Fig. 6: DFT calculations.

a (001) surface slab models with different terminations of La2Sr2PtO7+δ and the optimized structures. The yellow, red, gray, light and dark green balls represent H, O, Pt, La and Sr, respectively. b Gibbs free energy diagram for hydrogen adsorption at different catalytic sites on La2Sr2PtO7+δ and Pt (111). c The kinetic energy barrier of hydrogen migration/spillover process for La2Sr2PtO7+δ. (IS the initial state, TS the transition state, FS the final state). d The free energy profiles of Heyrovsky step in HER on La2Sr2PtO7+δ (with and without hydrogen migration/spillover). e Schematic illustration of catalysis mechanism for acidic HER via atomic-scale hydrogen spillover on the La2Sr2PtO7+δ oxide.