Physics of Nickel Clusters. 2. Electronic Structure and Magnetic Properties

A Perspective on Modelling Metallic Magnetic Nanoparticles in Biomedicine: From Monometals to Nanoalloys and Ligand-Protected Particles

The focus of this review is on the physical and magnetic properties that are related to the efficiency of monometallic magnetic nanoparticles used in biomedical applications, such as magnetic resonance imaging (MRI) or magnetic nanoparticle hyperthermia, and how to model these by theoretical methods, where the discussion is based on the example of cobalt nanoparticles. Different simulation systems (cluster, extended slab, and nanoparticle models) are critically appraised for their efficacy in the determination of reactivity, magnetic behaviour, and ligand-induced modifications of relevant properties. Simulations of the effects of nanoscale alloying with other metallic phases are also briefly reviewed.

Towards a morphology of cobalt nanoparticles: size and strain effects

Cobalt nanoparticles with diameters of 8 nm have recently shown promising performance for biomedical applications. However, it is still unclear how the shape of cobalt clusters changes with size when reaching the nanoparticle range. In the present work, density functional theory calculations have been employed to compare the stabilities of two non-crystalline (icosahedron and decahedron) shapes, and three crystalline motifs (hcp, fcc, and bcc) for magic numbered cobalt clusters with up to 1500 atoms, based on the changes in the cohesive energies, coordination numbers, and nearest-neighbour distances arising from varying geometries. Obtained trends were extrapolated to a 10⁴ size range, and an icosahedral shape was predicted for clusters up to 5500 atoms. Larger sized clusters adopt hcp stacking, in correspondence with the bulk phase. To explain the crystalline/non-crystalline crossovers, the contributions of the elastic strain density and twin boundary from the specimen surfaces to the cohesive energy of different motifs were evaluated. These results are expected to aid the design and synthesis of cobalt nanoparticles for applications ranging from catalysis to biomedical treatments.

Graphene and graphene nanomesh supported nickel clusters: electronic, magnetic, and hydrogen storage properties

Small-sized nanoparticles are widely used in applications such as catalysis, nanoelectronics, and hydrogen storage. However, the small size causes a common problem: agglomeration on the support template. One solution is to use templates that limit the mobility of the nanoparticles. Graphene nanomeshes (GNMs) are two dimensional porous structures with controllably passivated pores. In this work, we employ first principles calculations to investigate the potential for using GNMs as support templates for Ni clusters and, at the same time, study their magnetic and hydrogen storage properties. We consider two Ni clusters (Ni₆ and Ni₁₃) and two GNMs (O-terminated and N-terminated), comparing our results to those of isolated Ni clusters and those of Ni clusters on graphene. High stability of the Ni clusters is found on the N-GNM in contrast to the O-GNM. We quantify the hydrogen storage capacity by calculating the adsorption energy for multiple H₂ molecules. The values on Ni _x /N-GNM are significantly reduced as compared to the corresponding isolated Ni _x clusters, but a high hydrogen storage capacity is maintained. The fact that Ni _x /N-GNM hosts spin polarization is interesting for spintronic applications.

Hydrogenation of 3d-metal oxide clusters: Effects on the structure and magnetic properties

The geometrical structures and properties of the M₈ O₁₂ , M₈ O₁₂ H₈ , and M₈ O₁₂ H₁₂ clusters are explored using density functional theory with the generalized gradient approximation for all 3d-metals M from Sc to Zn. It is found that the geometries and total spin magnetic moments of the clusters depended strongly on the 3d-atom type and the hydrogenation extent. More than the half of all of the 30 clusters had singlet lowest total energy states, which could be described as either nonmagnetic or antiferromagnetic. Hydrogenation increases the total spin magnetic moments of the M₈ O₁₂ H₁₂ clusters when MMnNi, which become larger by four Bohr magneton than those of the corresponding unary clusters M₈ . Hydrogenation substantially affects such properties as polarizability, forbidden band gaps, and dipole moments. Collective superexchange where the local total spin magnetic moments of two atom squads are coupled antiparallel was observed in antiferromagnetic singlet states of Fe₈ O₁₂ H₈ and Co₈ O₁₂ H₈ , whereas the lowest total energy states of their neighbors Mn₈ O₁₂ H₈ and Ni₈ O₁₂ H₈ are ferrimagnetic and ferromagnetic, respectively. Hydrogenation leads to a decrease in the average binding energy per atom when moving across the 3d-metal atom series. © 2018 Wiley Periodicals, Inc.

