Singlet–triplet gaps for evaluating thermally activated delayed fluorescence: which one is the (b)E_ST?

Abstract

The singlet–triplet energy gap (ΔE_ST) serves as a central screening parameter for new thermally activated delayed fluorescence (TADF) materials, and is a valuable indicator of eventual OLED performance. Surprisingly though, various measurement methodologies and reporting standards for ΔE_ST persist across the research community. The resulting variability undermines direct comparisons of material properties across reported works, obfuscating structure–property relationships that would otherwise guide synthetic efforts and computational validation. Here we employ 4CzPyz and 4tCzPyz as model systems, and correlate their different possible ΔE_ST values with their reverse intersystem crossing (rISC) kinetics in films of common and device-relevant hosts. By comparing ΔE_ST values with emission decay kinetics and device roll-off performance for these two materials, we propose that the steady-state room-temperature photoluminescence onset should be used to determine E(S₁), in preference to either steady-state low-temperature or time-resolved singlet emission. Ultimately though, even this should only be taken as an indicator, as device performance is not always reliably predicted by comparing optically derived ΔE_ST gaps.

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1. Introduction

Thermally activated delayed fluorescence (TADF) has transformed organic light-emitting diode (OLED) technology by enabling complete harvesting of electrically generated excitons without requiring precious heavy-metal phosphors.^1–4 This breakthrough emerges from the thermal upconversion of non-emissive triplet states to emissive singlets through reverse intersystem crossing (rISC), avoiding the 25% efficiency limit imposed by spin statistics in conventional fluorescent materials.^5–7 The efficiency of this process depends exponentially on the singlet–triplet energy gap (ΔE_ST), establishing its accurate determination and comparison as a cornerstone of TADF material development.^8–10

Despite this central importance, ΔE_ST determination using different common spectroscopic methods sometimes yields dramatically conflicting values for identical materials, with variations exceeding 250 meV.^11–13 This inconsistency represents more than an experimental inconvenience; often silently, it undermines the fundamental premise of rational TADF design and precludes direct comparison of experimental results across different research groups.^14–16 Even in this context recent works attempt to directly minimize ΔE_ST,¹⁷ carefully quantify its different values,¹⁸ or examine its inversion all towards more efficient OLED operation.¹⁹ It therefore remains timely to consider what really is the most appropriate way to measure and report this seemingly simple spectroscopic parameter.

The different potential reporting methods for ΔE_ST primarily arise from the temporal complexity of TADF photophysics, itself a consequence of the conformational flexibility of donor–acceptor architectures (Fig. 1).²⁰ Following photoexcitation, molecules undergo conformational relaxation during prompt fluorescence (PF, nanosecond timescale), followed by intersystem crossing and thermal activation enabling rISC and delayed fluorescence (DF, microsecond to millisecond timescale).^21–23 Each of the commonly used reporting methods for ΔE_ST (discussed below) samples different temporal windows of this evolution, potentially capturing distinct conformational subsets with different emission energies.^24–27

Fig. 1 Temporal evolution of excited states in TADF materials (left), and the resulting range of reportable ΔE_ST values (right). Following photoexcitation, molecules undergo conformational relaxation during prompt fluorescence (PF, ns regime) and delayed fluorescence (DF, µs to ms regime) proceeding via reverse intersystem crossing (rISC). Steady-state methods (room-temperature, SS_RT; and low-temperature, SS_LT) provide single ensemble-averaged values. Time-resolved approaches (PF, DF) yield variable results depending on the selected temporal window. Phosphorescence (PH) measurements determine triplet state energies, but are often only accessible at low temperatures. The shaded sections (right) depict the ranges of possible singlet energies that could be selected from different measurements, thus illustrating the range of reportable ΔE_ST values (black/coloured bars) relative to the same triplet energy (red dotted line). Molecular structures of 4CzPyz and 4tCzPyz are shown in the upper right.

In principle the difference in energy between the S₁ and T₁ states simply defines ΔE_ST = E(S₁) – E(T₁). E(T₁) can be estimated from the high-energy onset of the phosphorescence (PH) spectrum acquired using low-temperatures and long acquisition delays following pulsed excitation to eliminate contribution from both PF (time-resolved) and DF (temperature suppressed). In cases where the phosphorescence arises from locally excited (LE) states with strong vibronic structured emission, the shortest wavelength peak of the spectrum is also occasionally used. For TADF materials with mixed charge transfer (CT) and LE excited state character such a peak is not always readily identifiable for T₁ assignment, and the onset is often more appropriate.

