Spin and orbital magnetism of coinage metal trimers (Cu3, Ag3, Au3): A relativistic density functional theory study

Afshar, Mahdi; Sargolzaei, Mohsen

doi:10.1063/1.4834336

Cited by 6 publications

(5 citation statements)

References 24 publications

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“…The magnetic moments obtained by Datta and co-workers are a bit lower, μ(Co 10 ) = 18 μ B and μ(Co 11 ) = 21 μ B , as well as those obtained by Ma et al, μ(Co 10 ) = 20 μ B , and μ(Co 11 ) = 21 μ B . The pure Ag N clusters show the expected odd/even effect, having magnetic moments of 1 μ B and 0 μ B for odd and even N , respectively, in agreement with previous works. , The reason is that each Ag atom contributes with an s electron to the electronic cloud, so Ag N clusters with odd and even N have odd and even numbers of electrons, respectively. However, our main purpose in this section is to study the changes of the magnetic moment as the concentration varies in each N family.…”

Section: Magnetic Momentssupporting

confidence: 90%

Nanoalloys of Metals Which Do Not Form Bulk Alloys: The Case of Ag–Co

et al. 2020

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Ag and Co metals do not form macroscopic solid or liquid alloys. However, Ag m Co n clusters have been produced in dual-target dual-laser vaporization experiments, and the same occurs for other pairs of immiscible metals. We have performed density functional calculations to shed light on this phenomenon. The main result, obtained for clusters with sizes m + n not larger than 11, is that the cohesive energies justify that those clusters can be formed starting from free Ag and Co atoms, which is the case in the vaporization experiments. At the same time, mixing of Ag and Co is difficult even at the nanoscale. This is revealed by the application of several miscibility criteria. Those two features become, nevertheless, compatible in the clusters. Even if the cluster sizes considered are small, the emerging trend becomes clear: Co atoms form a core in the inner part, surrounded by a shell of Ag atoms on the surface. A consequence is that core–shell clusters can be formed from pairs of metals that do not form macroscopic alloys. The magnetic moments μ of the Ag m Co n clusters are due mainly to the Co atoms, and the presence of Ag induces a reduction in the magnitude of μ.

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Section: Magnetic Momentssupporting

confidence: 90%

Nanoalloys of Metals Which Do Not Form Bulk Alloys: The Case of Ag–Co

et al. 2020

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“…It is then clear that performing calculations accurately in both ranges is extremely important. However, although several theoretical works based on DFT have studied the structure of small copper clusters [16,21,22,[30][31][32][33][34][35][36][37][38][39][40][41], to the best of our knowledge, no previous work has included the Hubbard U correction and van der Waals (vdW) dispersion forces simultaneously within a spin-polarized treatment (SGGA + vdW + U for short). By the end, we hope to convey the message that this level of treatment is indeed relevant, with important implications for future studies involving interactions between supported Cu clusters and molecules, where adsorbate-metal hybridization interaction, as well as physisorption governed by dispersion forces, are frequently present.…”

Section: Methodsmentioning

confidence: 99%

“…The interaction of Cu N cluster (N = 1-4) nanoparticles with ChCl:Urea deep eutectic solvent was studied by Ghenaatian and coworkers in 2021 [12], whereas the stability of Cu N clusters (N = 1-4) adsorbed on CuAlO 2 surfaces was studied using atomic thermodynamics by Wang and coworkers in 2022 [14]. The frequent use of these sizes of Cu N clusters motivated us to review the structures reported as stable for small copper clusters in vacuum, finding large differences between the results reported in previous works, despite the fact that some of them used the same level of theory [16,21,22,[30][31][32][33][34][35][36][37][38][39][40][41]. These differences further motivated us to carry out a study on the stability of small copper clusters, considering the frequently used cluster sizes (3-6 atoms), where the greatest discrepancies occur.…”

Section: Introductionmentioning

confidence: 99%

A DFT + U Study on the Stability of Small CuN Clusters (N = 3–6 Atoms): Calculation of Phonon Frequencies

