We calculate the formation enthalpies of PdHx (x = 0-3) by cluster expansion (CE) and calculations based on density functional theory. CE predicts the stable palladium hydride structures PdH, PdH2.62, and PdH2.75. The band structures and density of states indicate that the amount of hydrogen in the palladium lattice does not alter the metallic character of the palladium significantly. However, all PdH X structures with x > 1 have greater formation enthalpies than that of the given reaction path 4PdH(2) = 2PdH + 2Pd + 3H(2) and thus they are thermodynamically unstable. The shorter bond length of Pd-H and the smaller bond angle of Pd-H-Pd imply a higher cohesive energy in zincblende (ZB) PdH than that in rocksalt (RS) PdH. Bader charge analysis shows a stronger electronegativity of H atoms in ZB-PdH than that in RS-PdH. This results in a stronger Pd-H bond in ZB-PdH than that in RS-PdH. Thus ZB-PdH has lower formation enthalpy than that of RS-PdH. However, regarding the dynamic stability, we conclude that hydrogen atoms prefer to occupy the octahedral sites of the palladium lattice because of the lower zero-point energy and vibration free energy than that of occupying the tetrahedral sites. (C) 2018 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.