Advancing efficiency in deep-blue OLEDs: Exploring a machine learning–driven multiresonance TADF molecular design

Abstract

The pursuit of boron-based organic compounds with multiresonance (MR)–induced thermally activated delayed fluorescence (TADF) is propelled by their potential as narrowband blue emitters for wide-gamut displays. Although boron-doped polycyclic aromatic hydrocarbons in MR compounds share common structural features, their molecular design traditionally involves iterative approaches with repeated attempts until success. To address this, we implemented machine learning algorithms to establish quantitative structure-property relationship models, predicting key optoelectronic characteristics, such as full width at half maximum (FWHM) and main peak wavelength, for deep-blue MR candidates. Using these methodologies, we crafted ν-DABNA-O-xy and developed deep-blue organic light-emitting diodes featuring a Commission Internationale de l’Eclairage y of 0.07 and an FWHM of 19 nm. The maximum external quantum efficiency reached ca. 27.5% with a binary emission layer, which increased to 41.3% with the hyperfluorescent architecture, effectively mitigating efficiency roll-off. These findings are expected to guide the systematic design of MR-type TADF clusters, unlocking their full potential.

Machine learning drives the design of boron-doped polycyclic aromatic hydrocarbons for highly efficient deep-blue OLEDs.

INTRODUCTION

The search for promising pure-blue organic candidates suitable for emissive layers in organic light-emitting diodes (OLEDs) has been a formidable challenge spanning over two decades (1). Meeting stringent criteria such as a narrow emission profile, high efficiency, and operational stability adds complexity to this immense pursuit (2). Within the realm of organic electronics, strategies are being devised to overcome these intractable issues (3–8). Promising approaches include boron atom–based organic (i.e., organoboron) emitters, as these materials not only offer good color purity but also demonstrate commendable chemical stability (9). Specifically, boron-doped polycyclic aromatic hydrocarbons (PAHs) have garnered attention for their captivating photophysical characteristics, presenting a potential solution to the search for ideal blue organic compounds. Particularly noteworthy are boron atom–centered azatriangulene molecular cores, specifically 5,9-dioxa-13b-boranapthho[3,2,1-de]anthracene (DOBNA) (10) and 5,9-diaza-13b-boranaptholo[3,2,1-de]-anthracene (DABNA) (11). These compounds exhibit an intriguing opposite resonance effect on the tri-coordinated sp²-hybridized boron atom within their PAH molecular skeleton (12, 13). This characteristic is deemed to enhance their potential as promising deep-blue organic candidates that meet the demanding criteria as mentioned above. In other words, the electronic reconfiguration of a boron atom in compounds like O, B, O–membered DOBNA (with adjacent electron-donating oxygen atom) and N, B, N–embedded DABNA (with adjacent electron-donating nitrogen atom) within the frontier molecular orbitals (FMOs) results in a unique luminescent property termed multiresonance (MR)–induced thermally activated delayed fluorescence (TADF) (11). It is important to note that this TADF characteristic involves a series of endothermic spin-uphill processes for the triplet excitons from the lowest triplet excited (T₁) state to the lowest singlet excited (S₁) state, thereby harnessing the excitons as a form of delayed fluorescence (3, 14, 15).

In contrast to typical TADF molecules, which often feature a bridged phenyl core inducing spatially confined charge transfer (CT) between the electron donor (D) and acceptor (A) units on the molecular orbital scale, organoboron compounds exhibit MR-induced CT characteristics in the atomic orbital scale due to the electron localization in FMOs (16). This intrinsic feature helps to avoid substantial geometric changes between the ground (S₀) state and S₁ state, resulting in a narrow Gaussian-type CT band with a full width at half maximum (FWHM) value below 40 nm (17). As part of ongoing research, a compound named “ν-DABNA” has been recently proposed. This compound incorporates two pairs of DABNA cores to extend π-conjugation, thereby localizing FMO at individual atoms within the MR-TADF core (18). This inventive design effectively addresses the trade-off between the energy difference between the two lowest excited states under spin-multiplicity (ΔE_ST) and the spatial overlap of FMOs. The outcome is a strong oscillator strength (f_OSC) for the transition dipole moment (TDM) at the S₁ state and a small ΔE_ST (16, 19). This approach not only achieves a high photoluminescence quantum yield (PLQY) but also facilitates an efficient spin-uphill process, distinguishing it from conventional donor-acceptor (D-A) type blue TADF molecules (19). As a result, the use of ν-DABNA as an MR-TADF emitter has enabled the development of an OLED characterized by highly efficient pure-blue emission, leading to a maximum external quantum efficiency (η_EQE) of around 34% with a narrow FWHM of 18 nm (18, 20).

The structural feature of boron-doped PAHs plays a critical role in the development of MR-TADF compounds (21). However, the molecular design of these compounds relies heavily on a time-consuming iterative approach, involving repeated and varied attempts until successful outcomes are achieved. In response to this challenge, we propose a design strategy that integrates machine learning to expedite the search for potential deep-blue MR candidates. To support this innovative approach, we compiled experimental data from around 400 sets of MR-TADF compounds, extracted from the Science Citation Index-Expanded (SCIE) literature. The dataset includes essential parameters such as the main peak wavelength (λ_peak) and the FWHM of the PL spectra obtained from the compounds dissolved in specific solvents. By leveraging this assistant dataset, our objective was to use machine learning algorithms to discern patterns and relationships within the molecular structures and their corresponding photophysical properties (i.e., λ_peak and FWHM). This data-driven approach aims to streamline the design process, minimizing the need for exhaustive trial-and-error experimentation. Using these methodologies, we have identified a compound named “ν-DABNA-O-xy” as a promising candidate for deep-blue emitters and used it as a proof of concept for a deep-blue OLED with a Commission Internationale de l’Eclairage (CIE) y coordinate of 0.07 and a narrow FWHM of 19 nm (refer to table S1 and figs. S1 to S16 for details on their synthesis and characterization). The maximum external quantum efficiency (EQE) reached approximately 27.5% in a conventional binary emission layer (i.e., host-guest type) and 41.3% in a hyperfluorescent architecture. These findings are expected to play a pivotal role in the diverse exploration of MR-type clusters. Ultimately, the integration of machine learning is anticipated to facilitate the discovery of deep-blue MR candidates with enhanced optoelectronic characteristics.

RESULTS

Quantitative structure-property relationship model

Because of the intricate nature of organoboron compounds, there is a substantial demand for machine learning methods capable of constructing robust and predictive models connecting these PAH-type molecular clusters with their photophysical properties. In this context, we introduced quantitative structure-property relationship (QSPR) methods (22–24), grounded in the hypothesis that molecular structures are correlated with changes in the observed macroscopic properties of the corresponding molecular clusters, as illustrated in Fig. 1A. Notably, QSPR modeling employs a supervised learning algorithm that demands a reliable dataset including the target molecular structures and their corresponding well-defined macroscopic properties for the training set. To address this requirement, we extracted the PAH-type molecular structure along with its representative photophysical properties, specifically λ_peak (table S2) and FWHM (table S3), from the SCIE literature for the construction of a series of predictive models.

Fig. 1. An outline of machine learning–driven MR-type molecular design.

(A) Schematic diagram of machine learning–driven MR-type molecular design protocol in this work. (B) Scatter plot from the continuous model result (model A), showing the training/test set of λ_peak predictions. (C) Interpretable model visualization from radial-based KPLS regression model for λ_peak prediction. Note that in the case of symmetric structure (i.e., the boron-centered azatriangulene backbone), the left visualization is omitted for clarity. Refer to data S1, S2, and S3 for detailed data on machine learning training.

We constructed 400 predictive QSPR models using four types of machine learning algorithms as previously outlined (refer to Methods for details). Cross-validation (hold-out method) was carried out using multiple train/test set pairs randomly selected from the structure-property data, as indicated by the red (train)/yellow (test) rectangles in Fig. 1A. Subsequently, we ranked and ordered all QSPR models based on their predictive accuracy and retained only the top 10 models. In particular, the predictive model was selected based on the model score (S_Model) estimated by cross-validation results from randomly selected training and test sets. For model testing, descriptors and fingerprints were computed for unseen structures, and these features were then input into a pretrained QSPR model to generate property predictions. Herein, we randomly divided the training set and test set of the experimental λ_peak data by the ratio of 17:3 (i.e., 85% training set and 15% test set). A total of 403 different random splits were taken for the training and test sets.

Figure 1B depicts the most reliable continuous model for λ_peak predication, where the cross-validation coefficient of determination (Q²) for the test set data (i.e., 60 organoboron compounds) is around 0.8, and the coefficient of determination (R²) for the training data corresponds to the value of 0.87. In addition, the root mean square error (RMSE) for λ_peak in this model was 21.4 nm. This model has an S_Model of 0.75, supporting its prediction as a strong candidate for addressing our study. The scatter plot illustrates the comparison between the model prediction and the experimental value of λ_peak for the training/test set compounds. Here, we observed that the 10 top-ranked QSPR models were based on kernel-based partial least-squares (KPLS) regression (25). Of these, five models used MOLPRINT 2D fingerprints (26), four models used dendritic fingerprints (27), and the remaining model used radial fingerprints (24). It is important to note that the prediction of λ_peak for PAH-type compounds has effectively been conducted on the basis of nonlinear-type algorithms. In other words, the KPLS machine learning algorithm, in combination with 2D-type fingerprints, has been proven to keep a high model score of more than 0.73 (i.e., S_Model). In this context, Fig. 1B illustrates the chosen QSPR single model derived from KPLS fitting with a radial fingerprint, using the 14th split of the learning set into test and training subsets.

In addition to ensuring high model prediction accuracy, it is also crucial to visually connect the relationship between λ_peak and the PAH-type chemical structures within this study. This aspect is highly noteworthy, as a binary-type fingerprint-based KPLS model allows for visual interpretability (25). A visual representation of the atomic effect for a single KPLS model built from the radial fingerprint is shown in Fig. 1C for the organoboron candidates. Herein, atoms that increase the predicted value of λ_peak (i.e., a bathochromic shift) are colored red, whereas atoms that decrease the value of λ_peak (i.e., a hypsochromic shift) are in blue. The color intensity reflects the strength of the effect that we have focused on. In particular, this atomic effect is quantified by the atomic sensitivity (S_a), which approximates the influence of atom a on predicted λ_peak (refer to Methods for details). Using the interpretive model visualization from this KPLS model, we have identified that diphenylamine (DPA) in peripheral phenyl groups (PPGs) plays a critical role in raising the value of λ_peak for the ν-DABNA (control). Notably, we observed that this trend is inhibited when the nitrogen atom within the DPA in PPGs is replaced with an oxygen atom in the methoxy group (refer to candidates #1 and #2). This distinction becomes more evident when examining candidate #3, composed of two DABNA structures, each having a methoxy and DPA group separately. Considering candidate #3, it was expected that the introduction of the tolyl group for the PPGs would effectively induce steric hindrance regardless of the replacement of DPA with the methoxy group. As experimentally reported (19, 28), this could prevent the target molecule from undergoing the structural relaxation change, thereby shortening the value of λ_peak.

The significance of this research lies in the discovery that substituting the DPA group with a methoxy group can lead to a considerable change in λ_peak. It is noteworthy that previous studies have emphasized the necessity of DPA groups, enabling molecules to control both λ_peak and the side peak wavelength (λ_side) associated with vibrational modes (19, 28). Essentially, if reducing the value of λ_peak within the ν-DABNA backbone has been achieved through elemental oxygen substitution in outer parts (e.g., PPGs) rather than the PAH core, the importance and flexibility in the context of substituting the DPA group cannot be overstated. This is because the previous molecular design strategies of ν-DABNA have mainly focused on internal atom substitution (e.g., sulfur, oxygen, and selenium) centered on the PAH core (9, 21). This is partially consistent with our radial-based KPLS model, which successfully describes these pioneering designs for achieving a blue shift in ν-DABNA, particularly through oxygen or sulfur atom substitutions in the PAH backbone. This is demonstrated by the data for ν-DABNA-O-Me (index #4), BOBO-Z (index #5), and BSBS-Z (index #6) in table S2. In this regard, by introducing a tolyl group for all PPGs, which makes them lock on the basis of steric hindrance, and substituting oxygen with a methoxy group, we anticipate that the resulting λ_peak for ν-DABNA-O-xy will be approximately 9.1 nm shorter (target, λ_peak: 466.7 nm) than the original ν-DABNA molecule (control, λ_peak: 475.8 nm). In addition, we developed a dendritic-based KPLS regression model for predicting FWHM, as shown in fig. S17. Notably, FWHM for the control (ν-DABNA) was predicted to be 13.5 nm (observed at 14.8 nm), and for the target (ν-DABNA-O-xy), it was predicted to be 17.9 nm (observed at 13.8 nm). Considering the performance metrics of the model (S_Model = 0.74), with R² = 0.79, Q² = 0.75, and RMSE = 4.7 nm, the quantitative FWHM predictions for the target molecule appear to be reasonably accurate. However, the model does not sufficiently capture the changes in FWHM in response to variations in PPG, particularly for the target molecule. A more detailed discussion comparing the FWHM of ν-DABNA and its derivatives will be provided later.

Proof of concept for MR-TADF molecule: ν-DABNA-O-xy

Figure 2A presents the normalized absorption spectrum and room temperature photoluminescence (RTPL) profile for our target molecule (ν-DABNA-O-xy) dissolved in a toluene solution. For clarity in comparison, we have included the case for ν-DABNA as a control. The notable absorption band observed at 444 nm for the target molecule corresponds to the main electronic transition from S₀ to S₁ state. This spectral feature closely matches the simulated one by the vertical gradient Franck-Condon (VG-FC) method (illustrated by the dotted line). Likewise, the RTPL spectrum shows good agreement with the expected spectral shape, wherein the electronic transition occurs from S₁ to S₀ state, as modeled by the adiabatic Hessian FC (AH-FC) simulation (29, 30). Symmetrically mirrored from the first absorption band, the RTPL spectrum shows a sharp emission peak centered at 456.4 nm (λ_peak) with an FWHM of 13.8 nm. Comparatively, the control RTPL spectrum had a λ_peak of 469.0 nm and an FWHM of 14.8 nm. Note that the observed blue shift of approximately 14 nm at RTPL spectra aligns consistently with our machine learning–based prediction. We observed a similarity between the RTPL and low-temperature PL curves, suggesting that S₁ and T₁ states have similar MR-induced CT features (refer to fig. S18). This is consistent with the notably small ΔE_ST of 15 meV observed for our target molecule. It is also noteworthy that 14 nm of blue shift at RTPL compared to the control case (i.e., λ_peak: 469.0 nm → 456.4 nm) has been achieved without compromising its emitting performance; instead, the absolute PLQY remained at the near-unity value of 0.98.

Fig. 2. Optoelectronic characterization of ν-DABNA-O-xy molecule.

(A) Absorption spectrum of ν-DABNA-O-xy and fluorescence spectra for the target and control molecules in toluene (concentration, 0.05 mM). (B) Transient PL profiles for target and control system in toluene solution (0.05 mM). Inset, TDMv for ν-DABNA-O-xy from the electronic transition: S₁ → S₀—(X, Y, Z) = (3.41, −0.06, −0.46)—lies along with the five-membered ring plane (i.e., long axis of molecule). (C) Steady-state PL spectra of target molecule doped in DBFPO host (concentration, 1.0 to 10.0 wt %). (D) Calculated nonbonding energy (E_Cohesive) for each individual system integrated from 20-ns converged frame. The number (#) of dimer clusters collected at 100 ns snapshot. (E) Angular-dependent p-polarized PL profile of DBFPO: ν-DABNA-O-xy (3.0 wt %, BN-type). (F) EL spectra for a series of EML architecture for both target (ν-DABNA-O-xy) and control (ν-DABNA) molecules.

Similar to the findings on ν-DABNA derivatives (19), our target molecule also exhibited a TDM vector aligned along the plane of the five-membered ring, as shown in the inset of Fig. 2B. This alignment of TDM vector leads to orthogonality with respect to change in solvent-induced dipole moment. When examining the Tr-PL profiles within the measurement scales of 5, 20, and 50 μs, a decrease in the delayed fluorescence (DF) lifetime (τ_DF) was observed compared to the control in all cases, thereby yielding a rate constant of reverse intersystem crossing (RISC) (k_RISC) of 4.1 × 10⁵ s⁻¹ (refer to fig. S19 and tables S4 and S5). We have summarized both the RTPL (fig. S20) and Tr-PL profiles (fig. S21) for these ν-DABNA derivatives doped in 2,8-bis(diphenyl-phosphoryl)dibenzo[b,d]furan (DBFPO) host film, corresponding to the condensed solid-state case. The results are tabulated as tables S6 and S7 and will be delineated later. In addition, theoretical frameworks such as density functional theory and post-Hartree Fock methods corroborate the conclusion that substituting outer DPA moiety within PPGs with an oxygen atom (specifically, 2-methoxy-1,3-dimethylbenzene) leads to a shortened λ_peak, compared to that of the control case (refer to the “Computational results” section in the Supplementary Materials for details). In particular, the small Stokes shift of 12.4 nm and a narrow FWHM (13.8 nm) connote the minimized structural displacement between S₀ and S₁ states. This is further supported by the root mean square displacement (RMSD) comparison for ν-DABNA-O-xy at the respective states, as depicted in fig. S22. In line with this observation, the reorganization energies of ν-DABNA-O-xy for its S₁ (λ_S) and T₁ (λ_T) states are calculated to be as low as 0.06 and 0.07 eV, respectively, derived from the potential energy surface curves (refer to table S8). To enable a more direct comparison with the control molecule ν-DABNA, RMSD (refer to fig. S23) and λ_S, λ_T for ν-DABNA were also determined using the same method (refer to table S9).