While estimation of E(T₁) is usually relatively straightforward, the situation for E(S₁) is surprisingly fraught. Steady-state room-temperature (SS_RT) fluorescence emission is the most convenient and most frequently used to estimate the E(S₁) value, but this neglects any changes in molecular conformation that may impact E(T₁) (necessarily measured at low-temperature). Proponents of using steady-state low-temperature measurements (SS_LT) for E(S₁) can rightly claim that this version of ΔE_ST at least controls for any temperature-associated changes in molecular geometry, however it is the room-temperature value of E(S₁) and associated molecular conformers that are actually relevant to ambient operation of OLED devices. Steady-state measurements themselves present a single onset value as the intensity-weighted ensemble average of different conformers in a film sample, in contrast to time-resolved values that can change significantly depending on the delay time chosen as molecular conformations relax following excitation. The desirable removal of user choice in these steady-state values is therefore counterbalanced by the consideration that it is the molecular conformers emitting in the DF regime that are actually responsible for rISC in TADF devices. Hence of these four common variants of ΔE_ST (SS_RT-PH, SS_LT-PH, PF-PH, and DF-PH), none stands out as a clear ‘best’ choice for predicting rISC and OLED performance.

Here we examine this challenge through systematic comparison of 4CzPyz^28,29 and 4tCzPyz³⁰ as model systems, exhibiting similar spectra but different ΔE_ST and rISC kinetics. We take the view that the usefulness of any version of ΔE_ST is in its ability to predict trends in rISC and DF lifetimes, and thus also OLED performance. Hence by comparing these kinetic and spectroscopic properties, we come to the conclusion that the steady-state room-temperature E(S₁) is likely the best to use, but ultimately confirm that none of the ΔE_ST variants give anything more than an indication of device performance.

2. Results and discussion

To systematically evaluate these measurement approaches, we selected 4CzPyz^28,29 and 4tCzPyz³⁰ (shown in Fig. 1) as model systems. These compounds differ only by tert-butyl substitution on the carbazole donors, yet exhibit different rISC kinetics despite having similar excited states. We examined both compounds across three strategically chosen host environments: Zeonex (apolar), DPEPO (polar), and PPT (for which device results are already reported^29,30). Although the core utility of ΔE_ST measurements is usually to indicate these kinetics and device performance properties ahead of time, this full investigation instead allows us to confirm how faithfully the different versions of ΔE_ST make these predictions. The chemical similarity of these two emitters allows us to also confidently attribute changes in kinetics to changes in ΔE_ST, as both are expected to have similar spin–orbit coupling (D–A structure with no heavy atoms) and vibronic coupling between excited states (discussed below).^21,22

Fig. 2 presents comprehensive steady-state characterization of both emitters in the varying host environments, at both room-temperature (SS_RT) and 80 K (SS_LT). Both compounds exhibit broad emission bands characteristic of charge-transfer singlet states, with dramatic host-dependent spectral shifts reflecting their sensitivity to host environment. The phosphorescence spectra reveal very similar E(T₁) across the series, likely arising from the shared pyrazine core. For all measurements except 4CzPyz in PPT, the low-temperature spectra red-shift relative to room-temperature emission, although only by ∼0.03 eV.

Fig. 2 Steady-state photoluminescence characterization of 4CzPyz (a)–(c) and 4tCzPyz (d)–(f) across three host environments (1 wt% Zeonex, 10 wt% DPEPO, and 10 wt% PPT films). Each panel shows room-temperature steady-state emission (RT, black), low-temperature steady-state emission (LT taken at 80 K, red), and 80 K time-resolved phosphorescence spectra (PH taken at 80 ms following pulsed excitation, blue). Black dashed tangent lines indicate the spectral onsets used in determination of individual state energies and hence ΔE_ST.

Fig. 3 and 4 illustrate the continuous evolution of the singlet emission throughout both PF and DF regimes. These changes in onset demonstrate the challenge of selecting “representative” time points for E(S₁), and therefore also ΔE_ST determination. During PF (0.8–50 ns), systematic red-shifts reflect conformational relaxation from initially excited Franck–Condon geometries, toward thermally equilibrated structures. The DF regime exhibits even more dramatic spectral migration, with substantial shifts from early microsecond to late millisecond timescales. This pronounced evolution arises from the complex population dynamics in the emitting films, where different conformational subsets exhibit varying spectra and kinetics.²⁰ The continuous spectral evolution demonstrates that any single temporal snapshot provides an at-best incomplete and potentially misleading representation of the ensemble behavior. It is also unclear which of these subsets is primarily responsible for device performance.

