Data-driven prediction of Hubbard parameters for metal-organic frameworks

Data-driven prediction of Hubbard parameters for metal-organic frameworks Metal-organic frameworks (MOFs) are promising porous materials with a diverse number of applications ranging from gas capture and storage to catalysis. Since their structures are composed by organic ligands and metallic clusters, forming different building blocks, there is a high combinational space suited for the design of new materials with desired properties [1]. In this context, Computational Materials Physics is a fundamental tool to explore and accelerate the discovery of new materials, mainly through first-principles calculations based on the Density Functional Theory (DFT) [2]. Although DFT is a well-established methodology, some electronic properties of highly correlated materials are still not accurately described by the method [3]. To account for that, corrections can be added to the theory to improve the material description through the Hubbard parameters U and V, describing the intra-site and inter-site electronic correlations, respectively, in an approach denoted as DFT+U+V [4]. However, the self-consistent calculation of U and V can be computationally costly, as demonstrated by the TBHubbard database, where the calculations to compute the Hubbard parameters for 412 MOFs were equivalent to 127 CPU-years [5]. In this work, the construction of a machine learning model is proposed for the prediction of U and V parameters for MOFs, using structural variables and chemical identity as predictors. Exploratory analysis, outlier treatment and multicollinearity verification were performed, followed by the fitting of multiple linear regression models with stepwise selection for U and V, followed by a Random Forest model for V. The linear model for U showed excellent performance on the test set (R² = 0.970, MAE = 0.181 eV), highlighting chemical identity as the main determinant for the target prediction. For V, the linear model was inadequate, while the Random Forest satisfactorily captured the non-linear nature of the interaction (R² = 0.782, MAE = 0.050 eV), with the inter-site distance emerging as a physically relevant variable. The results demonstrated that atomic chemical identity and local geometric variables, extracted directly from crystal geometries, were sufficient to estimate Hubbard parameters, offering a computationally efficient alternative for large-scale screening of MOFs. As a next step, the use of a graph neural network (GNN) architecture for predicting V is suggested as it is naturally suitable to describing materials, where the nodes are atoms and the edges are bonds. Additionally, by including orbital-dependent electronic properties, the model is expected to better capture the non-local environment of the atomic sites. Figure: Illustrative representation of a metal-organic framework and the descriptors used in the models. References [1] Bavykina et al., Chemical Review, v. 120, p. 8468-8535, 2020 [2] Hohenberg et al., Physical Review, v. 136, p. B864–B871, 1964. [3] Pavarini, La Rivista del Nuovo Cimento, v. 44, p. 597–640, 2021. [4] Leiria Campo Jr. et al., Journal of Physics: Condensed Matter, v. 22, p. 055602, 2010. [5] Costa Carvalho et al., Scientific Data, v. 12, p. 1776, 2025.