Machine learning prediction of HSE06-level band gaps in two-dimensional semiconductors with reference-guided graph neural networks

Two-dimensional (2D) semiconductors have emerged as promising candidates in next-generation nanoelectronics and sustainable energy technologies, particularly in photoelectrochemical water splitting, due to their exceptional quantum confinement effects and tunable optoelectronic properties. Accurate determination of electronic band gaps remains a critical prerequisite for rational material design in advanced optoelectronic applications. However, the commonly used density functional theory approach with conventional functionals suffers from intrinsic deficiencies in predicting semiconductor band gaps, while calculations with higher hierarchy of functionals like the HSE06 hybrid functional or based on higher level methodologies such as GW approximation incur prohibitive computational costs. To address this challenge, here we propose a reference-guided graph neural network (RG-GNN) framework that achieves HSE06-level accuracy through efficient machine learning. Our approach uniquely embeds an input reference value for the target property with minimal elementary descriptors encoding the structural information of the materials in the model, enabling high-accuracy band gap prediction at the HSE06 level. The model achieves a mean absolute error of 0.15 eV on unseen 2D semiconductor systems compared to HSE06 band gaps. Systematic ablation studies reveal that the reference-guided mechanism reduces prediction error by 83.3% and significantly decreases training dataset requirements for model convergence compared to conventional GNN architectures. Our results demonstrates that topological atomic descriptors from primitive cells, when combined with appropriate reference values, contain sufficient information for highly accurate band gap prediction in 2D materials.