Methods Description Models: We have studied three layered materials, namely h-BN, MoS 2 , and graphite (see Figure ). For all the systems, the interaction of proton (H + ) and hydrogen atom (H) with the layers was investigated. We used the following supercells to describe the interactions: the 4×4×2 supercell was used for both h-BN and graphite, while 4×4×1 supercell for MoS Table . Calculated lattice parameters (a, b, and c) and the interlayer distances (d) in perfect h-BN, MoS 2 , and graphite, shown with and without H species bound to the layers. Available experimental data are given in parenthesis. Bond distances between H + or H atom and the binding atoms are also given. Methods: Well-tempered metadynamics (WTMetaD) simulations were performed using CP2K 3.0 package. The canonical NVT ensemble (constant number of atoms (N), constant volume (V) and constant temperature (T)) was employed for all WTMetaD simulations; the temperature was set to 300 K using CSVR (canonical sampling velocity rescaling) thermostat, with the temperature parameter delta_T of 1500 K and a time step of 0.5 fs. Every 200 steps, a