Fig. 7: The DFT calculation results.

a Gibbs free energy diagram of the CO2 hydrogenation to methyl (CH3*) on the GaN(100) surface. b Gibbs free energy diagram of the CO2 hydrogenation to formate (HCOO*) on the GaN(110) surface. c Gibbs free energy diagram for the coupling of HCOO* and CH3* to DME on the (110)/(100) interface. The corresponding structures of initial states (IS), transition states (TS), and final states (FS) are displayed in Supplementary Figs. 18–21. The zero-energy reference corresponds to the sum of Gibbs free energies (at 360 °C) of H2(g), CO2(g), and the respective clean surface. The state notations colored in green reflect that the reactions between these neighboring states are the diffusion of the surface adsorbents.