Next, we have simulated the diffusion process of the protons and H atoms through the interstitial space between the layers of 2D materials, again focusing first on h-BN. As both H and H + bind to atoms of the crystal lattice, we investigated the transport process between individual binding sites. As the system has many degrees of freedom, including low-energy vibrational modes, with rather large amplitudes, we employed well-tempered metadynamics (WTMetaD) to determine the free-energy surface (FES) and to analyze the diffusion barriers of H and H + travelling through the interstitial space of the layered materials (for details of WTMetD and DFT calculations see SI). The FES and the diffusion barriers for H + and H atom are discussed below in detail. Note that WTMetaD diffusion is governed by Brownian motion, thus, the directionality of the diffusion is not defined. However, below, we will refer to this as "path". The information that is the most important from these simulations is the lowest free energy barrier for the transfer of hydrogen species in between the layers. At the end, we will also comment on the directionality of the diffusion for both species, assuming the conditions present in the experiment.