Synergism between metal single-atom sites and S-vacant two-dimensional nanosheets for efficient hydrogen evolution uncovered by density functional theory and machine learning

H* is generated on Pd single atoms and then migrates to neighboring S sites on which H 2 is produced, representing catalytic synergism via hydrogen spillover, which enables Pd 1 /S v -MnPS 3 to be active and durable for the HER.