Fig. 5: DFT calculations.
The most stable structure and adsorption energy of the Ru3 cluster adsorbed on a HfO2-OP and b VO-HfO2-OP. c The differential charge density distributions between Ru3 clusters and VO-HfO2 with the isovalue of 0.001 e Å−3. Yellow represents positive charges and olive represents negative charges. d The Projected density of states (PDOS) of Ru, Hf, and O atoms at VO-Ru/HfO2-OP. e The Gibbs free energy diagrams for hydrogen evolution reaction (HER) relative to standard hydrogen electrode, f water adsorption energy and g kinetic barrier of water dissociation on the active sites of different catalysts. IS, TS, and FS represent initial, transition state, and final state, respectively. h Differential charge density distributions between adsorbed H2O and catalysts for Ru (001) (up) and VO-Ru/HfO2-OP (down) with the isovalue of 0.002 e Å−3. Yellow represents positive charges and olive represents negative charges. i The PDOS of adsorbed H2O and the 4d orbital of Ru atom that directly involved in HER for Ru (001), Ru/HfO2-OP, and VO-Ru/HfO2-OP, with corresponding Ru 4d-band center denoted by dash lines. j Crystal Orbital Hamilton population (COHP) of active Ru atom and adsorbed O atom for Ru (001), Ru/HfO2-OP, and VO-Ru/HfO2-OP.
