Conjugated polyelectrolytes (CPEs) are macromolecules combining π-conjugated backbones with ionic-functionalized alkyl side chains and counter ions. The π-electrons provide semiconducting properties, while ionic functionalities enable solubility in polar media, including water. CPEs find applications in various optoelectronic devices (organic and perovskite photovoltaics, light-emitting diodes, thermoelectrics) and as photocatalysts. Narrow bandgap CPEs (NBCPEs), containing electron-rich and electron-poor fragments, are particularly interesting due to intramolecular charge-transfer states and ease of oxidation/reduction. Anionic NBCPEs with sulfonate side groups can self-dope in aqueous media, unlike cationic CPEs, highlighting the interplay between electrostatic forces and redox chemistry in determining optoelectronic properties. However, systematic theoretical studies of CPEs are scarce, lacking fundamental understanding of electrostatic influence on optoelectronic properties and how structural components (backbone, side chain, ionic group, counter ions) affect these properties. Designing CPEs for specific applications remains challenging. This work addresses these challenges using a data-centric approach by integrating machine learning with high-throughput first-principles calculations. This strategy, previously applied to other materials, is novel for CPEs. The high-dimensional space of structural variations (donor/acceptor units, alkyl chain length, ionic group, counter ion) makes traditional methods impractical, but this modularity makes CPEs amenable to machine learning. The study aims to establish structure-property relationships, create a first-principles database of CPEs, examine the dependence of frontier orbitals (HOMO, LUMO, HOMO-LUMO gap (Eg)) on each structural component, use machine learning to uncover underlying structural features, predict properties of unknown CPEs, and ultimately, discover promising CPEs for optoelectronic and photocatalytic applications.

The introduction extensively reviews existing literature on conjugated polyelectrolytes (CPEs), their properties, and applications. It highlights the lack of systematic theoretical studies and the challenge in designing CPEs for specific applications. The authors cite numerous papers demonstrating CPE use in organic and perovskite photovoltaics, light-emitting diodes, thermoelectrics, and photocatalysis. The importance of narrow bandgap CPEs (NBCPEs) and the role of self-doping in anionic CPEs are discussed, emphasizing the need for a deeper understanding of the structure-property relationships governing their optoelectronic properties. The authors position their work within the context of existing data-driven materials discovery approaches using machine learning and high-throughput calculations, emphasizing the novelty of applying these methods to CPEs.

The study employed density functional theory (DFT) calculations using the Vienna Ab initio Simulation Package (VASP) with plane-wave bases and projector-augmented-wave pseudopotentials. Both Perdew-Burke-Ernzerhof (PBE) and HSE06 hybrid functionals were used, with PBE applied to the entire database and HSE06 to a subset. CPE oligomers with a single repeating conjugation unit were modeled, considering vacuum spacing to isolate periodic images. Fully extended, trans-conformational alkyl chains were used as initial structures, followed by relaxation to obtain equilibrium conformations. Ab initio molecular dynamics at 300 K confirmed the stability of these structures. An energy cutoff of 500 eV and convergence thresholds of 10⁻⁵ eV and 0.02 eV/Å for energy and force, respectively, were employed. The effect of van der Waals dispersion correction (PBE+D3) was found to be negligible. PBE was primarily used for efficiency, with HSE06 used for HOMO levels to improve accuracy. Scaling factors were determined to approximate HSE06 values from PBE values to minimize computation time. A database of over 2000 CPEs was created by varying five structural parameters (donor, acceptor, alkyl chain length, ionic group, and counter ion). This resulted in 1296 anionic CPEs focused on in this study. The HOMO, LUMO, and Eg were systematically examined. Machine learning, specifically Pearson correlation coefficient analysis and Random Forest Regression (RFR), were utilized to establish structure-property relationships and predict properties of unknown CPEs. Eight features (HOMO/LUMO of donor and acceptor, alkyl chain length, electronegativity of anionic group and counter cation, coordination number of anionic group) were initially considered. Later analysis used revised features (degree of unsaturation, differential electronegativity) to directly relate properties to molecular structure. Support Vector Regression (SVR) was used to predict HOMO and LUMO levels, and model performance was assessed by MAPE, RMSE, and R².

The study established several key structure-property relationships for CPEs. First, Eg was found to be primarily determined by the backbone, while HOMO and LUMO were more significantly influenced by electrostatic forces from the ionic functionality. Second, it was found that the alkyl chain length had a negligible effect on the energetics of neutral CPEs, while donor/acceptor units in the backbone strongly influenced HOMO, LUMO, and Eg. Third, electrostatic interactions between charged ions (or ionic groups) and π-orbitals on the backbone were shown to affect HOMO and LUMO levels. Smaller electronegativity of the counter ion, and shorter alkyl chain lengths resulted in higher HOMO levels. Fourth, machine learning analysis, using Pearson correlation and RFR, revealed that Eg depended primarily on backbone features (HOMOD and LUMOA), but also on LUMOD and HOMOA. HOMO depended strongly on HOMOD, LUMOD, and HOMOA, reflecting the interaction between donor and acceptor units. LUMO depended almost exclusively on LUMOA. Fifth, revised features characterizing donor and acceptor units (degree of unsaturation, differential electronegativity) were found to be important predictors of Eg, HOMO, and LUMO levels. Finally, Support Vector Regression (SVR) demonstrated high accuracy in predicting HOMO and LUMO levels for CPEs not included in the training set (MAPE < 2.1%, RMSE < 0.07 eV, R² > 0.97). The model effectively predicted properties of 'unknown' CPEs beyond the database.

The findings address the research question by establishing clear structure-property relationships for CPEs. The machine learning models successfully predicted CPE properties based on easily calculable structural features, which aids in rational materials design. The identified relationships, particularly the influence of the backbone, ionic functionality, and electrostatic interactions on the frontier orbitals, provide valuable insights into the design of CPEs for specific applications. The successful prediction of properties for unseen CPEs validates the model’s reliability and demonstrates the power of the data-driven approach. The discovery of promising CPE candidates for hole transport and photocatalysis highlights the potential of this method to accelerate materials discovery. The results pave the way for targeted synthesis and optimization of CPEs for optoelectronic and photocatalytic applications.

This study successfully established a first-principles database for CPEs and used machine learning to identify key structure-property relationships. The model accurately predicted properties of unknown CPEs. Promising CPE candidates for use as hole transport materials and photocatalysts were discovered. This data-driven approach accelerates the discovery of novel CPEs, offering a powerful tool for materials design and development in optoelectronics and photocatalysis. Future research should expand the database with more experimental data and incorporate more sophisticated theoretical models to capture charge transport, solvent effects, defects, and interfacial properties.

The study acknowledges limitations inherent in its approach. While the DFT calculations provide valuable insights, they might not fully capture the complexities of real-world systems. The model's reliance on DFT calculations limits its ability to directly account for experimental factors such as solvent effects, defects, and the dynamics of charge transport. The accuracy of predictions depends on the quality and quantity of data in the training set. Therefore, expanding the database with more experimental data is crucial for improving the prediction fidelity and exploring a wider range of CPEs. The current model also doesn't include detailed analysis of factors like charge transport mechanisms, and interfacial properties, which are relevant to optoelectronic performance.