Fig. 1: Computational studies to identify the optimal path for electrochemical C–C coupling on binary sites.

a Energy-global-optimisation scheme. The red, blue, and black paths show different reaction channels, where r_A, r_B, r_C refer to the limiting step in relevant paths (Supplementary Fig. 5). b Screening of CO adsorption energies on Cu-based binary active sites. CuM_Cu and CuM_M refer to the bridge sites for the adsorbate binding between two Cu atoms, and Cu and M atoms, where M is the first neighbour atom of Cu (Supplementary Fig. 4). The yellow band shows the expected promising activities. c Reaction phase diagram for CO₂R to C₂₊ at −0.6 V_RHE. The dashed lines (red: C–C coupling steps, blue: protonation steps) indicate the reaction free energies for all considered elementary steps. The solid lines indicate the G_RPD-limiting steps and energies. The points (triangle and circles) show the limiting energies calculated as the maximum of the reaction energy of R1 and R5. The black-filled triangle and red-filled circle refer to the reaction energy for Cu211 and CuZn_Zn (the most promising site). The subscript indicates the adsorption site. R1–R9 are detailed in Supplementary Table 5. d Activation energies for CO*–CO* coupling on Cu and CuZn (211). e Activation energies (black for Cu, blue for CuZn_Cu, and red for CuZn_Zn) plotted against the corresponding limiting potentials of the relevant paths (paths I and V for CO*–CHO*, paths II and VI for CO*–COH*, and paths III and IV for CO*–CO*; Supplementary Table 6). The squares, triangles, and circles show CO*–CO*, CO*–CHO*, and CO*–COH* coupling steps. The empty, filled, and shaded symbols correspond to the (111), (211), and (100) surfaces. f Reaction rates calculated using microkinetic models for CO₂R to C₂₊ at −0.6 V_RHE (Methods).