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A small amount of Fe3O4 catalyst is known to substantially improve the adsorption and desorption thermodynamics and kinetics of Mg-based materials. Using density functional theory in combination with nudged elastic band method, the dissociative chemisorptions of hydrogen on both pure and Fe-doped Mg(0001) surfaces were studied. The adsorption energy calculations show that a weakly physisorbed state above pure and Fe-doped Mg surface atoms can serve as a precursor state to dissociative chemisorption. Then, the dissociation pathway of H2 and the relative barrier were investigated. The calculated dissociation barrier (1.08 eV) of hydrogen molecule on a pure Mg(0001) surface is in good agreement with comparable experimental and theoretical studies. For the Fe-doped Mg(0001) surface, the activated barrier decreases to 0.101 eV due to the strong interaction between the s orbital of H and the d orbital of Fe.