Modeling Diffusion in Metal-Organic Frameworks Using On-the-fly Probability Enhanced Sampling-Based Machine Learning...

Machine learning potentials (MLPs) can help bridge the length- and time-scale gaps required to study diverse physicochemical phenomena in nanoporous materials with ab initio accuracy. These MLPs are typically trained on quantum chemical data obtained from traditional molecular dynamics (MD) simulations that predominantly sample near-equilibrium configurations. This often limits the model's ability to describe high-energy, off-equilibrium states required to study rare events. To address this capability gap, we introduce a novel active learning curriculum using the On-the-fly Probability Enhanced Sampling (OPES) method. Using imidazole diffusion in the SALEM-2 metal-organic framework (MOF) as a prototypical example, we apply time-dependent OPES biases with temperature- and distance-based collective variables to systematically sample the most relevant regions of the potential energy surface. This strategy enables nanosecond-scale MD simulations with near-DFT accuracy, capturing both the expected diffusion pathway across the 6-membered window and a previously unreported ring-opening mechanism through the more constrained 4-membered window. The latter process, which involves the transient dissociation of a Zn-N bond, cannot be captured using classical force fields and is prohibitively expensive with DFT. Thus, this study highlights how enhanced sampling methods can overcome data scarcity challenges associated with training MLPs for studying rare events in nanoporous materials.