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• On (2 1 0) surface, the hydrogen dissociation is spontaneous. • The chemical bonding analysis is employed to elucidate the interaction between adsorbate and substrate. • At high coverage, the hydrogen adsorption configuration is surface-dependent. • On (2 1 0) surface, the surface sulfur atoms are easily to be removed by hydrogen. Elucidating the interactions between hydrogen and catalysts under complex realistic conditions is of great importance in rationally modulating the catalytic performance of hydrogenation processes. Herein, we have investigated the interaction between hydrogen and four typical surfaces, (1 0 0), (2 1 0), (2 1 1), and (3 1 1) of pyrite FeS 2 through density functional theory calculations. On (2 1 0) surface, the hydrogen dissociative adsorption on unsaturated-coordination sulfur atoms is favorable both in thermodynamics and kinetics. The hydrogen activation barrier is 0.83 eV with slight exothermic of 0.12 eV on (3 1 1). While on (1 0 0) and (2 1 1) surface, the hydrogen dissociation is unfavorable due to the high activation barriers and remarkable positive reaction energies. For high adsorption coverage, the pure molecule adsorption mode is favorable on (1 0 0) facet, opposed to the other surfaces which have temperature and pressure dependence. The saturated coverage sequence is (1 0 0) > (2 1 0) > (2 1 1) > (3 1 1) for a wide range of temperature and pressure. The remove of sulfur atoms most likely occurs on (2 1 0) surface. Our atomistic insights might be useful in engineering hydrogen-involved processes catalyzed by iron sulfide. [ABSTRACT FROM AUTHOR]