Fig. 3: Validation of the pre-trained MLP model for atomic interactions in crystal hydrogenated carbon systems.

Bonding energy curves of (a) hydrogen atom at graphene surface and (b) hydrogen atom at diamond (100) surface. Energy barriers for (c) hydrogen atom transferring along armchair at graphene surface with distance of 1.1 Å and (d) hydrogen atom transferring along [010] direction at diamond (100) surface with distance of 1.1 Å. The total energy change versus separation distance of (e) layers of graphite in AB stacking mode, (f) decohesion simulations for diamond (111) surface, (g) layers of hydrogenated graphite in AB stacking mode and hydrogenated diamond (111) surfaces. The ‘D’ in (a) and (b) represented the distance between the atomic centers of hydrogen and carbon atoms, in (e), (g), (h) represented the minimum distance between carbon atoms in the out-of-plane direction between adjacent atomic layers, and in (f) represented the separated distance between the created surfaces. The ‘d’ in (c) and (d) represented the distance of atomic centers of hydrogen atom moving in the in-plane direction. The snapshots for different processes were inserted with the gray and blue spheres representing the carbon and hydrogen atoms. The ‘Distance’ axis represented the ‘D’ perpendicular to the surface in (a), (b), (e–h), and the ‘d’ parallel to the surface in (c, d). The Energy error represented the absolute error between DFT and MLP calculations.