The role of electron localization in the atomic structure of transition-metal 13-atom clusters: the example of Co13, Rh13, and Hf13

Abstract

The crystalline structure of transition-metals (TM) has been widely known for several decades, however, our knowledge on the atomic structure of TM clusters is still far from satisfactory, which compromises an atomistic understanding of the reactivity of TM clusters. For example, almost all density functional theory (DFT) calculations for TM clusters have been based on local (local density approximation--LDA) and semilocal (generalized gradient approximation--GGA) exchange-correlation functionals, however, it is well known that plain DFT fails to correct the self-interaction error, which affects the properties of several systems. To improve our basic understanding of the atomic and electronic properties of TM clusters, we report a DFT study within two nonlocal functionals, namely, the hybrid HSE (Heyd, Scuseria, and Ernzerhof) and GGA+U functionals, of the structural and electronic properties of the Co(13), Rh(13), and Hf(13) clusters. For Co(13) and Rh(13), we found that improved exchange-correlation functionals decrease the stability of open structures such as the hexagonal bilayer (HBL) and double simple-cubic (DSC) compared with the compact icosahedron (ICO) structure, however, DFT-GGA, DFT-GGA+U, and DFT-HSE yield very similar results for Hf(13). Thus, our results suggest that the DSC structure obtained by several plain DFT calculations for Rh(13) can be improved by the use of improved functionals. Using the sd hybridization analysis, we found that a strong hybridization favors compact structures, and hence, a correct description of the sd hybridization is crucial for the relative energy stability. For example, the sd hybridization decreases for HBL and DSC and increases for ICO in the case of Co(13) and Rh(13), while for Hf(13), the sd hybridization decreases for all configurations, and hence, it does not affect the relative stability among open and compact configurations.

Complex magnetic orders in small cobalt–benzene molecules

“…We used typical values of U = 3 eV for on-site Coulomb repulsion and J = 0.9 eV for the exchange. 41 The magnetic orders are qualitatively the same as the results shown in Fig. 2 and they still are separable into the same three groups.…”

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.…”

“…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.…”

“…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).…”

Investigação <i>ab initio</i> dos mecanismos de formação de nanoligas <i>core-shell</i> com platina e metais de transição dos períodos 3<i>d</i>, 4<i>d</i> e 5<i>d</i>

“…Os nanoclusters pGMC de MT 55 De modo geral, as estruturas compactas apresentam momentos magnéticos maiores do que as de baixa compactação ou baixa simetria, isto porque as estruturas compactas tendem a aumentar a localização dos elétrons-d na estrutura, como sugere Piotrowski et al 93 para MT 13 , o que permite que soluções ferromagnéticas sejam obtidas. Além disso, fatores como baixa coordenação e baixa dimensionalidade também corroboram para o aumento do ferromagnetismo; quanto maior o número de átomos expostos ao vácuo, menor será número de coordenação dos átomos e maiores serão os momentos magnéticos, sendo este o principal motivo pelo qual os nanoclusters possuem momento magnético maior do que os respectivos sólidos.…”