Integrating machine learning and generative models for the intelligent design of TADF materials with circularly polarized luminescence

Abstract

Unlocking the potential of circularly polarized thermally activated delayed fluorescence (CP-TADF) molecules for advanced optoelectronic applications necessitates an accurate understanding of the luminescent dissymmetry factor (g_lum). To develop a robust predictive framework, we first conducted a comprehensive statistical analysis of reported experimental |g_lum| values and their theoretical predictions, which revealed significant discrepancies between experimental and calculated results. Based on these findings, we employ machine learning (ML) models with Morgan fingerprints to predict |g_lum|, complemented by Klekota-Roth fingerprints and Shapley additive explanations for detailed structural insights. Using this predictive model, we perform inverse design of CP-TADF materials through a generative model based on a modified variational autoencoder, with |g_lum| as the objective function. This integrative approach successfully identifies CP-TADF molecules with both high |g_lum| values and favorable synthetic accessibility. Our framework serves as a powerful tool for the intelligent design of CP-TADF materials, bridging theoretical predictions with experimental realization and accelerating the discovery of next-generation CP-TADF materials.

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Introduction

Circularly polarized thermally activated delayed fluorescence (CP-TADF) molecules have garnered significant attention as a cutting-edge class of emitters for advanced optoelectronic applications. By combining the high efficiency of TADF mechanisms^1–3 with the ability to emit circularly polarized light,^4,5 these materials offer unique advantages in next-generation technologies such as circularly polarized organic light-emitting diodes (CP-OLEDs),^6,7 3D displays,^8–11 and optical data storage.¹² Unlike conventional emitters, CP-TADF molecules uniquely combine efficient light emission with circularly polarized light generation, addressing key optoelectronic challenges.

A key parameter for evaluating the performance of CP-TADF materials is the circularly polarized luminescence dissymmetry factor (g_lum), which quantifies the degree of polarization in the emitted light. Recent studies on CP-TADF materials have primarily concentrated on the design of novel molecular structures to achieve higher |g_lum| values,¹³ alongside improving stability and efficiency.¹⁴ However, the development of CP-TADF materials is still limited by challenges in accurately predicting |g_lum| and understanding the structural factors that govern their chiroptical properties.

Machine learning (ML) techniques have become invaluable tools in materials science, offering advanced capabilities to analyze complex relationships between molecular structures and their properties. ML-driven quantitative structure–property relationship (QSPR) approaches have been successfully applied in various domains, including the prediction of material properties such as electronic energy levels,¹⁵ bond dissociation energies,¹⁶ and key photophysical parameters.¹⁷ Beyond material-centric studies, ML has also been employed to investigate OLED-specific properties.¹⁸ By handling high-dimensional data, ML enables both automatic and targeted feature selection, allowing researchers to identify the most relevant molecular descriptors and establish precise structure–property–performance relationships.

In our previous work, we demonstrated that ML-driven QSPR can predict the photoluminescence quantum yield (PLQY) of multi-resonance thermally activated delayed fluorescence (MR-TADF) materials, aiding the design of high-performance structures.¹⁹ In this work, we focus on the design and optimization of CP-TADF materials with enhanced circularly polarized |g_lum| values using ML techniques. Through a comprehensive analysis of the discrepancies between reported experimental |g_lum| values and theoretical predictions by density functional theory (DFT) calculations, we develop a robust ML framework to accurately predict and optimize |g_lum| for CP-TADF molecules. Furthermore, we enhance a variational autoencoder (VAE) model by incorporating |g_lum| as an optimization objective, enabling the inverse design and generation of novel CP-TADF structures with superior chiroptical properties.

Results and discussion

Evaluating |g_lum| through theoretical calculations by DFT

In organic circularly polarized luminescence (CPL) materials, the degree of circular polarization is typically quantified using g_lum is expressed in the following equation:²⁰
here, I_L and I_R represent the intensities of left and right-handed circularly polarized light, respectively. Accurate determination of |g_lum| is critical for guiding the design of CPL-active materials. While experimental measurements are indispensable, they often require sophisticated instrumentation, strict experimental conditions, and significant time and resources. As a result, theoretical approaches, such as quantum chemical calculations based on DFT, have emerged as promising alternatives for estimating |g_lum| directly from molecular structures.

