Fig. 5: DFT calculations.

a Atomic models of various types of graphene lattice. The numbers under the graphene lattices are the calculated energy barriers for proton penetration through the lattices. A positive or negative value indicates that the shape of the potential energy surface involves a peak or a trough (details in Supplementary Fig. 36). b Energy barriers for proton hopping between bilayer SV-3N graphene lattices (the first layer is white and the second layer is grey). Orange arrows indicate the hopping direction. c Energy diagram for proton penetration through a bilayer SV-3N graphene lattice. The proton was adsorbed on a NiMo nanoparticle after penetrating through the graphene-covering bilayer. Colour code: carbon (white), nitrogen (red), proton (blue), nickel (cyan), molybdenum (purple), oxygen (light yellow), and hydrogen (dark yellow).