It is worth mentioning, however, that alterations in PPGs can often induce changes in molecular vibrational modes, potentially leading to increased Stokes shift and FWHM (19, 28). A thorough examination conducted under the harmonic oscillator approximation (31) revealed the influencing components on λ_S of ν-DABNA-O-xy. The analysis indicated that the largest Huang-Rhys (HR) factor (S_i), representing electron-vibration coupling, corresponds to the vibrational twist mode 10 (30.4 cm⁻¹), associated with the proposed PPGs (refer to fig. S24). Nonetheless, even the highest HR factor (S₁₀) remains modest at 0.14, with the total HR factor for all involved 438 vibrational modes estimated to be as small as 1.21. For ν-DABNA, the total HR factor (${\displaystyle \sum _{i=1}^{414}}{S}_{\mathrm{i}}=0.68$) is smaller than the target value of 1.21 (see fig. S25). In addition, the RMSD for S_1,geo/S_0,geo is 0.14 Å for control and 0.17 Å for the target. Although modifications to PPGs may influence molecular vibrational modes and potentially increase the Stokes shift and FWHM, our design strategy ensures that the target molecule maintains a low HR factor, thereby preserving its narrow FWHM and small Stokes shift. Through TDM analysis, a high degree of horizontal orientation (Θ_h) was expected for this target molecule (fig. S26). In addition, the natural transition orbital analysis (32) revealed that both excited states (i.e., S₁ and T₁ states) exhibit a CT character in their excited natures (refer to figs. S27 to S29). This CT character originated from the MR effect with electron participation of the methoxy part, strongly supported by the electron density plots as depicted in fig. S30 (refer to the calculated spin-orbit coupling matrix element value tabulated in table S10). When engaging molecular engineering to achieve specific objectives, it is crucial to preserve the advantageous qualities of the original molecule (control). Hence, considering the points mentioned earlier, it can be concluded that ν-DABNA-O-xy retains all the benefits of the control while also demonstrating improved photophysical properties in the solution state.

These advantages were found to exhibit consistency when doped into the DBFPO host. Despite achieving a 15.6-nm blue shift in RTPL with a 3.0 wt % doping of DBFPO film (binary-type, BN) compared to the control case (i.e., λ_peak: 475.9 nm → 460.3 nm), the absolute PLQY remained at 0.90. In the case of control, the necessity for a low concentration (below 1.0 wt %) arises due to the planar molecular π-framework of ν-DABNA, rendering this material susceptible to excimer formation via π-π intermolecular interactions (refer to two excimer configurations in the inset of Fig. 2C). For ν-DABNA itself, a report (28) indicates that even at a low doping concentration of 1.0 wt %, notable excimer formation is observed, which is a major source of exciton quenching. The fundamental photophysical behaviors of this excimer formation in ν-DABNA and its derivatives have been extensively studied in previous reports (19, 28). In this context, this excimer formation leads to the emergence of an excimer shoulder peak (λ_side) at a longer wavelength compared to λ_peak and thus tends to overshadow the advantages of a narrow FWHM and high PLQY at low doping concentrations. For a detailed comparison between control and target compounds, refer to table S6. In the case of ν-DABNA-O-xy, we note that the contribution from λ_side to the overall PL spectra is completely suppressed even with a relatively large doping concentration change from 3.0 to 10.0 wt % within the DBFPO host layer, as depicted in Fig. 2C. Consistent with observations in BN-type systems, hyperfluorescent (HF)–type systems based on the codeposition of ν-DABNA-O-xy with the TADF assistant dopant, 10-(5,9-dioxa-13b-boranaphtho[3,2,1-de]anthracen-7-yl)-10H-spiro[acridine-9,9′-fluorene] (DBA-SAF), exhibit less pronounced shoulder peak than those reported previously for ν-DABNA, although it is higher and broader than that of the BN-type film (18–20, 28).

To gain a deeper insight into excimer formation, directly associated with λ_side, in films doped with ν-DABNA-O-xy, we conducted molecular dynamics simulations for both BN- and HF-type systems. As expected, in the case of the BN-type system, it was observed that for both target and control molecules, the cohesive energy (E_Cohesive) for each system tends to increase with higher doping concentrations (i.e., 1.0 to 40.0 wt %), as shown in Fig. 2D. Specifically, as tabulated in tables S11 and S12, there is a noticeable rise in van der Waals energy, while the electrostatic energy demonstrates a decreasing trend. This suggests that as the doping concentration increases, the Coulombic interaction with the polar DBPFO host diminishes, while the dipole-induced interactions between dopants (i.e., ν-DABNA derivative) themselves intensify. Note that the increase in E_Cohesive with the doping ratio is clearly less significant in the ν-DABNA-O-xy case (49.30 kcal/mol at 40.0 wt %) than in the case of ν-DABNA (51.21 kcal/mol). Another key observation is that in HF-type systems, the presence of DBA-SAF results in a more pronounced decrease in E_Cohesive compared to BN-type systems at the same concentration (refer to tables S13 and S14). For these convergent models, the density profiles and cohesive energy profiles as functions of MD simulation time are provided in figs. S31 and S32. This trend was identified in both control and target molecules, but it was particularly apparent in ν-DABNA-O-xy (target). By extracting the excimer clusters (i.e., center of mass below 15 Å) from the snapshot at 100.0 ns, it was found that within the 20.0 wt % condition for target materials, the number of excimer formations for the HF-type (39 sets) is smaller by approximately 25% than that for the BN-type (51 sets). In this context, it can be inferred that the target molecules have the potential to inhibit excimer formation even at high concentrations compared to control molecules for both BN-type and HF-type systems.

Device performance and exciton dynamics for the electrical model

From an angle-dependent p-polarized PL profile for the BN-type as shown in Fig. 2E, Θ_h of the proposed material is estimated to be very high, at 0.97. As previously reported, Θ_h of control was also estimated to be high at 0.95 (refer to fig. S33) (19). Nevertheless, considering that the TDM of the target lies in the plane of the PAH core along the long axis (refer to fig. S26), it can be said that the molecular anisotropy may increase as the bulky DPA groups in PPGs are substituted with methoxy. We further investigated molecular anisotropy in the HF-type system for both control and target, but the value of Θ_h did not change with respect to those of the BN-type system (refer to figs. S33 and S34). To fully harness the potential of our target molecule as a deep-blue emitter in OLEDs, we have designed and tested the following sample architectures: For Dev. A (target) and Dev. D (control), we implemented a BN-type EML with a 3.0 wt % doped DBFPO host. For Dev. B (target) and Dev. E (control), we used an HF-type architecture, comprising a 3.0 wt % ν-DABNA derivative, 30.0 wt % DBA-SAF, and a DBFPO host. For those interested in direct comparisons with the ν-DABNA–based OLED samples, detailed information, including the device characteristics, has been summarized in Table 1, Fig. 2F, and figs. S35 to S40.