In DFT-based calculations, g_lum is typically calculated using the following equation:²¹

here, [small mu, Greek, vector] and m⃑ represent electric dipole moment and magnetic dipole moment. This equation provides a theoretical framework to predict |g_lum| values, offering a systematic and efficient method for molecular evaluation.

To evaluate the reliability of DFT-based predictions, we conducted a detailed comparison between theoretically calculated |g_lum| values and experimentally reported data. As shown in Fig. 1 and Fig. S1, we selected 50 CP-TADF materials^{1–3,6,7,9,10,22–38} from various literature sources and computed performed with the electric dipole moments ([small mu, Greek, vector]) and magnetic dipole moments (m⃑) by DFT calculations using BDF software (B3LYP/6-31G(d,p)). It is worth noting that the def2-TZVP basis set is considered an excellent choice for dipole moment calculations.³⁹ However, due to its high computational accuracy, our tests revealed that it imposes stringent convergence requirements in the calculations of CP-TADF materials. Moreover, the computation for a single material is both time- and energy-intensive, making it unsuitable for the high-throughput screening we aim to achieve. The comparison reveals notable inconsistencies between calculated and reported |g_lum| values, both in magnitude and trend. To further validate this observation, we performed additional calculations using Gaussian 16⁴⁰ based on B3LYP/6-31G(d,p) functional and basis set on three materials sourced from different studies: BN-DCz, TRZ-MeIAc and SFOT. The calculated |g_lum| values for these materials were 0.019, 0.4765, and 0.4735, respectively, which deviate significantly from the reported experimental values of 0.0013, 0.00059, and 0.0022. The emergence of this difference could have many reasons, such as the choice of functionals, basis sets, and computational approximations. These limitations underscore the need for alternative approaches that can integrate experimental data with theoretical insights to improve prediction accuracy. To address these challenges, we adopted an ML-driven approach, which combines experimental data and computational insights.

Fig. 1 Comparison between calculated and reported |g_lum| values for 30 CP-TADF materials.

Overall workflow and ML models

The overall workflow for the discovery of CP-TADF materials is depicted in Fig. 2. First, a dataset comprising over 200 reported CP-TADF materials (non-polymeric) was compiled (SI), and corresponding molecular descriptors and molecular fingerprints were generated. These materials exhibit diverse structural features, including central chirality, planar chirality, helical chirality, and others. Next, ML models were developed and applied to analyze various feature sets, aiming to identify the optimal feature representation for predicting |g_lum| values. Advanced feature analysis and engineering methods, such as SHapley Additive exPlanations (SHAP), Klekota-Roth fingerprints (KRFP), were employed to uncover key structural factors and other critical influences on |g_lum|. Building on these insights, a molecular generative model based on VAE was optimized by modifying its objective function to prioritize the generation of molecules with higher |g_lum| values. From the generated top candidates, we further performed DFT calculations to evaluate their photophysical properties, identifying molecules that not only exhibit high |g_lum| values but also possess favorable luminescence characteristics. Additionally, synthetic feasibility analysis and proposed synthetic routes were provided for the most promising candidates, ensuring their practical viability for future experimental validation.

Fig. 2 Schematic representation of the ML workflow employed for the discovery of CP-TADF molecules.

To begin with, we selected three ML models for analysis: random forest (RF), extreme gradient boosting (XGBoost), and neural network (NN), training these models using Morgan fingerprints as input features to determine the best-performing model, with hyperparameter optimization carried out through Optuna.⁴¹ The scatter plots in Fig. 3(a) depict the predictive capabilities of these models. The data points from the RF model show less dispersion on the test set and align more closely with the ideal prediction line, demonstrating its superior ability to capture the critical factors influencing |g_lum| and achieve higher fitting accuracy. Meanwhile, the results shown in Table 1 indicate that the RF model achieves the highest Pearson coefficient (r = 0.97), the highest determination coefficient (R² = 0.93), and the lowest root mean squared error (RMSE = 2 × 10⁻³) on the test set, outperforming both XGBoost and NN. The superior performance of the RF model can be attributed to its ability to effectively handle the high-dimensional (2048 dimensions) and complex nature of Morgan fingerprints, capturing key relationships between molecular structures and |g_lum| values with high accuracy. While XGBoost also shows strong predictive capabilities, its slightly lower performance compared to RF may stem from its sensitivity to hyperparameter tuning and its tendency to lose precision at higher |g_lum| values, as indicated by the scatter plots in Fig. 3(a). On the other hand, NN exhibits poor performance, with significant deviations from the diagonal line in both training and test sets, likely due to overfitting and its higher dependency on larger datasets for optimal generalization. Overall, these results establish RF as the most suitable model for predicting |g_lum|, offering a robust balance between predictive accuracy and consistency, particularly in scenarios involving limited datasets.

