Accurate Band Gap Prediction in Porous Materials using $\Delta$-Learning

Metal-organic frameworks (MOFs) are versatile materials with tunable crystal structures, morphologies, and chemistries, offering diverse physical and chemical properties. Although typically electrically insulating, specific combinations of organic and inorganic components can impart electrical conductivity to MOFs. The virtually limitless chemical space of MOFs, however, presents a significant challenge in identifying optimal candidates for electrochemical applications. Although Density Functional Theory (DFT) can probe their electronic structure, its high computational cost hinders the discovery of novel electroactive MOFs using machine learning due to limited data. To tackle these challenges, a semi-empirical extended tight binding approach (GFN1-xTB) is employed to compute electronic properties of a dataset of MOFs, and it is shown that GFN1-xTB approximates MOF band gaps well, as compared to semi-local DFT. This data is used to train an interpretable $\Delta$-learning model that predicts the difference between low and high fidelity band gaps, given by xTB and DFT data at the hybrid level, respectively. This model outperforms direct models trained using only the DFT values. With limited high-quality DFT band gaps, taking advantage of $\Delta$-learning using low-cost GFN1-xTB leads to better predictions as opposed to relying on DFT data alone.