Fig. 3 Time-resolved photoluminescence spectra of 4CzPyz showing temporal evolution during (a)–(c) prompt fluorescence (PF, 0.8-31 ns) and (d)–(f) delayed fluorescence (DF, µs-ms) regimes across three host environments (1 wt% Zeonex, 10 wt% DPEPO, and 10 wt% PPT films).

Fig. 4 Time-resolved photoluminescence spectra of 4tCzPyz showing temporal evolution during (a)–(c) prompt fluorescence (PF, 0.8-52 ns) and (d)–(f) delayed fluorescence (DF, µs-ms) regimes across three host environments (1 wt% Zeonex, 10 wt% DPEPO, and 10 wt% PPT films).

The different onset-derived values for ΔE_ST (or possible ranges for time-resolved onsets) are presented in Table 1. The same values are also shown graphically in Fig. 5a. Inspecting this figure, we attempt to identify trends in the values of ΔE_ST when comparing 4CzPyz and 4tCzPyz in the same host environment, which correspond to performance predictions that can be later compared to the actual kinetics and device measurements. In Zeonex, 4tCzPyz is found to have a smaller ΔE_ST than 4CzPyz regardless of measurement method, and there is no overlap between their respective ΔE_ST value ranges whether derived from PF or DF onsets. This agrees with theoretical calculations for these two emitters in vacuum using a nuclear ensemble approach^31–33 (NEA, Fig. 5b), sampling across 500 geometries from a harmonic Wigner distribution of the T₁ state at 80 K.

Table 1 Comparison of singlet–triplet energy gaps (ΔE_ST, eV) for 4CzPyz and 4tCzPyz determined using four different measurement methods: room-temperature steady-state (SS_RT-PH), low-temperature steady-state (SS_LT-PH), prompt fluorescence onset (PF-PH), and delayed fluorescence onset (DF-PH) approaches across 1 wt% Zeonex, 10 wt% DPEPO, and 10 wt% PPT host environments. For PPT, an additional version using previously reported device^29,30 electroluminescence onsets is also provided (EL-PH)

Host	Compound	SSRT - PH	SSLT - PH		PFmax - PH	PFmin - PH		DFmax - PH	DFmin - PH		EL - PH
Note: All ΔEST values calculated using singlet energies from the respective methods and triplet energies from 80 K phosphorescence (PH) onset. PF max/min and DF max/min represent the largest/smallest ΔEST values obtained from different spectra within the respective temporal regimes (See Fig. 3 and 4).
Zeonex	4CzPyz	0.30	0.27		0.35	0.33		0.34	0.26		—
	4tCzPyz	0.21	0.19		0.25	0.24		0.26	0.23		—
DPEPO	4CzPyz	0.26	0.25		0.30	0.23		0.30	0.21		—
	4tCzPyz	0.29	0.28		0.39	0.32		0.38	0.28		—
PPT	4CzPyz	0.23	0.24		0.31	0.26		0.30	0.25		0.26
	4tCzPyz	0.22	0.21		0.29	0.13		0.27	0.19		0.22

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Fig. 5 (a) Comparison of ΔE_ST values obtained using different approaches for 4CzPyz and 4tCzPyz across three host environments (1 wt% Zeonex, 10 wt% DPEPO, and 10 wt% PPT). Dark blue diamonds indicate ΔE_ST values from SS_RT onset, while cyan diamonds indicate ΔE_ST values from SS_LT onsets. Navy bars represent the range of ΔE_ST values inferable from prompt fluorescence (PF) onset measurements, with green bars showing similar for delayed fluorescence (DF) onsets. Orange circles indicate the ΔE_ST values derived from the device electroluminescence (EL) onset (PPT film only) ref. 29 and 30. All ΔE_ST values were calculated using triplet energies derived from 80 K phosphorescence (PH) onsets. (b) Histogram of ΔE_ST values calculated using DFT/TDDFT across ensembles of molecules in their T₁ geometries at 80 K.

