Fig. 4: DFT calculations exploring surface charge distributions and reaction kinetics.

a and d Model structures for Pd₁₅Zn₁₅-ZnO (a) and Pd₃₀-ZnO (d). b and e Charge density difference plots for Pd₁₅Zn₁₅-ZnO (b) and Pd₃₀-ZnO (e). The Pd, Zn, and O atoms are shown in purple, gray, and red. The yellow and cyan surfaces correspond to regions of charge gain (accumulation) and loss (depletion). The isovalue of the isosurfaces is 3.0 × e Å^–3. (c and f) Bader charge distributions for Pd₁₅Zn₁₅-ZnO (c) and Pd₃₀-ZnO (f). The red and blue spheres indicate the extent of charge depletion (positive) and accumulation (negative). g Density of states of Pd atoms in Pd₁₅Zn₁₅-ZnO and Pd₃₀-ZnO. The horizontal dashed lines indicate the calculated d-band center. E-E_F represents the energy relative to the Fermi energy level. h Calculated potential energy diagrams for ODHE to C₂H₄ on Pd₁₅Zn₁₅-ZnO and Pd₃₀-ZnO.