Study of the Structural and Electronic Properties of Rh_N and Ru_N Clusters (N < 20) within the Density Functional Theory

Abstract

Using the density-functional theory (DFT) with the generalized gradient approximation to exchange and correlation, we compute the geometries, electronic structure, and related properties of free-standing rhodium and ruthenium atomic clusters with sizes below 20 atoms. We explore different structural and spin isomers per size, for which we determine the interatomic distances, binding energy, magnetic moment, HOMO-LUMO gap, and electric dipole moment. For many sizes, different implementations of DFT predict different properties for the lowest-energy isomers, thus illustrating the complex nature of these 4d transition metal elements at the nanoscale. We discuss our results for rhodium clusters in the context of recent electric deflection measurements.

Probing the structures of gas-phase rhodium cluster cations by far-infrared spectroscopy

“…[21][22][23][24] Comparison of the performance of different functionals when applied to small, late TM clusters [25][26][27] indicates that the favored class of structural motif (either close-packed or open) is dependent on whether the functional under consideration is purely density dependent or a hybrid, including a portion of Hartree-Fock (exact) exchange. While these data demonstrate the sensitivity of the theoretical results to the details of the calculations, they provide little guidance as to the real structures of the clusters.…”

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

“…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).…”

“…(iv) Atomic structures reported in the literature. 3,[12][13][14][15][16]18,[23][24][25][26]47 (v) A large number of different magnetic configurations were calculated for every atomic structure.…”