Fig. 6: Theoretical understanding of the HOR/HER process.

The differential charge density image of H2O adsorbed on a Cos-SO-Ru and b Cos-Ru. The yellow contour indicates electron accumulation, and the cyan contour denotes electron depletion. c H2O* adsorption energy on different sites. d Gibbs free energy diagram of adsorbed H* (ΔGH*) on different catalytic sites. e The HBE and H2OBE calculated on different catalytic sites. f Hydroxyl adsorption energy on different catalytic sites. Source data are provided as a Source Data file.