Cluster-based machine learning potentials to describe disordered metal-organic frameworks up to the mesoscale

Metal-organic frameworks (MOFs) are highly interesting and tunable materials. By incorporating spatial defects into their atomic structure, MOFs can be finetuned to exhibit precise chemical functionalities, extending their applicability in various technological fields. Defect engineering requires a fundamental understanding of the nature of spatial disorder and consequent changes in material properties, which is currently lacking. We introduce the cluster-based learning methodology, enabling the development of state-of-the-art machine learning potentials (MLPs) from defective systems at any length scale. Our method identifies atomic interactions in bulk structures and extracts local environments as finite molecular fragments to augment the model's training data where needed. We show that cluster-based learning delivers MLPs capable of accurately describing spatial defects in mesoscopic systems with over twenty thousand atoms. Afterwards, we select our best model to investigate some major mechanical properties of spatially disordered UiO-66-derived structures, elucidating the influence of defect concentration and composition on material behaviour. Our analysis includes large supercell structures, demonstrating that (near-) ab initio accuracy is within reach at the mesoscale.