the scope of the correlations. Organic TADF molecules were chosen as listed in Table S12 (ESI†) and their photophysical properties were collected from literature.^{13,49,57–77} Although the theoretical methods used to determine values for the NTO overlap were the same as those applied for the coinage metal complexes, different methods used to obtain experimental values for organic TADF molecules make the comparisons problematic. Nevertheless, the theoretical ΔE_ST values can still be evaluated as all compounds were calculated using the same method and basis set and show a clear increase with greater NTO overlap (Fig. 8a). It is apparent that coinage metal TADF complexes give smaller ΔE_ST than organic compounds with the same NTO overlap value. It is also noteworthy that for organic TADF molecules the calculated oscillator strength of the S₁ state increases significantly only when the NTO overlap is greater than 0.45 (Fig. 8b). The variation of the measured k^TADF_r values for organic TADF emitters as a function of NTO overlap is shown in Fig. 8c. The value for k^TADF_r in the organic TADF molecules also peaks at NTO overlaps of 0.2–0.3, albeit with slower rates than values found for two-coordinate coinage metal TADF complexes having comparable NTO overlaps. Thus, analysis of NTO overlaps can provide meaningful screening of organic TADF molecules for potential to have high k_TADF values as well.

Fig. 8 Relationship between NTO overlap versus (a) theoretically calculated ΔE_ST, (b) calculated S₁ state oscillator strength and (c) TADF radiative decay rate in organic TADF molecules; data of organometallic TADF complexes newly reported in this paper are shown as empty red circles.

Conclusion

In summary, a series of twelve two-coordinate Cu, Ag and Au complexes were synthesized with a cMa structure. They all display TADF emission from ICT states with fast decay lifetimes and high luminescence efficiency. NTO overlaps of the emissive ¹ICT states were quantified using theoretical calculations. The use of different metal ions and chemical modification on both ligands leads to NTO overlap values that cover a wide range (from 0.21 to 0.41). Detailed theoretical and experimental investigations shed light on the influence of NTO overlap on ΔE_ST and , indicating that both parameters increase exponentially with increasing NTO overlap. However, since increasing ΔE_ST and k^ICT_r exerts opposing effects on k^TADF_r, the radiative rate will increase up to a maximum value with greater NTO overlap before subsequently declining. Thus, an ideal zone for fast k^TADF_r occurs between NTO overlap values of 0.25 to 0.30. More importantly, other cMa complexes agree well with these trends, whether monometallic or bimetallic and regardless of the identity of the coinage metal ion. Thus, NTO overlap values can be used as a general method to evaluate k^TADF_r in such two-coordinate TADF ICT emitters. Further studies will focus on the following points: (1) examine additional cMa complexes, especially those with NTO overlap in the range from 0.1 to 0.25 to establish more accurate trends in the photophysical properties and, (2) use NTO overlap as a metric to identify molecules with a high likelihood of having fast k^TADF_r. This work not only provides a quantifiable metric to improve intrinsic k^TADF_r for two-coordinate coinage metal complexes, but also provides a new perspective to evaluate photophysical properties in other molecular systems with charge transfer excited states by using NTO overlap as a method to theoretically appraise potential candidate emitters.

Conflicts of interest

One of the authors of this paper (M. E. Thompson) has a financial interest in the Universal Display Corporation, who is one of the sponsors of this work.

Acknowledgements

The authors would like to thank the Universal Display Corporation for supporting this work and the National Science Foundation (award: CHE-2018740) for the acquisition of the diffractometer used to solve the crystal structures reported here. Special thanks to Dr Daniel S. M. Ravinson for the development of calculation software for NTO overlap values.

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Footnote

† Electronic supplementary information (ESI) available: Experimental details, crystallographic data, calculation results, complete photophysical characteristics and analysis. The *.xyz files are given for the geometry optimized structures. CCDC 2117673, 2117674, 2117675 and 2117672. For ESI and crystallographic data in CIF or other electronic format see DOI: 10.1039/d2tc00163b

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