Benchmarking First-Principles Approaches for the Band Gap Prediction of Nanoporous Materials

We present a comprehensive benchmarking study of first-principles calculation methods, based on density functional theory (DFT) and its extensions, to evaluate the fundamental and optical band gaps of nanoporous materials, including metal-organic frameworks (MOFs), covalent-organic frameworks (COFs), and a zeolite. We find that a hybrid approach using the HSE06 functional generally underestimates the fundamental band gaps compared to the nonself-consistent GW (G₀W₀) approximation, and a DFT approach incorporating self-consistent extended Hubbard interactions shows varying agreement with G₀W₀ results depending on the electronic characteristics of materials. Using the Bethe-Salpeter equation (BSE) on top of G₀W₀ calculations (G₀W₀+BSE) and time-dependent DFT (TDDFT) with the PBE functional, we compute optical band gaps and absorption spectra that are in good agreement with experiments. In particular, G₀W₀+BSE outperforms TDDFT with mean absolute errors (MAEs) of 0.68 and 1.00 eV, respectively, for the computed optical band gaps. Furthermore, we find that exciton binding energies in nanoporous materials are significantly larger than those of inorganic systems, attributed to the spatial localization of the valence band maximum (VBM) and conduction band minimum (CBM) on the same structural subunit. These results provide valuable insights into the performance of different computational methodologies for nanoporous materials and offer practical guidance for the development and application of first-principles approaches in materials with high porosity.