How Morphological Descriptors Capture the Stability Order in Palladium Nanoparticles

Palladium nanoparticles were optimized at different levels of density functional theory, including spin polarization and van der Waals interactions. Atomistic models were developed in the range of 7-1925 atoms by examining six ordered high-symmetry families and showed ferromagnetism with a weak magnetic moment per atom, in agreement with measurements. The stability order against nanoparticle size was predicted by several descriptors. Linear correlations were found between the cohesion energy per palladium and <i>N</i>^-1/3 for each morphology. Truncated octahedra are the more stable nanoclusters above 100 atoms, with Marks-decahedra being competitive at the nanometer size. The nanoparticle surface energy was correlated almost linearly with the surface atomic density. The truncated octahedra and Marks-decahedra exhibit a minimal surface energy because of an average surface metal-metal optimal distance close to the bulk value. Our original results pave the way for exploring temperature and pressure effects on palladium nanoparticles in the context of cost-efficient catalytic processes.