Table 1. Characteristics of the tested OLED devices based on ν-DABNA-O-xy.

Item*	Type/Dopant conc. (wt %)	λEL (nm)	Voltage (V)†	EQE (%)‡	Power efficiency (lm/W)§	Current efficiency (cd/A)¶	λFWHM (nm)	CIE (x, y)	Blue index (cd/A)
Dev. A	BN/3.0	460	4.0/5.8	27.5/16.2	14.4/5.8	16.1/9.5	19	(0.14, 0.07)	230
Dev. B	HF/3.0	460	3.4/5.2	41.3/28.2	33.9/15.2	32.3/22.1	21	(0.14, 0.10)	323
Dev. C#	HF/3.0	460	3.2/4.8	58.2/42.4	58.4/28.3	92.5/67.4	21	(0.14, 0.12)	771
Dev. D	BN/3.0	474	4.0/5.4	24.5/17.4	22.3/11.7	28.5/20.3	20	(0.12, 0.17)	168
Dev. E	HF/3.0	475	3.6/5.4	31.3/17.9	35.3/13.4	40.8/23.3	22	(0.12, 0.20)	204
Dev. F#	HF/3.0	475	3.4/5.2	49.8/30.9	60.1/24.4	101.4/62.9	21	(0.12, 0.21)	483

*ITO (70 nm)/HAT-CN (10 nm)/TAPC (40 nm)/TCTA (10 nm)/mCP (10 nm)/EML (25 nm)/DBFPO (5 nm)/TPBi (35 nm)/LiF (1 nm)/Al (100 nm), with the binary (BN)–type composition (3.0 wt % doped DBFPO host) for Dev. A (ν-DABNA-O-xy) and Dev. D (ν-DABNA, control) and the ternary (HF-type) film (3.0 wt % Emitter: 30.0 wt % DBA-SAF: DBFPO host) for Dev. B (ν-DABNA-O-xy) and Dev. E (ν-DABNA, control), respectively.

†Applied voltage at a luminance of 1 cd/m² and 1000 cd/m².

‡External quantum efficiency: maximum, then values at 1000 cd/m².

§Power efficiency: maximum, then values at 1000 cd/m².

¶Current efficiency: maximum, then values at 1000 cd/m².

#With a half-ball (HB) lens.

Figure 3 (A to D) displays the current density-voltage-luminance (J-V-L), EQE (η_EQE)–luminance, EL spectra (Dev. A, BN-type), and angle-dependent EL profiles for the ν-DABNA-O-xy–based sample devices in this study. It is noted that the maximum η_EQE of Dev. A (target), reaching 27.5%, is noteworthy, especially when considering that the BN-type control sample (Dev. D) exhibited a maximum η_EQE of 24.5%. As expected, the devices using an HF-type system (Dev. B) exhibited a notable enhancement in the maximum η_EQE of OLEDs, reaching 41.3% (58.2% with a half-ball lens, Dev. C). Herein, we designed optimal HF architecture for both control and target scenarios to ensure sufficient dipole-dipole energy transfer (ET) from DBA-SAF to the ν-DABNA derivatives. Detailed ET aspects for both cases are depicted in table S15 and figs. S41 and S42. As evident from Fig. 2F, compared to the control (ν-DABNA) case, the target (ν-DABNA-O-xy) exhibits the minimized occurrence of a long tail for λ > 475 nm when implemented in HF-type configuration. This trend is consistent with the RTPL profile for solid-state films observed in Fig. 2C. Notably, the FWHM and CIE y coordinate for the EL spectral emission of Dev. A (Dev. B) are 19 nm (21 nm) and 0.07 (0.10), respectively. This corresponds to a blue index (the color coordinate-corrected current efficiency) of 230 cd/A (323 cd/A), which belongs to the highest tier among the existing reports.

Fig. 3. OLED performance.

(A) J-V-L characteristics. (B) EQE-luminance curves of tested OLED samples. (C) Angle-dependent EL spectra for BN-type (3.0 wt %, ν-DABNA-O-xy) and (D) EL intensity profiles in steps of 5°.

As illustrated in Fig. 3B, the ratio of EQE measured at 1000 nits to that measured at 1 nit is measured to be 68.2 and 72.9% for Dev. B and Dev. C, respectively, while for Dev. A, this ratio is only 58.9%. This efficiency decrease observed in ν-DABNA-O-xy–based OLED samples aligns well with the bi-excitonic roll-off model for triplet-triplet annihilation (TTA) and singlet-triplet annihilation (STA), recognized as predominant factors contributing to the efficiency drop in MR-TADF–based OLEDs. By taking Dev. B (HF-type) as an exemplary model in Fig. 4A, the exciton dynamics analysis under steady-state conditions shows that the rate constant for STA (k_STA) is 1.0 × 10⁻⁹ cm³ s⁻¹, whereas the rate constant for TTA (k_TTA) was 1.0 × 10⁻¹¹ cm³ s⁻¹. We can gain a deeper understanding of this roll-off behavior based on the modeling result presented in Fig. 4B for Dev. B (or ν-DABNA-O-xy–based HF architecture), which shows the relative contributions of TTA (orange hatched area) and STA (red hatched region) to the internal quantum efficiency (represented by the blue-colored area). As carrier injection increases (i.e., as J increases), it is evident that, compared to the ideal scenario with no roll-off, the densities of singlet (N_S,Ideal) and triplet (N_T,Ideal) states at steady state decrease by approximately one order of magnitude (refer to N_S,Quenching and N_T,Quenching, respectively).

Fig. 4. Roll-off characteristics.

(A) J-EQE curves for BN- and HF-type OLED samples. The dashed line represents the simulated J-EQE model based on bi-excitonic annihilation processes. (B) Quantification of roll-off in ν-DABNA-O-xy–based HF architecture. Orange and red hatched area present TTA and STA-based roll-off contribution to the total efficiency (i.e., the unity) as a function of J. Relative exciton reduction ratio and the time-dependent population change at (C) singlet (N_Singlet) and (D) triplet (N_Triplet) states with or without the consideration of STA and TTA processes. The assessments are made at G = 3.12 × 10¹⁶ cm³ s⁻¹ for singlet exciton generation and G′ = 9.36 × 10¹⁶ cm³ s⁻¹ for triplet generation ratio via electrical pumping. (E) Time evolution of N_Triplet for the electrical model at initial state (G′). The star symbol (N_T96) marks the particular time when the triplet population is reduced by 96% compared to the concentration at the initial electrical pumping. (F) N_Triplet/N_Singlet profile versus time in the electrical model. The star symbol indicates the quasi-equilibrium state (or the onset of triplet accumulation) for the various electrical excitations.

To provide a comprehensive understanding of exciton annihilation processes in Dev. B, we introduced time-evolution exciton dynamics into our electrical system (refer to Methods for the details). Figure 4 (C and D) illustrates the simulated dynamics of singlet and triplet populations, including the relative contribution of STA and TTA within the system. In the given system, the initial density of generated excitons (per second) comprises 3.12 × 10¹⁶ cm⁻³ s⁻¹ for the singlet state (G) and 9.36 × 10¹⁶ cm⁻³ s⁻¹ for the triplet state (G′). Notably, the corresponding triplet density in Fig. 4E undergoes a 4% reduction from its initial state (N_T96) within approximately 0.1 μs, indicating a scenario characterized by frequent exciton collisions (refer to the time evolution of singlet density in fig. S43). Here, the solid line represents the simulation results for the triplet population in an ideal case, while the dotted line corresponds to the modeling results considering the nonideal situation with the roll-off.

We identified that within the time frame of t = 10⁻¹² s, approximately 23% of singlet excitons are deactivated by STA, the primary mechanism responsible for reducing excitons at the S₁ state, as shown in Fig. 4C. Concurrently, the maximal contribution from TTA occurs during the early stages of decay at the T₁ state. As illustrated in Fig. 4D, TTA accounts for 64.2% of the decrease in the triplet population, consequently impacting the overall singlet population due to the scarcity of triplets available for RISC from T₁ to S₁. Nevertheless, it is noteworthy that the TTA process also yields singlet excitons, thereby positively influencing the total singlet population through spin-uphill processes. As more time elapses (around t = 10⁻⁵ s), the exciton density decreases notably compared to the initial state. Consequently, bi-excitonic loss diminishes in both S₁ and T₁ states. In particular, STA occupies only 0.6% of the overall process in the S₁ state, while TTA comprises only 3.7% of the total processes in the T₁ state.

As shown in Fig. 4E and fig. S43, it was observed that as the initially generated exciton density increases by an order of magnitude, the reduction time of singlet/triplet density is substantially shortened. This suggests that exciton-exciton collisions contribute to the changes even in the initial state, as discussed in Fig. 4 (C and D). To further clarify this observation, we propose plotting the N_Triplet/N_Singlet ratio against the time domain, as illustrated in Fig. 4F, to elucidate the origin of the roll-off behavior. In the ideal scenario, where roll-off is not considered, the onset of triplet accumulation—defined as the point where the N_Triplet/N_Singlet ratio shows no change—typically occurs approximately 10 ns after electrical excitation, regardless of the initial exciton densities at t = 0. However, when roll-off is taken into account, as in Dev. B, this onset of triplet accumulation is reached instantaneously after electrical excitation, and a substantial number of excitons persist throughout the entire time domain until reaching a steady state. This assertion is strongly supported by the collection of Tr-EL profiles, where the pulse width was extended from 1.0 to 30.0 μs under constant voltage driving (at 18 V) conditions (refer to fig. S44).

The operational stability of EL devices, as shown in fig. S45, followed this sequence: Dev. E (HF-type, control), Dev. B (HF-type, target), Dev. D (BN-type, control), and Dev. A (BN-type, target), with the initial luminance (L₀) set at a constant current density of 2.0 mA/cm². In addition, photostability tests were conducted on the ν-DABNA derivative, as depicted in fig. S46. These tests, compared to the electrical case, shows consistency with the previous EL device stability results. While further research and effort will be required to fully understand the operational stability of the tested devices, it is notable that, based on the machine learning–driven de novo study, it is possible to identify molecules that retain all the advantages of ν-DABNA (control) while achieving a blue shift in the peak wavelength by more than 14 nm. This highlights the potential of the proposed methodology and, importantly, that of ν-DABNA-O-xy, the exemplary molecule discovered as a result.

DISCUSSION

We believe that incorporating machine learning models for predicting molecular properties holds great promise as a transformative approach to understanding MR-TADF molecules and advancing molecular design. Beyond the photophysical properties discussed here, such as λ_peak and FWHM, we will aim to expand our understanding of critical factors influencing MR-TADF molecule performance, including PLQY, SOCME, ΔE_ST, and kinetic factors such as k_ISC or k_RISC, which are highlighted in Fig. 1A. However, obtaining reliable raw data that could serve as a definitive standard—accounting for variables like measurement conditions, solvent, concentration, and the state of the medium (solution or solid)—remains challenging. Nonetheless, our QSPR model (model A or B), initially trained with 403 (or 404) molecular structures available at the time of manuscript submission, predicted the target properties of newly published MR-TADF structures (refer to fig. S47), including those beyond the ν-DABNA framework. Furthermore, a retrained machine learning model (model C), incorporating 63 additional molecules, demonstrated even greater predictive accuracy than the initial models (refer to tables S16 to S19). We believe that this approach provides a robust foundation for generating MR-TADF molecules and enhancing our understanding of their photophysical properties.

METHODS

QSPR models for MR-TADF molecular design

As previously discussed, the model training process involves using target structures and photophysical properties as inputs. Molecular descriptors and fingerprints are then computed to train machine learning models aimed at predicting continuous properties. The numeric (or classical) descriptors encompass topology-based features, physicochemical properties, graph-theoretical indices, and functional group counts (33). In addition, four types of binary fingerprints—linear (27), dendritic (27), radial (34), and MOLPRINT 2D (26)—were generated based on the molecular structures and used as independent variables (x). For feature extraction, descriptors with an absolute Pearson correlation coefficient (p) value exceeding 0.8 with another descriptor were eliminated, ensuring that no pair of descriptors exhibited linear correlation. For the fingerprints, the selection process considered the most important 10,000 bits (within a single bit space of 2³²) with the highest variance across the training set (24).