Fig. 3 (a) Comparison between predicted and actual |g_lum| values for CP-TADF materials using different models based on Morgan fingerprint. (b) Performance of RF model on the test set using three feature systems: Morgan fingerprints, molecule descriptors and their combined system, for predicting |g_lum|. (c) and (d) SHAP analysis and visualized structures of KRFP for CP-TADF materials by RF model. Each dot represents the SHAP value for a feature across the dataset, with the color indicating the actual value of the feature. Features are ranked by the impact on the model output, where positive SHAP values contribute to higher |g_lum| predictions, while negative values correspond to a reduction in |g_lum|.

Table 1 Performance of different models using Morgan fingerprints as input features

Metric	RF		XGBoost		NN
	Train	Test	Train	Test	Train	Test
Root mean squared error (RMSE)		2 × 10^−3		3.2 × 10^−3		4.8 × 10^−3
Pearson coefficient (r)	0.98	0.97	0.83	0.92	0.98	0.86
Determination coefficient (R^2)	0.92	0.93	0.65	0.86	0.86	0.70

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Fig. 3(b) compares the performance of RF model on three descriptor systems: Morgan fingerprints, molecular descriptors (including Cheminformatics and E-state indices obtained from Padel⁴² and CDK Descriptor), and their combination in predicting |g_lum|. Among these, the Morgan fingerprint system demonstrates the best performance, achieving the highest correlation metrics (r and R²), along with the lowest prediction error (RMSE) on the test set. In contrast, the molecular descriptor system shows moderate performance, with slightly lower correlation metrics and higher prediction error compared to the Morgan fingerprint system. This suggests that molecular descriptors, which primarily capture global or statistical properties, may not be as effective in representing the local structural features critical for predicting |g_lum|. Interestingly, the combined system, which integrates both Morgan fingerprints and molecular descriptors, performs the worst. It results in higher prediction error and noticeably lower correlation metrics, likely due to the introduction of redundant or irrelevant features that interfere with the model ability to generalize effectively.

To further validate the predictive performance of our model on new data, we selected several recently reported CP-TADF materials^31,43–45 that were not included in the previous training and testing datasets, and evaluated their predicted performance, as shown in Table S1. Overall, the predictions align reasonably well with the experimental results, with most data points located near the reference line, indicating the reliability and generalization capability of the RF model on unseen compounds. Deviations observed for certain molecules (e.g., CzCzP, R-DWBN) may arise from structural features or measurement conditions not fully captured in the training data, yet the model successfully preserves the relative ranking of |g_lum| across the new materials. This result highlights the robustness of the model in guiding the design and screening of novel high-performance CP-TADF candidates.

While Morgan fingerprints demonstrate strong predictive performance for modeling |g_lum|, their abstract and high-dimensional nature poses challenges in directly correlating predictions with specific structural features. To overcome this limitation, we employed KRFP combined with SHAP analysis, as illustrated in Fig. 3(c) and (d), to identify key structural factors influencing |g_lum| values. The analysis highlights the top 20 KRFP features with the most significant impact, among which the four most influential structures were visualized in Fig. 3(d). These structures exhibit distinct electronic and geometric characteristics that are closely tied to chiroptical properties. For instance, nitrogen-containing heterocycles, such as KRFP 3141, introduce asymmetry and electronic polarization, significantly influencing electric and magnetic dipole moments. Similarly, structures like KRFP 3587 and KRFP 3602, with amine or alkyl-substituted aromatic units, may contribute to electronic effects that impact |g_lum|. Additionally, the fused aromatic system in KRFP 3084 enhances molecular rigidity, stabilizing chiral configurations and improving |g_lum| values. These findings offer deeper insights into the structural attributes that govern |g_lum|, shedding light on how specific electronic and geometric factors contribute to chiroptical performance. This knowledge can guide the rational design of CP-TADF materials with enhanced |g_lum| values.

