ABSTRACT: Recent experiments have demonstrated transport and separation of hydrogen isotopes in layered materials, such as hexagonal boron nitride and molybdenum disulphide. Here, based on first-principles calculations combined with well-tempered metadynamics simulations, we report the chemical interactions and mobility of protons (H + ) and protium (H atoms) in the interstitial space of these layered materials. We show that both H + and H can be transported between the layers of h-BN and MoS 2 with low free energy barriers, while they are immobilized in graphite, in accordance with the experimental observations. In h-BN and MoS 2 , the transport mechanism involves a hopping process between the adjacent layers, which is assisted by the lowenergy phonon shear modes. Defects present in MoS 2 suppress the transport and act as traps for H species.