Estimating and Correcting DFT Error of Metal-Organic Frameworks Through Molecular Derivatives

Metal-organic frameworks (MOFs) are composed of metal clusters linked by organic molecules, forming a porous structure that is suitable for a range of applications, including catalysis, hydrogen storage, and CO₂ capture. While an accurate theoretical analysis is crucial for characterizing and designing functional MOFs, the presence of transition metals makes MOFs exhibit strong static correlation and considerable errors in their density functional theory (DFT) calculations. Additionally, post-DFT methods are computationally prohibitive for MOFs due to the large number of atoms per unit cell. We estimate the magnitude of static correlation of MOFs using low-cost multireference diagnostics based on finite-temperature DFT, which is the first time they are applied to solid-state systems. By comparing the behavior of the diagnostics on MOFs and their molecular derivatives, we demonstrate that the DFT-based multireference diagnostics are equally applicable to solids as to their molecular derivatives. Moreover, we show that estimates provided by multireference diagnostics of a MOF have a good correlation with those of its molecular derivatives, which can be calculated much more affordably in comparison to those of the full MOF. The additivity of the multireference character discussed here suggests the set of molecular derivatives to be a good representation of a MOF, allowing it to be utilized to extract empirical parameters. Therefore, we propose to determine the Hubbard U parameter by fitting DFT results of molecular derivatives to their theoretical benchmark, and apply the same parameter to DFT+U calculations of MOFs to effectively correct the multireference error. The quality of fitted U parameters was evaluated on the adsorption energy of N₂, O₂, and CO₂ gas molecules. The ability to perform high-level calculations for molecular systems and the low cost of DFT+U make this procedure a practical strategy for designing MOFs with improved accuracy and efficiency.