In this work, polymorphic models of the structures of PdO is considered. We used a relevantrnquantum mechanical and molecular simulation methods to investigate the formationrnenergy, surface energy, polymorphic structure, lattice constants and the reaction path ofrnthe reactants and products in the electrolyte of a solid oxide fuel cell. These conceptsrnwere approached through possible presence of favored reaction sites in the structures ofrnthe geometries. We used the atomic simulation environment to make the models andrnwe made calculations of the equations of state with density functional theory methodsrnto obtain the most optimized geometries of the structures. Phase diagram calculationsrnwas included to describe the stable geometries from thermodynamic point of view. Thernbarriers of dissociation was investigated with nudged elastic band method