A hybrid DFT–machine learning approach for fast HOMO–LUMO gap prediction in naphthalene diimide MOF linkers

Naphthalene diimides (NDIs) are a class of electron-deficient aromatic compounds widely explored for applications in organic electronics, photovoltaics, and metal-organic frameworks (MOFs), owing to their high electron affinity, robust stability, and tunable optoelectronic properties. Precise modulation of the HOMO-LUMO energy gap is critical to optimize their performance, yet accurate prediction remains challenging due to the limitations of conventional density functional theory (DFT) approaches, including functional sensitivity and computational cost. In this study, we present a hybrid DFT-machine learning (ML) framework to efficiently and accurately predict the energy gaps of 195 structurally diverse NDI derivatives with a broad spectrum of electron-donating and electron-withdrawing substituents. DFT calculations were performed only to compute the reference HOMO-LUMO gap used as the regression target. All machine-learning input features were generated solely from the molecular SMILES representations using RDKit-based cheminformatics descriptors. Among the tested algorithms, LightGBM achieved the best performance (R 2 = 0.86, RMSE = 0.25 eV), exhibiting robust generalization, low error dispersion, and meaningful uncertainty estimates. SHAP analysis revealed that topological, electronic, and steric descriptors play a central role in modulating the energy gap. Compared to baseline models, our hybrid approach significantly reduces computational time while capturing complex structure-property relationships. Beyond virtual screening, the model offers mechanistic interpretability and enables the rational design of NDI with tailored gaps for optoelectronic and MOF-based applications. This work lays the foundation for integrating active learning, transfer learning, and uncertainty quantification in future workflows targeting π-conjugated systems with high functional diversity.