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.

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.

We overcome the great theoretical computational challenge of mixed perovskites, providing a rigorous and efficient model by including quasiparticle, spin−orbit coupling, and disorder effects. As a benchmark, we consider the mixed MAPb 1−x Sn x I 3 perovskites. The calculations are based on the generalized quasichemical approach and the DFT-1/2 approximated quasiparticle correction. Both cubic and tetragonal structures are investigated. By mapping the entire range of compositions, we correctly describe the bowing-like behavior for the energy gaps with 1.24 eV as the minimum value at x = 0.70, in very good agreement with the experimental data. Furthermore, while the tetragonal alloy reaches the maximum absorbance with a limit for the red shift at x = 1.0, the cubic alloy sets a maximum absorbance/red shift for the optimal composition at x = 0.70.