Continuous constant potential model for describing the potential-dependent energetics of CO2RR on single atom catalysts

In this work, we have proposed a Continuous Constant Potential Model (CCPM) based on grand canonical density functional theory for describing the electrocatalytic thermodynamics on single atom electrocatalysts dispersed on graphene support. The linearly potential-dependent capacitance is introduced to account for the net charge variation of the electrode surface and to evaluate the free energetics. We have chosen the CO2 electro-reduction reaction on single-copper atom catalysts, dispersed by nitrogen-doped graphene [CuNX@Gra (X = 2, 4)], as an example to show how our model can predict the potential-dependent free energetics. We have demonstrated that the net charges of both catalyst models are quadratically correlated with the applied potentials and, thus, the quantum capacitance is linearly dependent on the applied potentials, which allows us to continuously quantify the potential effect on the free energetics during the carbon dioxide reduction reaction instead of confining it to a specific potential. On the CuN4@Gra model, it is suggested that CO2 adsorption, coupled with an electron transfer, is a potential determining step that is energetically unfavorable even under high overpotentials. Interestingly, the hydrogen adsorption on CuN4@Gra is extremely easy to occur at both the Cu and N sites, which probably results in the reconstruction of the CuN4@Gra catalyst, as reported by many experimental observations. On CuN2@Gra, the CO2RR is found to exhibit a higher activity at the adjacent C site, and the potential determining step is shifted to the *CO formation step at a wide potential range. In general, CCPM provides a simple method for studying the free energetics for the electrocatalytic reactions under constant potential.