Density Functional Theory Investigation on the Nucleation and Growth of Small Palladium Clusters on a Hyper-Cross-Linked Polystyrene Matrix

Density functional theory calculations were employed to investigate the nucleation and growth of small palladium clusters, up to Pd 9, into a microcavity of the porous hyper-cross-linked polystyrene (HPS). The geometries and the electronic structures of the palladium clusters inside the HPS cavity, following the one-by-one atom addition, are affected by a counterbalance between the Pd–phenyl (Pd−Φ) and Pd–Pd interactions. The analysis performed on energetics, cavity distortions, and cluster geometries indeed suggest that the cluster growth is dominated by the Pd−Φ interactions up to the formation of Pd 4 aggregates, whereas the metal–metal interactions actually rule the growth of the larger clusters. The elasticity of the hyper-cross-linked polystyrene matrix also plays an important role in the cluster development processes.