The reactivity of CO on bimetallic Ni3M clusters (M = Sc, Ti, V, Cr, Mn, Fe, Co, Cu, Rh, Ru, Ag, Pd and Pt) by density functional theory

Surface C and O overlap with bimetallic clusters in σ, π and δ-type bonding; for example, C is a σ-donor at −15.23 eV and a π-donor at −9.29 eV, and O is a δ-acceptor at −7.76 eV in Ni₃Fe clusters.

First principles study of bimetallic Ni13-nAgn nano-clusters (n = 0-13): Structural, mixing, electronic, and magnetic properties

Using spin polarized density functional theory based calculations, combined with ab initio molecular dynamics simulation, we carry out a systematic investigation of the bimetallic Ni_13-nAg_n nano-clusters, for all compositions. This includes prediction of the geometry, mixing behavior, and electronic properties. Our study reveals a tendency towards the formation of a core-shell like structure, following the rule of putting Ni in a high coordination site and Ag in a low coordination site. Our calculations predict negative mixing energies for the entire composition range, indicating mixing to be favored for the bimetallic small sized Ni-Ag clusters, irrespective of the compositions. The magic composition with the highest stability is found for the NiAg₁₂ alloy cluster. We investigate the microscopic origin of a core-shell like structure with negative mixing energy, in which the Ni-Ag inter-facial interaction is found to play a role. We also study the magnetic properties of the Ni-Ag alloy clusters. The Ni dominated magnetism consists of parallel alignment of Ni moments while the tiny moments on Ag align in anti-parallel to Ni moments. The hybridization with the Ag environment causes reduction of Ni moment.

An efficient genetic algorithm for structure prediction at the nanoscale

We have developed and implemented a new global optimization technique based on a Lamarckian genetic algorithm with the focus on structure diversity. The key process in the efficient search on a given complex energy landscape proves to be the removal of duplicates that is achieved using a topological analysis of candidate structures. The careful geometrical prescreening of newly formed structures and the introduction of new mutation move classes improve the rate of success further. The power of the developed technique, implemented in the Knowledge Led Master Code, or KLMC, is demonstrated by its ability to locate and explore a challenging double funnel landscape of a Lennard-Jones 38 atom system (LJ₃₈). We apply the redeveloped KLMC to investigate three chemically different systems: ionic semiconductor (ZnO)_1-32, metallic Ni₁₃ and covalently bonded C₆₀. All four systems have been systematically explored on the energy landscape defined using interatomic potentials. The new developments allowed us to successfully locate the double funnels of LJ₃₈, find new local and global minima for ZnO clusters, extensively explore the Ni₁₃ and C₆₀ (the buckminsterfullerene, or buckyball) potential energy surfaces.

DFT studies of Ni cluster on graphene surface: effect of CO2 activation

The activation of CO₂ can be significantly enhanced by Ni cluster deposited onto monovacancy graphene surface.

The spin and orbital contributions to the total magnetic moments of free Fe, Co, and Ni clusters

We present size dependent spin and orbital magnetic moments of cobalt (Con (+), 8 ≤ n ≤ 22), iron (Fen (+), 7 ≤ n ≤ 17), and nickel cluster (Nin (+), 7 ≤ n ≤ 17) cations as obtained by X-ray magnetic circular dichroism (XMCD) spectroscopy of isolated clusters in the gas phase. The spin and orbital magnetic moments range between the corresponding atomic and bulk values in all three cases. We compare our findings to previous XMCD data, Stern-Gerlach data, and computational results. We discuss the application of scaling laws to the size dependent evolution of the spin and orbital magnetic moments per atom in the clusters. We find a spin scaling law "per cluster diameter," ∼n(-1/3), that interpolates between known atomic and bulk values. In remarkable contrast, the orbital moments do likewise only if the atomic asymptote is exempt. A concept of "primary" and "secondary" (induced) orbital moments is invoked for interpretation.

