Comprehending the interaction of metal clusters with two-dimensional (2D) carbon materials at the atomic level is important for the rational design of relative materials for various applications. The geometrical and electronic modulation of graphene and graphdiyne (GDY) by the adsorption and nucleation of Cun, Irn, and Pdn (n = 1–5) and the effect on hydrogen evolution reaction (HER) were studied employing dispersion-corrected density functional theory methods. The bonding strength between the metal Mn (n = 1–5) clusters and the considered 2D materials generally followed the order of Irn-substrate > Pdn-substrate > Cun-substrate. The modified electronic properties induced by the metal decoration affected the H adsorption. According to the Sabatier’s principle, the Mn@graphene present better HER catalytic properties than the pristine graphene, while the Mn@GDY depends. Based on the calculated ΔG0(H) and H diffusion barrier, H can easily diffuse from the C site of graphene to the metal site and show better HER activities. The reverse H diffusion from the metal site to the carbon site of GDY for GDY supported Pd1, Pd5, and Ir5 could happen at room temperature, thereby improving the HER activity at pH = 0. A series of linear relationships are found, revealing the possible structure–activity relations.
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