Molecular design and generation for novel CP-TADF materials

Currently, numerous molecular generation methods are available, among which VAEs stand out due to its ability to efficiently explore chemical space, generate structurally diverse molecules, and integrate property optimization into the generation process. In our previous work, we utilized NP-VAE,⁴⁶ a VAE-based molecular generation method designed with natural product-likeness (NP-likeness) as its optimization objective. While this approach is effective for generating structurally complex and diverse molecules, this method is less suited to the specific requirements of CP-TADF materials, which rely heavily on precise chiral structures to achieve optimal performance. Hence, we modified the optimization objective and structural framework of NP-VAE, shifting the focus from NP-likeness to maximizing |g_lum| values, resulting in a tailored g-VAE. Unlike a purely random generation process, this g-VAE is guided by several chiral units as target structures, which enhances the reliability of the generated results This modified VAE method ensures that the generated molecules predominantly feature reasonable chiral structures or chiral units. To further assess the performance of the g-VAE, we systematically evaluated the diversity and stability of the generated molecules. The model produced a total of 5690 SMILES strings, all of which were chemically valid, giving a validity rate of 100%. Only 5 molecules (0.088%) exhibited ring breakage, no molecules showed multiple disconnected fragments, and functional group conflicts were found in just 3 molecules (0.053%), indicating high structural integrity and chemical plausibility. Diversity analysis based on pairwise Tanimoto distances (Morgan fingerprints, radius = 2, nBits = 2048) for a random sample of 1000 molecules yielded a mean of 0.833, a median of 0.850, and a standard deviation of 0.088, suggesting that the generated set maintains broad structural diversity while avoiding excessive similarity.

Further analysis was conducted to evaluate the generative performance of the g-VAE model by visualizing its latent space. Both generated molecules and reported CP-TADF molecules were projected into a two-dimensional chemical space using t-distributed stochastic neighbor embedding (t-SNE) and uniform manifold approximation and projection (UMAP) based on 2D Morgan fingerprints. As shown in Fig. 4, the t-SNE projection reveals a widely dispersed distribution of generated molecules, with partial overlap with reported molecules, indicating that the g-VAE effectively explores diverse regions of the chemical space while retaining structural relevance to experimentally validated compounds. In contrast, the UMAP projection presents more compact and locally aggregated clusters, highlighting its ability to preserve neighborhood relationships and reveal subtle structural similarities. The coexistence of overlapping regions and distinct clusters in both projections demonstrates that the g-VAE latent space is well-organized and capable of generating novel chemotypes that are chemically meaningful, structurally reasonable, and consistent with high-performance CP-TADF design principles.

Fig. 4 (a) t-SNE and (b) UMAP projections of the generated molecules and reported CP-TADF molecules based on 2D Morgan fingerprints.

To identify high-performing candidates, we conducted a multi-step screening process. Initially, generated molecules were selected not only for their high predicted |g_lum| values, but also for possessing structurally reasonable configurations. Furthermore, to ensure novelty, only molecules with a maximum Tanimoto similarity of ≤80% to any reported material were retained. Subsequently, DFT calculations were performed to evaluate the photophysical properties of the filtered molecules, focusing on their potential for efficient luminescence. Through this systematic screening, we successfully identified a top promising candidate.

Fig. 5(a) presents the |g_lum| distribution of all generated molecules, as predicted by RF model based on Morgan fingerprints. It is evident that the majority of |g_lum| values fall below 3 × 10⁻³, prompting us to focus on the top-performing molecules in the upper range of the distribution. Among these high |g_lum| candidates, we further conducted DFT calculations to evaluate their oscillator strengths (f_osc), a key parameter for determining luminescence efficiency. From this analysis, D4_0633, a CP-TADF molecule based on the binaphthol structure, emerged as the most promising candidate due to its high predicted |g_lum| and f_osc, as shown in Fig. 5(b). D4_0633 exhibits several advantageous features for CP-TADF performance. Its rigid binaphthol framework provides a stable chiral backbone, which is essential for enhancing |g_lum| values. The extended conjugation with multiple aromatic units promotes charge transfer, while the donor and acceptor groups facilitate intramolecular charge transfer, improving both luminescence efficiency and circularly polarized light emission. With a predicted |g_lum| value of 1.18 × 10⁻², D4_0633 stands out as a promising candidate for CP-TADF applications.

