Theoretical Study of the Structural, Energetic, and Electronic Properties of 55-Atom Metal Nanoclusters: A DFT Investigation within van der Waals Corrections, Spin–Orbit Coupling, and PBE+U of 42 Metal Systems

An atom-level ab initio understanding of the structural, energetic, and electronic properties of nanoclusters with diameter size from 1 to 2 nm figures as a prerequisite to foster their potential technological applications. However, because of several challenges such as the identification of ground-state structures by experimental and theoretical techniques, our understanding is still far from satisfactory, and further studies are required. We report a systematic ab initio investigation of the 55-atom metal nanoclusters, (M₅₅), including alkaline, transitional, and post-transitional metals, that is, a total of 42 systems. Our calculations are based on all-electron density functional theory within the Perdew–Burke–Ernzerhof (PBE) functional combined with van der Waals (vdW) correction, spin–orbit coupling (SOC) for the valence states. Furthermore, we also investigated the role of the localization of the d states by using the PBE+U functional. We found a strong preference for the putative PBE global-minimum configurations for the compact Mackay icosahedron structure, namely, 16 systems (Na, Mg, K, Sc, Ti, Co, Ni, Cu, Rb, Y, Ag, Cs, Lu, Hf, Re, Hg), while several systems adopt alternative compact structures such as 6 polytetrahedron (Ca, Mn, Fe, Sr, Ba, Tl) and 10 structures derived from crystalline face-centered cubic and hexagonal close-packed (HCP) fragments (Cr, Nb, Mo, Tc, Ru, Rh, Pd, Ta, W, Os). However, the 10 remaining systems adopt less compact structures based on the distorted reduced-core structure (V, Zn, Zr, Cd, In, Pt, Au), tetrahedral-like (Al, Ga), and one HCP wheel-type (Ir) structure. The binding energy shows a quasi-parabolic behavior as a function of the atomic number, and hence the occupation of the bonding and antibonding states defines the main trends (binding energy, equilibrium bond lengths, etc.). On average, the binding energy of the M₅₅ systems represents 79% of the cohesive energy of the respective bulk systems. The addition of the vdW correction changes the putative global-minimum configurations (pGMCs) for selected cases, in particular, for post-transitional metal systems. As expected, the PBE+U functional increases the total magnetic moment, which can be explained by the increased localization of the d states, which also contributed to increase the number of atoms in the core region (increase coordination) of the pGMCs. In contrast with the effects induced by the vdW correction and localization of the d states, the addition of the SOC coupling cannot change the lowest energy configurations, but it affects the electronic properties, as expected from previous calculations for 13-atom clusters.