Excited state energies and hence ΔE_ST values for these geometries were calculated using DFT/TDDFT (see computational details in SI), with the gas-phase calculations most comparable to the measurements of the dilute and inert Zeonex films. Indeed the lower-energy onsets of the ΔE_ST histograms appear to reproduce the experimental SS_RT/LT ΔE_ST measurements, at approximately 0.2 and 0.3 eV for 4tCzPyz and 4CzPyz respectively. Although the modes of the histograms occur at larger ΔE_ST values, we propose that it is the molecules with the smallest values that will most strongly contribute to the DF properties. We were also required to restrict our investigation to T₁ geometries and low temperatures in this work in order to manage computational costs. This combination would most closely correspond to experimental ΔE_ST measurements derived from DF-PH comparisons of time-resolved measurements taken at low temperature, as DF emission arises initially from rISC in triplet molecular geometries. Experimentally this specific measurement is not accessible though, as at low temperatures the DF itself would be suppressed. Future investigations may allow this computational approach to also simulate and predict changes in ΔE_ST as derived from measurements across the PF and SS_RT, by considering energies of separate S₁ geometry distributions at elevated temperatures. The impact of host molecules can also be included, although again at considerable computational expense.³⁴

Returning to Fig. 5a, for the measurements in DPEPO both steady-state measurements (SS_RT and SS_LT) lead to smaller ΔE_ST values for 4CzPyz, although there is overlap and potential disagreement in predictions between methods depending on which of the time-resolved measurements are selected for comparison. In PPT this overlap is even more severe, although both PF and DF extend across smaller ΔE_ST values for 4tCzPyz. 4tCzPyz in PPT also gives a particularly wide range of PF-derived ΔE_ST values (visible in Fig. 4c), which may arise from a wider range of microenvironment heterogeneity, or from a wider range of donor–acceptor dihedral angles in the molecules in the film (disorder), that relax gradually upon photoexcitation.²⁰ Regardless of the cause, it appears that this major shift across the PF has no subsequent impact on the DF kinetics compared to 4CzPyz (Fig. 6c). Interestingly, for PPT the ordering of the room- and low-temperature steady-state (SS_RT and SS_LT) ΔE_ST measurements inverts for 4CzPyz, in contrast to all other measurements.

Fig. 6 Room-temperature photoluminescence decay profiles of 4CzPyz and 4tCzPyz in (a) 1 wt% Zeonex, (b) 10 wt% DPEPO, and (c) 10 wt% PPT host environments.

To critically evaluate the ability of the different versions of ΔE_ST to predict rISC performance, Fig. 6 shows the time-resolved photoluminescence decays of the same films. RT decay profiles reveal only subtle differences in delayed emission kinetics, as might be predicted from their overall similar ΔE_ST values. In Zeonex films 4CzPyz exhibits slightly slower and lower intensity DF compared to 4tCzPyz, in agreement with the ΔE_ST of the latter being smaller for all four considered variants and in calculations. In DPEPO the kinetic ordering inverts, with 4CzPyz showing faster-decaying DF with comparable intensity. This outcome is predicted by both the SS_RT and SS_LT ΔE_ST values as well as those derived from PF spectra (smaller for 4CzPyz), however the overlap of DF onset ranges means this prediction cannot also be confidently made for this version of ΔE_ST.

PPT films yield nearly identical photoluminescence decay profiles, shown in Fig. 6c. This is consistent with SS_RT ΔE_ST values being nearly identical, while the SS_LT variant of ΔE_ST incorrectly predicts faster decay kinetics for 4tCzPyz by a similar expected magnitude of difference as seen for DPEPO. Here as well the time-resolved ranges of ΔE_ST values significantly overlap, such that any predictive power is overshadowed by the choice of specific spectra used. Hence, it appears from the measurements in PPT that the SS_RT variant of ΔE_ST is the most predictive of the time-resolved kinetics and underpinning rISC. We do not attempt to directly quantify these rISC rates though, as they can similarly strongly depend on the range of decay used to fit prompt and delayed lifetimes.⁷

Before progressing we must consider other possible mechanisms by which the tBu groups in 4tCzPyz can impact rISC, and hence justify the earlier assertion that the structural similarity of 4CzPyz and 4tCzPyz allows the changes in TADF kinetics to be attributed to changes in ΔE_ST. In the first instance, by increasing the electron-donating strength of the Cz groups the tBu substituents are able to directly impact E(S₁) and hence modify ΔE_ST.³⁵ In addition, tBu groups have been shown to reduce the formation of aggregate states,^36,37 although for the low-concentration films investigated here this is not of primary concern. While tBu groups can also influence the steric environment of donor groups in crowded multi-Cz emitters,³⁸ we have previously shown that the pyrazine heteroatoms in 4CzPyz²⁸ and similar materials³⁹ significantly alleviate steric congestion near the D–A bond. This environment limits the potential for outwardly-pointing tBu groups to influence the equilibrium D–A dihedral angle, although any such changes will also then reflect in ΔE_ST itself through changes in the electronic coupling between donor and acceptor units. Separately, any 'inertial' effects of the tBu groups reducing vibronic coupling (by dampening the relevant D–A bond torsions) are expected to be small – inertial impacts on rISC were only modest in fluid solutions for previously reported materials featuring much larger and more axially-displaced adamantyl substituents, and only barely discernable in solids films.⁴⁰

