Fig. 4: Influence of potential on ^*CO₂ hydrogenation process.

a One-dimensional projection of the FES along the distance of ions (^*COOH and OH⁻), with three distinct stages identified: CO₂ protonation (Stage 1), dissociation of the ion-pair of ^*COOH and OH⁻ (Stage 2), and OH⁻ diffusion (Stage 3). The endpoint of stage 2 is used as the reference point to align the free energy curves to allow a direct comparison of the free energy of OH⁻ diffusion under two potential conditions. In the inset, the Ag slab is shown in light gray, C in dark gray, O in red, and H in white. b Representative snapshots illustrating three stages of ^*CO₂ hydrogenation process, captured from the biased trajectory at CP condition. The colors in the snapshots represent Ag in light gray, C in dark gray, O in red, and H in white. Only the water molecules involved in the reaction are shown in ball-and-stick style, while others are displayed in transparent stick style for clear illustration. The green transparent ball illustrates the location of hydroxyl or OH⁻. c Probability distribution of the vertical distance between OH⁻ and the surface from 10 independent unbiased trajectories of OH⁻ diffusion. The inset shows the probability distribution of OH⁻ orientation when the ion stays within the interfacial region (with a vertical distance less than 5 Å).