First–Principles Study Including Zero Point Energy on Hydrogen in Palladium for Hydrogen Membranes Applications

Density functional theory calculations at the generalized gradient approximation level are performed on cube clusters that comprise both the metal lattice (Pd) and the interstitial lattice (H). The calculations consider H on the octahedral sites of the metal lattice, i.e., cubes structures Pd4H4-x (x=0–4). For each structure, the cell volume, the total energy, the bulk modulus and the derivative of the bulk modulus have been calculated. Zero point energy (ZPE) corrections have been included using the direct method. The calculations confirm that including ZPE effects in the harmonic approximation has a significant effect on the calculated properties by increasing the cell-volumes and decreasing the bulk modulus. The absorption energies of hydrogen in palladium without including ZPE are found to be exothermic processes. When the ZPE is included, adding the first three Hs atom are exothermic processes while the fourth atom is found to be endothermic.