Theoretical study of size effects on the direct synthesis of hydrogen peroxide over palladium catalysts

•H2O2 synthesis on low-coordinated sites of Pd catalysts was thoroughly studied.•Low-coordinated Pd sites showed poorer performance than extended surfaces.•Remarkable size-dependence of H2O2 synthesis has proved by DFT calculations.•Both site coordination and site geometry play critical roles in H2O2 synthesis.