Most QSPR modeling methods typically incorporate regression techniques. For numerical models within continuous property space in this work, the used machine learning methods include the multiple linear regression (MLR) (35), principal component regression (PCR) (36), partial least square (PLS) regression (37), and kernel-based PLS (KPLS) regression (25, 38). As an instance, the most straightforward QSPR modeling method, MLR, operates on the assumption that the property of interest being modeled is a linear function of the descriptors, as follows

$$y_i=w_0+{\displaystyle \sum _1^n}{w}_n{x}_{\mathit{\text{in}}}$$ (1)

where y_i represents the property, x_i denotes the descriptors, and w_i shows the fitted coefficient derived from the least-squares criterions for the ith materials. Given Eq. 1, MLR models can frequently encounter overfitting issues, leading to the construction of models that may struggle to predict new data reliably, particularly when the number of descriptors exceeds the size of the dataset. PLS and PCR can effectively address this problem by reducing the size of the descriptors’ space, thereby generating models that are less prone to overfitting. In contrast to linear algorithms such as MLR, PCR, and PLS, it is important to note that the KPLS model is capable of identifying nonlinear patterns in the data. This is achieved by using a kernel trick to transform a nonlinear problem into a linear one, enabling the resolving of complex structure-property relationships where simple multi-linear regression schemes based on connectivity indices may not be applicable.

A kernel function is defined as a function that computes the inner product (or similarity) between examples after they have been mapped to a higher-dimensional feature space. For a mapping ϕ that takes data from the input space (D) to a feature space (F), the kernel function (K) is expressed as (38)

$$K(d_i,d_j)=<\mathrm{\varphi }(d_i),\mathrm{\varphi }(d_j)>$$ (2)

where d_i and d_j are examples from the input space, and ϕ(d_i) and ϕ(d_j) are their corresponding mappings in the feature space. The mapping ϕ transforms each example d∈D into an N-dimensional feature vector

$$\mathrm{\varphi }(d)=[{\mathrm{\varphi }}_1(d),\dots ,{\mathrm{\varphi }}_{\mathrm{{\rm N}}}(d)]$$ (3)

Direct feature extraction in this high-dimensional space can be computationally expensive. However, a kernel function provides an efficient alternative by allowing the computation of inner products without explicit data mapping. This approach enables the definition of a feature space with an effectively infinite number of dimensions (38).

Before constructing a series of KPLS models using a training set of compounds, the process begins with the assembly of an initial set of independent variables (x), as illustrated in Fig. 1A. These variables are created by combining all binary fingerprint bits that are “on” in at least one MR-TADF molecule within the training set. Each x variable is a binary descriptor (i.e., 0 or 1) that indicates the presence of a specific structural fragment found in at least one MR-TADF compound (25).

Subsequently, any x variable with a mean value deviating by more than 7 standard deviations (SD) from the overall mean of all the x variables in the pool is filtered out. This step removes descriptors that are nearly always off (mean value close to 0) or nearly always on (mean value close to 1). In addition, pairs of x variables with a correlation higher than 0.95 are reduced by discarding one variable from each pair. Last, the remaining variables are then standardized by setting their mean to zero and their standard deviation to 1. For a pair of standardized variables, denoted by column vectors x_i and x_j, we apply the Gaussian kernel function in our KPLS model as follows

$$K_{\mathit{ij}}=e^{-\frac{{\Vert x_i-x_j\Vert }^2}{2{\mathrm{\sigma }}^2}}$$ (4)

The parameter σ, which controls the nonlinearity of the kernel, was fixed at 20 for all computations in this work. This choice was based on the report (25) that model prediction became stable and insensitive to σ when its value was set to 20 or higher.

When a sufficiently large set of independent variables is available to construct factors (or latent variables), it becomes feasible to develop a model that fits the dependent variable to any desired level of accuracy by using a sufficiently large number of factors. For many types of experimental datasets, it is possible to attain a high-quality fit with only a limited number of factors (i.e., the optimal number of factors in this work) (24). To mitigate the risk of overfitting in this context, the inclusion of the addition of factors is curtailed once the coefficient of determination (R²) reaches 0.9. Further increasing the number of factors beyond this threshold is likely to result in overfitting for most experimental endpoints (refer to figs. S48 and S49).

We developed 400 predictive QSPR models, consisting of 50 MLR, 50 PCR, 50 PLS, and 50 KPLS models with descriptors, and 50 × 4 KPLS models (with four different binary fingerprints) using four distinct machine learning algorithms, as depicted in Fig. 1A. Cross-validation, particularly the hold-out method, was performed by selecting multiple train/test set pairs randomly from the structure-property data. The dataset was partitioned to ensure a similar distribution of photophysical properties (i.e., experimental values for λ_peak and FWHM) in the training and test sets. Initially, the dataset was sorted in ascending order of the observed property and then segmented into bins based on a 17:3 split (i.e., 85% training set and 15% test set). To provide an intuitive explanation, if we assume a 75:25 split, each bin would contain four compounds (e.g., the first bin would include compounds 1 to 4, the second bin would include compounds 5 to 8, the third bin would include compounds 9 to 12, and so forth). A single compound (i.e., MR-TADF molecule) is then selected randomly from each bin and allocated to the test set. For each machine learning model, we applied different random splits by initializing the random number generator with a unique seed when selecting a compound from each bin.

