Structure and dynamics of sulfur vacancies in monolayer MoS2 studied by DFT-based machine learning potentials

We have developed a multi-step strategy for training stable and precise machine learning potentials (MLPs) for activated processes that are accurate for both in-domain interpolation and out-of-domain (OOD) extrapolation regimes and applied it in the realm of vacancies in 2D materials. An essential part of obtaining well-performing MLPs is balanced and properly sampled datasets. To achieve this, we have designed a sampling technique based on the nudged elastic band and constrained molecular dynamics. Our analysis goes well beyond the calculation of conventional metrics, such as the root mean square error on the validation dataset. We use tailor-made metrics that focus on the atoms that critically determine the defect migration process. In the context of chalcogen vacancy dynamics in monolayer MoS2, we extensively benchmarked the MACE MLP model and checked its behavior for atoms close to the vacancy or in near-barrier configurations, which are the most difficult to describe since they require very robust OOD generalization performance. Generally, we found that a properly trained MACE model is able to reliably reproduce energies and forces even in these extreme cases. To demonstrate the utility of our approach, we calculated relaxations and minimum energy paths for single- and multi-vacancy transitions in monolayer MoS2, as well as free energy barriers utilizing thermodynamic integration. We believe our conclusions are also valid for other equivariant message passing neural network potentials due to their general similarity. Finally, we discuss the possibility of tuning the density functional theory-based MLP toward quantum Monte Carlo accuracy.