From the near identical ΔE_ST values and near identical emission decays in PPT, we would therefore infer near-identical rISC rates and hence expect near-identical OLED performance from 4CzPyz and 4tCzPyz. Indeed, previously reported devices of these emitters in identical stacks with PPT host show very similar EQE_max (Fig. 7a). However, while EQE_max relies on both rISC and emitter PLQY (reported at 75 and 73% for 4CzPyz and 4tCzPyz, respectively in PPT), the roll-off of this EQE is more strongly determined by rISC and shows significant unexpected differences at higher operating brightnesses. Comparing the two devices together, the roll-off for 4tCzPyz is significantly improved, in contrast to the similar spectroscopic ΔE_ST and even rISC inferred from comparison of time-resolved emission kinetics. This comparison therefore demonstrates that none of the variants of ΔE_ST are able to make ‘ironclad’ predictions of device performance for 4CzPyz and 4tCzPyz specifically, and thus proves by contradiction that similar skepticism should be applied for TADF materials more broadly.

Fig. 7 OLED device performance and electroluminescence characterization. (a) External quantum efficiency (EQE) versus luminance (cd m⁻²) characteristics for OLED devices. (b) Normalized electroluminescence (EL) spectra of OLED devices based on 4CzPyz and 4tCzPyz at 10 wt % in PPT. Dashed blue tangent lines indicate the spectral onsets used for determining ΔE_ST from EL-PH. Device data taken from ref. 29 and 30.

Instead, here ΔE_ST taken from the onset of device electroluminescence (EL, Fig. 7b) does correspond with the device roll-off, and is considerably smaller for 4tCzPyz as shown in Fig. 5a and Table 1. It is unclear whether these different device-emission onsets are a result of the EL process, or potentially the evaporated nature of the emissive films. In either case though, requiring device preparation and characterization to enable accurate ‘prediction’ of device performance is of limited strategic value, as the ‘prediction’ made by this version of ΔE_ST is itself immediately superseded by the direct device measurements.

While the use of ΔE_ST to broadly or qualitatively predict trends in TADF materials (where these values sufficiently differ) is therefore still useful, and our recommended standardization of reporting using SS_RT measurements may help support greater meta-analytical insight across the research community, we ultimately demonstrate that the performance of devices is not guaranteed to be predicted by this factor in any of its spectroscopic variants. This work therefore justifies the abandonment of pedantic or over-zealous support of any single reporting method, while weakly favoring SS_RT measurements primarily for their convenience and towards a unified approach.

3. Conclusion

Through systematic evaluation and comparison to further spectroscopic and optoelectronic characterization, we demonstrate that room-temperature steady-state (SS_RT) measurements provide the most convenient and reliable approach for determining predictive ΔE_ST, albeit by only a narrow margin. The more important performance of actual devices is only loosely tied to any version of ΔE_ST, and quantitative comparisons are not necessarily insightful especially when the differences are small. While it will benefit the community to adopt a single reporting standard across the research field, the direct benefits of choosing any particular method within a single investigation are limited. Based on experimental convenience and the removal of user choice, we recommend the use of SS_RT E(S₁) measurements, but stress that none of these methods can be uncritically relied on to fully predict eventual device performance.

Conflicts of interest

There are no conflicts to delcare.

Data availability

All relevant data is presented in the main text. Supporting information (SI): general and computational methods, synthetic procedures, and characterization data for 4tCzPyz. See DOI: https://doi.org/10.1039/d5tc03735b.

Acknowledgements

The authors gratefully acknowledge the Kuwait Foundation for the Advancement of Science (KFAS, grant number CN22-15SC-1583). The authors also thank Kuwait University for for providing access to Research Sector Project Units (RSPU) general facilities of the Faculty of Science (GFS; GS 01/01, GS 01/03, GS 01/05, GS 01/08, GS 02/01, GS 02/13, GS 03/01, GS 03/08). We further thank Prof Eli Zysman-Colman for providing access to device data previously published for 4CzPyz and 4tCzPyz in PPT.

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Footnote

† These authors contributed equally to this work.

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