Single-Atom Electrocatalysis for Hydrogen Evolution Based on the Constant Charge and Constant Potential Models

DFT calculations are performed at constant charge, while practical electrochemical reactions often take place under constant potential. To unravel the effect of the model difference on single-atom electrocatalysis, we implement benchmarked DFT and grand-canonical DFT calculations to systematically investigate the hydrogen adsorption on 99 single-atom M-NC motifs. We find that the initial electrode potentials for all M-NC are negative, leading to the loss of system electrons once their electrode potentials are fixed at 0 V/SHE. We prove that the quantitive difference of Δ(*H) between the CCM and CPM is proportional to the square difference of total charge change before and after H adsorption, which originates from the adjustment of electronic occupation states. Our work provides theoretical insight into the differential capacitance model in the graphene-confining SACs for the HER and emphasizes the importance of CPM for design of electrocatalysts.