The Simple Cubic Structure of Ruthenium Clusters

Abstract

Ruthenium clusters of up to 64 atoms were studied using density-functional theory with a plane wave basis set. The simple cubic structure was found to be the most stable structure in the formation of small ruthenium clusters. A strong trend of trimer formation was also observed in the linear ruthenium clusters. All the ruthenium clusters investigated in this work are ferromagnetic with large magnetic moments and have small energy gaps between the highest occupied and the lowest unoccupied molecular orbitals. A quantitative correlation was established between the energetic, electronic, and magnetic properties of ruthenium clusters and the cluster size and structure. Our analysis showed that the atoms in similar bonding environments have similar binding energies. On the basis of this analysis, estimations were made on the binding energy for certain planar and simple cubic ruthenium clusters. The estimated binding energies are in good agreement with those from the density-functional theory calculations.

Hybrid density functional study of small Rhn(n=2−15)clusters

“…21,[30][31][32][33][34] Among those studies, hybrid-DFT calculations combined with experimental far-infrared multiple photon dissociation 24,25 have reported that Rh + n clusters have compact structures based on octahedron motifs for n = 6-12 (i.e., only compact structures can explain the vibrational spectra). This finding is consistent with recent screened hybrid-DFT calculations reported for Rh 13 , 27 which identified that an increase in the amount of exact Fock exchange in the hybrid functionals favors compact structures for Rh 13 , and hence, in better agreement with vibrational data. 24,25 However, it has been reported that low coordinated Rh n structures obtained by plain DFT calculations yield magnetic moments m T , in good agreement with experimental results.…”

“…24,25 However, it has been reported that low coordinated Rh n structures obtained by plain DFT calculations yield magnetic moments m T , in good agreement with experimental results. 10,[12][13][14][15][16] For example, plain DFT yields m T = 0.69 μ B /atom for Rh 13 , while results have obtained 0.48 ± 0.13 μ B /atom, 10 however, hybrid-DFT calculations yield higher magnetic moments for compact Rh n clusters (i.e., m T = 1.62 μ B /atom for Rh 13 ). 27 Therefore, the deviation between theory and experimental is substantially larger for hybrid-DFT calculations.…”

“…6,9 Furthermore, experimental studies reported unexpected large magnetic moments for Rh n (n = 9-34), 10 which is in contrast with the nonmagnetic crystalline phase of bulk Rh. 11 Beyond that, density functional theory (DFT) calculations within local and semilocal functionals have reported low coordinated structures for the lowest energy Rh n configurations (6 n 20), [12][13][14][15][16][17] which are based on cubic unit motifs and in contrast with the compact face-centered cubic (fcc) structure of the ground-state crystalline Rh phase. 11 In order to improve the atomistic understanding of those problems, a wide range of experimental and theoretical studies have been reported for rhodium clusters in the neutral, cationic, and anionic states.…”

“…11 In order to improve the atomistic understanding of those problems, a wide range of experimental and theoretical studies have been reported for rhodium clusters in the neutral, cationic, and anionic states. Most of the studies have addressed the atomic structure of Rh n as a function of size, [12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27] the vibrational spectra, 24,25,28 magnetic moments, 3,10,12,14,16,18,22 polarizabilities, 16,29 and the catalytic activity for small molecules. 21,[30][31][32][33][34] Among those studies, hybrid-DFT calculations combined with experimental far-infrared multiple photon dissociation 24,25 have reported that Rh + n clusters have compact structures based on octahedron motifs for n = 6-12 (i.e., only compact structures can explain the vibrational spectra).…”

Probing C–O bond activation on gas-phase transition metal clusters: Infrared multiple photon dissociation spectroscopy of Fe, Ru, Re, and W cluster CO complexes

“…We have considered multiple possible explanations for the observed shifts in the frequency based on predicted trends in the electronic and structural properties. However, most of these predictions are based on the assumption of cubic cluster structures, 43,44 which may not be the real ground-state structures but merely an artifact of neglecting exact exchange in the density functional theory calculations. 45,46 Clearly, a better understanding of the bare ruthenium clusters is required before an explanation of the observed trends in ν(CO) can be given.…”