Vertical-orbital band center as an activity descriptor for hydrogen evolution reaction on single-atom-anchored 2D catalysts

The d-band center descriptor based on the adsorption strength of adsorbate has been widely used in understanding and predicting the catalytic activity in various metal catalysts. However, its applicability is unsure for the single-atom-anchored two-dimensional (2D) catalysts. Here, taking the hydrogen (H) adsorption on the single-atom-anchored 2D basal plane as example, we examine the influence of orbitals interaction on the bond strength of hydrogen adsorption. We find that the adsorption of H is formed mainly via the hybridization between the 1s orbital of H and the vertical d(z2) orbital of anchored atoms. The other four projected d orbitals (d(xy)/d(x2-y2), d(xz)/d(yz)) have no contribution to the H chemical bond. There is an explicit linear relation between the d(z2)-band center and the H bond strength. The d(z2)-band center is proposed as an activity descriptor for hydrogen evolution reaction (HER). We demonstrate that the d(z2)-band center is valid for the single-atom active sites on a single facet, such as the basal plane of 2D nanosheets. For the surface with multiple facets, such as the surface of three-dimensional (3D) polyhedral nanoparticles, the d-band center is more suitable.