Evolution of the structural, energetic, and electronic properties of the 3d, 4d, and 5d transition-metal clusters (30 TMn systems for n = 2–15): a density functional theory investigation

Subnanometric transition-metal (TM) clusters have attracted great attention due to their unexpected physical and chemical properties, leastwise compared to their bulk counterparts. An in-depth understanding of the evolution of the properties as a function of the number of atoms for such systems is a basic prerequisite to leverage countless applications, from catalysis to magnetic storage, as well as to answer fundamental questions related to their intrinsic stability. Here, we reported a systematic density functional study to investigate the structural, electronic properties and stability of all TMn (30 elements) unary clusters as a function of the number of atoms (n = 2–15). We provided the complete structural patterns for all TM periodic table groups, considering the growth evolution as well as the main trends of the structural and electronic properties. The combination of the occupation of the bonding/anti-bonding d-states and the s–d hybridization is found to be the main stabilization mechanism, helping in the understanding of the structural patterns. Most TMn clusters have a magic number of atoms, for which there are peaks in s–d hybridization and null electric dipole moments. Thus, our extensive and comparative study addresses size effects along with the evolution of d-orbital occupation for the TMn gas-phase cluster properties.