Capturing Nuclear Quantum Effects in Hydrogen Diffusion through MoS2 via Machine-Learning-Enhanced Path-Integral Simulations

Hydrogen transport through layered two-dimensional (2D) materials is central to technologies such as hydrogen storage, fuel cells, and isotope separation. Among these materials, MoS2 exhibits tunable interlayer diffusion properties, whose accurate theoretical description requires accounting for nuclear quantum effects (NQEs), including zero-point motion and tunneling. Here, we present a machine-learning-enhanced atomistic study of hydrogen and deuterium diffusion in layered MoS2 based on interatomic potentials trained on r2SCAN+rVV10 density-functional-theory data. Combining well-tempered metadynamics with path-integral molecular dynamics, we investigate diffusion across multiple MoS2 polytypes and twisted bilayer structures while explicitly incorporating NQEs. Our simulations show that NQEs substantially lower free-energy barriers for hydrogen diffusion at 300 K, significantly increasing the hydrogen self-diffusion coefficient compared to classical nuclei simulations. We further identify a pronounced kinetic isotope effect, with a 35 meV difference between hydrogen and deuterium quantum free-energy barriers. In twisted bilayer MoS2, hydrogen transport exhibits strong spatial variations governed by the local stacking environments within the moir\'e superlattices. These results highlight the critical role of NQEs in hydrogen transport through layered materials and provide atomistic insight intoisotope-selective diffusion in structurally complex 2D systems.