Alcalá-Varilla,

Ponnefz-Durango,

Seriani

et al. 2023

Condensed Matter

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Despite the interest in copper clusters, a consensus on their atomic structure is still lacking. The experimental observation of isolated clusters is difficult, and theoretical predictions vary widely. The latter is because one must adequately describe the closed shell of d electrons both in its short- and long-range effects. Herein, we investigate the stability of small copper clusters (CuN, N = 3–6 atoms) using spin-polarized DFT calculations under the GGA approximation, the Hubbard U correction, and the van der Waals forces. We found that the spin-polarized and vdW contributions have little effect on the binding energies of the isomers. The inclusion of U represents the most relevant contribution to the ordering of the CuN isomers, and our calculated binding energies for the clusters agreed with the experimental values. We also found that atomic relaxations alone are not enough to determine the stability of small copper clusters. It is also necessary to build the energy landscape or calculate the vibrational frequencies of the isomers. We found that the vibrational frequencies of the isomers were in the THz range and the normal modes of vibration were discrete. This approach is relevant to future studies involving isolated or supported copper clusters.

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“…However, the spin-orbit coupling is expected to be important. There exist theoretical studies regarding spin-orbit coupling effect using effective core potentials or plane-wave basis sets [13][14][15][16][17][18][19]. These studies mainly focused on the spin-orbit coupling effect on the highest-occupied lowest-unoccupied (HOMO-LUMO) energy gaps, geometries, binding energies per atom and optical absorption of gold clusters.…”

Section: Introductionmentioning

confidence: 99%

“…Rusakov et al [16] have used two-component relativistic density functional theory with accurate small-core shape-consistent relativistic pseudopotentials and spin-orbit corrections to refine the isomerization energy profile of Au3 computed by spin-orbit free coupled cluster methods. The noble metal trimers, Au3, Ag3 and Cu3, have also been investigated applying four-component Kohn-Sham-Dirac equation in the framework of relativistic density functional theory [17].…”

Section: Introductionmentioning

confidence: 99%

Spin-Orbit Coupling Effect on the Electrophilicity Index, Chemical Potential, Hardness and Softness of Neutral Gold Clusters: A Relativistic Ab-initio Study

Sani

2021

HighTech. Innov. J.

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Electrophilicity index (𝜔) is related to the energy lowering associated with a maximum amount of electron flow between a donor and an acceptor and possesses adequate information regarding structure, stability, reactivity and interactions. Chemical potential (μ) measures charge transfer from a system to another having a lower value of μ, while chemical hardness (η) is a measure of characterizing relative stability of clusters. The main purpose of the present research work is to examine the Spin-Orbit Coupling (SOC) effect on the behavior of the electrophilicity index, chemical potential, hardness and softness of neutral gold clusters Aun (n=2-6). Using the second-order Douglas-Kroll-Hess Hamiltonian, geometries are optimized at the DKH2-B3P86/DZP-DKH level of theory. Spin-orbit coupling energies are computed using the fourth-order Douglas-Kroll-Hess Hamiltonian, generalized Hartree-Fock method and all-electron relativistic double-ζ level basis set. Then, spin-orbit coupling (SOC) corrections to the electrophilicity index, chemical potential, hardness and softness are calculated. It is revealed that spin-orbit correction to the vertical chemical hardness has important effect on Au3 and Au6, i.e. SOC decreases (increases) the hardness of gold trimer (hexamer). Due to the relationship between hardness and softness, σ = , inclusion of spin-orbit coupling increases (decreases) the softness of Au3 (Au6) and thus destabilizes (stabilizes) it. Spin-orbit coupling (SOC) also has more important effect on the chemical potential of Au3 by decreasing its value. It is found that spin-orbit coupling has considerable effect on the electrophilicity index of gold trimer and greatly increases its value. Furthermore, SOC increases the maximal charge acceptance of Au3 more and thus destabilizes it more. As a result, spin-orbit coupling effect appears to be important in calculating the electrophilicity index of the gold trimer. Doi: 10.28991/HIJ-2021-02-01-05 Full Text: PDF

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Spin and orbital magnetism of coinage metal trimers (Cu3, Ag3, Au3): A relativistic density functional theory study

Cited by 6 publications

References 24 publications

Nanoalloys of Metals Which Do Not Form Bulk Alloys: The Case of Ag–Co

Nanoalloys of Metals Which Do Not Form Bulk Alloys: The Case of Ag–Co

A DFT + U Study on the Stability of Small CuN Clusters (N = 3–6 Atoms): Calculation of Phonon Frequencies

Spin-Orbit Coupling Effect on the Electrophilicity Index, Chemical Potential, Hardness and Softness of Neutral Gold Clusters: A Relativistic Ab-initio Study

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