Fig. 5 (a) The distribution of predicted |g_lum| values for over 5000 CP-TADF molecules generated by g-VAE. (b) Analysis of |g_lum| values for some reported binaphthol-based CP-TADF molecules compared with the screened high-performing g-VAE-generated molecule D4_0633 and its modified version D4_0633_1, with the red fitting line representing predicted |g_lum| equal to actual |g_lum|. (c) DFT and TD-DFT calculations results for D4_0633 and D4_0633_1. Calculations results include the HOMO/LUMO distributions, the NTO distribution and the calculated fosc/excitation energy/ΔE_ST values.

To further optimize the structure, we replaced the methyl group attached to the nitrogen with a phenyl ring, which enhanced the structure conjugation and rigidity. This modification results in an improved derivative, D4_0633_1, which exhibits an even higher |g_lum| of 1.25 × 10⁻². The predicted |g_lum| values of D4_0633 and D4_0633_1 exceed those of the reported binaphthol-based CP-TADF molecules (compounds 1-10 in Fig. 5(b)) by an order of magnitude, demonstrating their exceptional chiroptical properties. This significant improvement highlights the effectiveness of integrating ML predictions with property-directed molecular generation in discovering high-performance CP-TADF materials.

In Fig. 5(c), we conducted detailed quantum calculation analysis of D4_0633 and D4_0633_1. The highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) energy levels are similar for D4_0633 and D4_0633_1. The distributions of the natural transition orbitals (NTOs) for the first singlet excited state (S₁) and the first triplet excited state (T₁), along with key photophysical parameters such as oscillator strength (f_osc), S₁, T₁, T₂ excited energy, and the singlet–triplet energy gap (ΔE_ST) are also presented in Fig. 5(c). For D4_0633, the ΔE_ST is 0.24 eV. After modification, D4_0633_1 exhibits slightly lower excited energy of S₁ and T₁, with a reduced ΔE_ST of 0.21 eV. This reduction in ΔE_ST is beneficial for reverse intersystem crossing (RISC), a critical process for CP-TADF performance. The NTO analysis reveals that the electron and hole distributions in the S₁ and T₁ states remain largely consistent for both molecules. For D4_0633, the calculated SOC values indicate that the SOC between S₁ and T₂ (〈S₁|Ĥ_SOC|T₂〉 = 0.65 cm⁻¹) is significantly larger than that between S₁ and T₁ (〈S₁|Ĥ_SOC|T₁〉 = 0.26 cm⁻¹). This highlights the largely localized T₂ state act as the dominant channel for RISC, as the stronger coupling facilitates faster transitions between S₁ and T₂. After modification, D4_0633_1 exhibits reduced SOC values, with 〈S₁|Ĥ_SOC|T₂〉 = 0.33 cm⁻¹ and 〈S₁|Ĥ_SOC|T₁〉 = 0.11 cm⁻¹. The SOC reduction for both T₁ and T₂ arises from decreased spatial overlap and an extended CT distance. This effect originates from the substitution of the peripheral methyl group with a phenyl ring in D4_0633_1, which increases the π-conjugation length and introduces additional steric hindrance, thereby twisting donor–acceptor dihedral angles. These changes reduce the spatial overlap between Frontier orbitals and extend the CT distance. According to perturbation theory and the El-Sayed rule, such reduced overlap weakens wavefunction interactions and lowers SOC magnitudes. Despite these decreases, the modified compound retains an energetically accessible T₂–S₁ channel and favorable orbital configuration, enabling efficient RISC.

Importantly, the calculated f_osc values of S₁–S₀ transition for both D4_0633 and D4_0633_1 both exceed 0.17. For luminescent materials, a higher f_osc value is generally desirable as it correlates with stronger radiative transitions and higher PLQY. For donor–acceptor type TADF materials, an f_osc value of 0.17 is reasonable for strong radiative transition. This suggests that these materials have the potential for efficient light emission, making them promising candidates for TADF-based applications.

