Facile DFT Band Gap Correction toward the Hybrid Density Functional Level for 2D-Covalent Organic Frameworks

Density functional theory (DFT) is the method of choice for predicting the majority of structural, physical, and electronic properties of organic and inorganic materials. Accurate band gaps are particularly important for assessing the suitability of materials for (opto-)electronic applications such as photocatalysis or green energy harvesting. Fast semilocal DFT approaches, while widely used, are known to significantly underestimate fundamental electronic band gaps. In contrast, hybrid density functionals provide improved predictions for semiconductor band gaps but come with a high computational cost, limiting their applicability in the case of complex extended systems such as covalent organic frameworks (COFs)─a highly versatile class of materials owing to their tunable structure and properties. In this work, we establish and rationalize a robust linear correlation between semilocal Perdew–Burke–Ernzerhof (PBE) and hybrid HSE06 band gaps, with a focus on two-dimensional COFs. Based on a set of 16 molecular reference systems, we derive a simple correction formula and assess its accuracy using a larger independent set of structures. In total, more than 50 structures were considered, including organic molecules, COF building blocks, polymers, monolayer COFs, and layered COFs. Crucially, this enables hybrid-quality band gap predictions at the computational cost of semilocal DFT. For two-dimensional COFs, the root-mean-square error is as low as 80 meV, and an explicit analysis of potential exceptions supports the robustness of the scheme. In practice, this reduces the computational effort by up to a factor of 54, substantially lowering the resources required compared to direct HSE06 calculations. Additionally, a k-point-resolved correction improves band structures and effective masses beyond the scissors-shift approach.