Following this, we ranked and organized all 400 QSPR models according to their predictive accuracy, retaining only the top 10 models. The model score (S_Model) was quantified using the following equation (24, 33)

$$S_{\text{Model}}={Q_{\text{Acc}.}}^2\times (1-\mid R^2-{Q_{\text{Acc}.}}^2\mid )$$ (5)

Note that S_Model can assign an accuracy score within the interval [0,1], with 1 representing a perfect prediction and 0 indicating a completely incorrect prediction

$$R^2=1-\frac{{{\mathrm{\sigma }}_{\text{Err}.,@\text{train}}}^2}{{{\mathrm{\sigma }}_{\text{Exp}.,@\text{train}}}^2}$$ (6)

$$Q^2=1-\frac{{{\mathrm{\sigma }}_{\text{Err}.,@\text{test}}}^2}{{{\mathrm{\sigma }}_{\text{Exp}.,@\text{test}}}^2}$$ (7)

Continuously valued methods in this work produce a least square fit to the dependent data, with R² serving as an appropriate measure of accuracy for the training set. Here, ${{\mathrm{\sigma }}_{\text{Err}.,@\text{train}}}^2$ represents the variance in the prediction errors (Err.) across the training set, while ${{\mathrm{\sigma }}_{\text{Exp}.,@\text{train}}}^2$ denotes the variance of the dependent variable (e.g., experimental values for λ_peak and FWHM) within the training set.

Similarly, Q² is derived as the equivalent of R² for the test set. However, Q² is sensitive to the variance of the dependent variable over in the test set (${{\mathrm{\sigma }}_{\text{Exp}.,@\text{test}}}^2$) due to the smaller size of the test set compared to the training set, which leads to significant fluctuation in the test set variance. To address this issue, we modified Eq. 7 to achieve an appropriate test set accuracy by incorporating the variance of the dependent variable over the entire learning set (${{\mathrm{\sigma }}_{\text{Exp}.,@\text{total}}}^2$)

$${Q_{\text{Acc}.}}^2=1-\frac{{{\mathrm{\sigma }}_{\text{Err}.,@\text{test}}}^2}{{{\mathrm{\sigma }}_{\text{Exp}.,@\text{total}}}^2}$$ (8)

To visualize atomic effects in the KPLS model using binary fingerprints, it is essential to recognize that the QSPR model intrinsically demonstrates that the predicted photophysical property (ŷ_i) of a given ith MR-TADF structure is based on the fragments (f_j) present in the structure, which correspond to the independent variables used in this work. In this context, each variable is set to 1 when the target fragment is present in the MR-TADF structure, indicating that the fragment activates on the corresponding bit (25).

Subsequently, we introduced a perturbation to a fragment to observe whether it increases or decreases the predicted photophysical property of the compound. A small change was made to the variable, and the corresponding property was recalculated, resulting in a shift in the predicted activity. Last, the sensitivity ($S_{f_j}$) of the fragment (f_j) was then calculated as the change (Δŷ_ij) divided by a small perturbation. If we assume that each atom in the fragment (f_j) contributes equally to the sensitivity ($S_{f_j}$), the sensitivity per atom is defined as $S_{f_j}$/$n_j$ where n_j denotes the number of heavy atoms in the fragment. Therefore, the overall sensitivity (S_a) of a specific atom (a) is determined by summing the contributions from all fragments that include that atom (25).

$$S_a=\sum _{j:a\in f_j}\frac{S_{f_j}}{n_j}$$ (9)

For model testing, descriptors and fingerprints were computed for the unseen structures, and these features were then input into a pretrained QSPR model to generate property predictions. Herein, we randomly divided the experimental data for λ_peak into training and test sets at a ratio of 17:3 (i.e., 85% training set and 15% test set). For FWHM prediction, the experimental data were randomly split into training and test sets at a ratio of 17:3 (i.e., 85% training set and 15% test set). A total of 50 different random splits were generated for the training and test sets. Here, QSPR models were developed using machine learning algorithms, AutoQSAR (24), which is implemented in the Materials Science Suite developed by Schrödinger (39). In addition, the Canvas cheminformatics package (27, 40) was used to generate molecular descriptors and fingerprints for building QSPR models.

Exciton dynamics for electrical model

To accurately simulate the behavior of an electrically driven TADF system (Dev. B), we can integrate roll-off processes into the electrical model, including bi-excitonic annihilations (i.e., STA and TTA), which has been recognized contributors to the critical roll-off in TADF-based OLED devices (19, 41–44). Here, we presented an exciton model founded on time-dependent population rate equations as follows (19, 41, 45).

$$\begin{array}{c}\frac{d{N}_{\mathrm{S}}(t)}{\mathit{dt}}=-(k_{\mathrm{r}}^{\mathrm{s}}+k_{\text{nr}}^{\mathrm{s}}+k_{\text{ISC}})N_{\mathrm{S}}(t)+k_{\text{RISC}}{N}_{\mathrm{T}}(t)-\hfill \\ k_{\text{STA}}{N}_{\mathrm{S}}(t)N_{\mathrm{T}}(t)+\frac{1}{8}{k}_{\text{TTA}}{N}_{\mathrm{T}}^2(t)+\frac{J}{4\mathit{qd}}\hfill \end{array}$$ (10)

$$\frac{d{N}_{\mathrm{T}}(t)}{\mathit{dt}}=-(k_{\text{nr}}^{\mathrm{T}}+k_{\mathrm{r}}^{\mathrm{T}}+k_{\text{RISC}})N_{\mathrm{T}}(t)+k_{\text{ISC}}{N}_{\mathrm{S}}(t)-\frac{5}{8}{k}_{\text{TTA}}{N}_{\mathrm{T}}^2(t)+\frac{3J}{4\mathit{qd}}$$ (11)

k_STA and k_TTA (in cm³ s⁻¹) represent the rate constants for bi-excitonic quenching, specifically STA and TTA processes, respectively. k_r^S, k_r^T, k_nr^S, and k_nr^T (s⁻¹) denote the rate constants for radiative singlet decay, the radiative triplet decay, nonradiative singlet decay, and the nonradiative triplet decay, respectively. In addition, k_ISC and k_RISC are the rate constants of ISC and RISC in the TADF model, respectively. The rate constants for ν-DABNA-O-xy doped on DBFPO film are summarized in table S6. In this model, J represents the current density (mA/cm²), and q denotes the elementary charge. As stated in Fig. 4 (C and D), the symbols G and G′ correspond to J/4qd in Eq. 10 and 3J/4qd in Eq. 11, respectively. We assumed that the thickness of recombination zone (d) is equal to that of the EML (i.e., 25 nm) in this study.

Supplementary Materials

The PDF file includes:

Supplementary Text

Figs. S1 to S49

Tables S1 to S19

Legends for data S1 to S3

References

Other Supplementary Material for this manuscript includes the following:

Data S1 to S3