Harnessing DFT and machine learning for accurate optical gap prediction in conjugated polymers

Conjugated polymers (CPs), characterized by alternating σ and π bonds, have attracted significant attention for their diverse structures and adjustable electronic properties. However, predicting the optical band gap (Eexpgap) of CPs remains challenging. This study presents a rational model that integrates density functional theory (DFT) calculation with a data-driven machine learning (ML) approach to predict the experimentally measured Eexpgap of CPs, using 1096 data points. Through alkyl side chain truncation and conjugated backbone extension, the modified oligomers effectively capture the electronic properties of CPs, significantly improving the correlation between the DFT-calculated HOMO-LUMO gap (Eoligomergap) and Eexpgap (R² = 0.51) compared to the unmodified side-chain-containing monomers (R² = 0.15). Moreover, we trained six ML models with two categories of features as input: Eoligomergap to represent the extended backbone and molecular features of unmodified monomers to capture the alkyl-side-chain effect. The best model, XGBoost-2, achieved an R² of 0.77 and an MAE of 0.065 eV for predicting Eexpgap, falling within the experimental error margin of ∼0.1 eV. We further validated XGBoost-2 on a dataset of 227 newly synthesized CPs collected from literature without further retraining. Notably, XGBoost-2 exhibits both excellent interpolation for BT-, BTA-, QA-, DPP-, and TPD-based CPs, and exceptional extrapolation for PDI-, NDI-, DTBT-, BBX-, and Y6-based CPs, which are attributed to the integration of DFT methods with rationally designed oligomer structures. For the first time, we demonstrated a novel and effective strategy combining quantum chemistry calculations with ML modeling for accurate and efficient prediction of experimentally measured fundamental properties of CPs. Our study paves the way for the accelerated design and development of high-performance CPs in photoelectronic applications.