Gaussian hill was spawned, the adopted Gaussian hills height and width were set to 1x10 -3 hartree and 0.1 (internal cp2k units), respectively. Each simulation was preceded by standard molecular dynamics simulations (MD; NVT, 300K, time step of 0.5 fs). During WTMetaD simulations, we have defined two collective variables (CVs) to trigger the process of H + or H transfer (see Figure ). Exemplary explanation for H + in h-BN supercell of CVs: all the nitrogen atoms in h-BN are divided into three different kinds: N1 (inner layer with H + bound), N2 (inner layer neighboring N1), and N (outermost layers). One of the collective variables, CV1, is defined as the coordination number of H + to N1, while the other collective variable, CV2, is defined as the coordination number of H + to N2. Similar CVs were defined for MoS 2 and graphite. The form of the coordination function is defined in CP2K as follows: