No abstract

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 TM (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 TM 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 TM gas-phase cluster properties.

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, (M 55 ), 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 M 55 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.

In general, because of the high computational demand, most theoretical studies addressing cationic and anionic clusters assume structural relaxation from the ground state neutral geometries. Such approach has its limits as some clusters could undergo a drastic structural deformation upon gaining or losing one electron. By engaging symmetry-unrestricted density functional calculations with an extensive search among various structures for each size and state of charge, we addressed the investigation of the technologically relevant Cu(n) and Pt(n) clusters for n = 2-14 atoms in the cationic, neutral, and anionic states to analyze the behavior of the structural, electronic, and energetic properties as a function of size and charge state. Moreover, we considered potentially high-energy isomers allowing foresight comparison with experimental results. Considering fixed cluster sizes, we found that distinct charge states lead to different structural geometries, revealing a clear tendency of decreasing average coordination as the electron density is increased. This behavior prompts significant changes in all considered properties, namely, energy gaps between occupied and unoccupied states, magnetic moment, detachment energy, ionization potential, center of gravity and "bandwidth" of occupied d-states, stability function, binding energy, electric dipole moment and sd hybridization. Furthermore, we identified a strong correlation between magic Pt clusters with peaks in sd hybridization index, allowing us to conclude that sd hybridization is one of the mechanisms for stabilization for Pt(n) clusters. Our results form a well-established basis upon which a deeper understanding of the stability and reactivity of metal clusters can be built, as well as the possibility to tune and exploit cluster properties as a function of size and charge.

Bimetallic platinum-based transition-metal (PtTM, TM = Fe, Co, Ni, Cu, and Zn) nanoclusters are potential candidates to improve and reduce the cost of Pt-based catalysts; however, our current understanding of the binary PtTM nanoclusters is far from satisfactory compared with binary surfaces. In this work, we report a density functional theory investigation of the structural, energetic, and electronic properties of binary PtTM nanoclusters employing 55-atom model systems (Pt n TM 55−n ). We found that the formation of the binary PtTM nanoclusters is energetically favorable for all systems and compositions. Except small deviations at the icosahedron (ICO) core−shell configuration, Pt 42 TM 13 , we found that the excess energy, which measures the relative stability, and the chemical order parameter follow nearly a parabolic behavior as a function of the Pt concentration with a minimum at nearly 50% for both properties and all systems. From our structural analysis, the difference in the atomic size of the Pt and TM chemical species contributes to increase the segregation, which reaches its maximum for the ICO core−shell configuration, and hence, an ideal homogeneous distribution cannot be reached. Except for PtZn, we found that the average bond lengths increase almost linearly by replacing TM by Pt atoms in the Pt n TM 55−n systems, and hence, it follows approximately the Vegard's law. We found that the center of gravity of the occupied d-states of the surface atoms changes almost linearly for PtCo, PtNi, and PtZn; hence, the d-band center can be tuned by controlling the composition of the chemical species, while there are deviations from the linear behavior for PtFe and PtCu.