To facilitate experimental realization, we calculate the synthetic accessibility (SA) scores for D4_0633 and D4_0633_1 and compared them with those of all reported CP-TADF molecules in the dataset. As shown in Fig. 6(a), the SA scores of D4_0633 and D4_0633_1 fall within the interquartile range of the reported compounds. In the overall molecular space, SA scores range from 2 to 7, with most reported CP-TADF materials concentrated between 3 and 4.5. The SA scores of D4_0633 and D4_0633_1 are both around 4, which lies within this dominant range and indicates that these molecules are highly likely to be synthetically accessible.

Fig. 6 (a) Comparison of SA scores between reported CP-TADF molecules and D4_0633 and D4_0633_1. (b) Practical synthetic routes for D4_0633 and D4_0633_1.

Practical synthetic routes were also designed for both molecules, as shown in Fig. 6(b), which rely on well-established reactions such as Buchwald–Hartwig couplings and controlled substitution steps. These routes are designed to ensure the accessibility of the starting materials, scalability of the synthesis, and overall practicality. This combination of favorable SA scores and robust synthetic strategies underscores the experimental realization of these high-performing CP-TADF molecules both practical and efficient.

Conclusions

In this study, we utilized a ML-enabled framework integrated with g-VAE to investigate and optimize the |g_lum| values of CP-TADF materials. By combining molecular fingerprints and ML models, we accurately predicted |g_lum| and identified key fingerprint features influencing chiroptical performance through multiple analysis. The g-VAE model generated over 5000 unique molecular structures, among which D4_0633 and its optimized version D4_0633_1 emerged as top-performing candidates, exhibiting |g_lum| values exceeding 1.1 × 10⁻², significantly surpassing those of previously reported CP-TADF molecules based on binaphthol structure. Practical synthetic routes were proposed to facilitate experimental validation. This work establishes an effective and scalable approach for designing high-performing CP-TADF materials and provides a foundation for the discovery of advanced chiral optoelectronic materials.

Method

Machine learning method

Python (version 3.7) was employed as the platform for machine learning. NN, RF, and XGBoost algorithms were used for learning based on Keras, sklearn-ensemble and xgboost functions, respectively. Splitting the training and test sets for all algorithms is accomplished by the sklearn module. The hyperparameter optimization process was implemented using Optuna.

Quantum chemistry calculations

The theoretical calculations were carried out with Gaussian 16 program package.⁴⁰ DFT calculations on the geometrical and electronic properties of the ground-state were performed based on B3LYP functional with 6-31G(d,p) basis set. Time-dependent DFT (TD-DFT) calculations were used to optimize the excited state geometries by the same method. The distributions of holes and electrons for the S₁ and T₁ states of the materials were depicted using Multiwfn 3.8, a software created by Tian Lu and colleagues.⁴⁷ The spin–orbit coupling (SOC) calculations and dipole moments calculations were carried out by BDF^48–52 software. Specifically, The SOC matrix calculated by BDF based on B3LYP functional with x2c-SVPall basis set in TDDFT-SOC calculation type, with the Hamiltonian of xf-X2C.^48,50–55 The electric dipole moments and magnetic dipole moments are read in the ECD spectrum at the TDDFT level, based on B3LYP functional with 6-31G(d,p) basis set in TDDFT-OPT calculation type.

Model evaluation metrics

The algorithms were evaluated by the RMSE, r², r, accuracy, precision and recall values, which are defined by the following equations.

Author contributions

All authors read and approved the final manuscript.

Conflicts of interest

There are no conflicts to declare.

Data availability

All data used during this study are included in this published article supplementary information (SI). Supplementary information is available. See DOI: https://doi.org/10.1039/d5tc02451j.

The code for this study is uploaded to https://github.com/SpartAce7012/CP-TADF. They are made available to qualified researchers on reasonable request from the corresponding author.

Acknowledgements

This work is supported by Beijing Natural Science Foundation (2242054). The authors gratefully acknowledge HZWTECH for providing computation facilities. The authors thank Kui Gong, Yibin Hu and Yin Wang (all from HZWTECH) for help and discussions regarding this study.

Notes and references

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