Extended Data Fig. 3: The schematic diagram of the coulomb interaction.

The interaction takes place between the surface Na⁺ (or H⁺) with activated hydrogen species and corresponding electrostatic potential energy (a, b) II(II’) and (c, d) III(III’). The Ru(Na) surface displays a stronger Na⁺···H_a⁻ attraction than that between H⁺ and H_a⁻ on Ru(H), indicating that the surface Na⁺ can stabilize the hydride species. During the H transfer from Ru to O, the Ru(III) would be reduced to Ru(I) while the H_a⁻ would be oxidized into H_a⁺. From viewpoint of electrostatic interaction, such a redox process is unfavorable because the attraction interaction between H_a⁻ and Na⁺(H⁺) is replaced by the repulsion between H_a⁺ and Na⁺(H⁺) that is highlighted as the light red bars in (b) and (d). Considering Na⁺ is electronically more positive than H⁺, the presence of Na⁺ favors the formation H_a⁻ while disfavors the formation of H_a⁺, nicely explaining why the introduction of Na⁺ can improve the reduced-sintering resistance of the atomically dispersed Ru catalysts.

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