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Interaction of hydrogen with palladium surface in the presence of high electric field leads to the formation of complexes, which have been recorded as PdHx+ (x = 1, 2, 3, 4). In the present work, quantum chemical calculations with Becke’s three parameter hybrid functional using the LYP correlation functional (B3LYP) for hydrogen interaction with both single palladium atom and four- or six-atom clusters (such us tetra- and octahedral voids) have been performed. The binding energies, ionization potentials and free-space dipole moments for PdHx (x = 1, 2, 3, 4) molecules have been determined and the “critical” field values, characteristic of palladium hydrides field dissociation have been determined. The model of hydrogen adsorption in the threefold hollow site on the surface together with a subsurface interstitial chemisorption has been discussed. It has been found that hydrogen is bound more strongly in the tetrahedral void than in the octahedral one.