Thiolate-protected Ni39 and Ni41 nanoclusters: synthesis, self-assembly and magnetic properties

Thiolate-protected soluble nickel clusters, Ni(39)(SC(2)H(4)Ph)24 and Ni(41)(SC(2)H(4)Ph)25, were synthesized via a wet chemical method. The cluster formulae were identified by MALDI-TOF. Possible structures of the clusters were discussed. These clusters exhibit ferromagnetism with hysteresis loops in the 1.8-300 K range. By solvent evaporation, the clusters can self-assemble into simple cubic structured crystals with a width in the range of 1-10 μm and length up to 300 μm. These properties shed light on their application potentials in nanomagnetics working at room temperature.

Spin and orbital magnetic moments of free nanoparticles

The determination of spin and orbital magnetic moments from the free atom to the bulk phase is an intriguing challenge for nanoscience, in particular, since most magnetic recording materials are based on nanostructures. We present temperature-dependent x-ray magnetic circular dichroism measurements of free Co clusters (N=8-22) from which the intrinsic spin and orbital magnetic moments of noninteracting magnetic nanoparticles have been deduced. An exceptionally strong enhancement of the orbital moment is verified for free magnetic clusters which is 4-6 times larger than the bulk value. Our temperature-dependent measurements reveal that the spin orientation along the external magnetic field is nearly saturated at ~20 K and 7 T, while the orbital orientation is clearly not.

Density Functional Study of Structural and Electronic Properties of Small Bimetallic Silver−Nickel Clusters

Theoretical study on the structure and electronic properties of small AgmNip (m + p < or = 6) clusters has been carried out in the framework of density functional theory. Structural features, cohesive energies, vertical ionization potentials, and charge transfers are evaluated for each Ag/Ni ratio. In all the AgmNip clusters, the nickel atoms are brought together, yielding a maximum of Ni-Ni bonds, and the silver atoms are located around a Ni core with a maximum of Ag-Ni bonds. The ionization potential and the highest occupied molecular orbital shape are directly related to the two- or three-dimensional character of the cluster's geometry. A very low electronic charge transfer from Ni to Ag is found, and the magnetic moment is located on Ni atoms but with a low spin polarization on silver in the Ni-rich clusters.

Influence of Single Impurity Atoms on the Structure, Electronic, and Magnetic Properties of Ni5 Clusters

With a gradient-corrected density functional method, we have studied computationally the influence of single impurity atoms on the structure, electronic, and magnetic properties of Ni5 clusters. The square-pyramidal isomer of bare Ni5 with six unpaired electrons was calculated 23 kJ/mol more stable than the trigonal bipyramid in its lowest-energy electronic configuration with four unpaired electrons. In a previous study on the cluster Ni4, we had obtained only one stable isomer with an O or an H impurity, but we located six minima for ONi5 and five minima for HNi5. In the most stable structures of HNi5, the H atom bridges a Ni-Ni edge at the base or the side of the square pyramid, similarly to the coordination of an H atom at the tetrahedral cluster Ni4. The most stable ONi5 isomers exhibit a trigonal bipyramidal structure of the Ni5 moiety, with the impurity coordinated at a facet, (micro3-O)Ni5, or at an apex edge, (micro-O)Ni5. We located four stable structures for a C impurity at a Ni5 cluster. As for CNi4, the most stable structure of the corresponding Ni5 complex comprises a four-coordinated C atom, (micro4-C)Ni5, and can be considered as insertion of the impurity into a Ni-Ni bond of the bare cluster. All structures with C and five with O impurity have four unpaired electrons, while the number of unpaired electrons in the clusters HNi5 varies between 3 and 7. As a rough trend, the ionization potentials and electron affinities of the clusters with impurity atoms decrease with the coordination number of the impurity. However, the position of the impurity and the shape of the metal moiety also affect the results. Coordination of an impurity atom leads to a partial oxidation of the metal atoms.

Structure, stability, electronic and magnetic properties of Ni4 clusters containing impurity atoms

Using a gradient-corrected density functional method, we studied computationally how single impurity atoms affect the structure and the properties of a Ni4 cluster. H and O atoms coordinate at a Ni-Ni bond, inducing small changes to the structure of bare Ni4 which is essentially a tetrahedron. For a C impurity, we found three stable structures at a Ni4 cluster. In the most stable geometry, the carbon atom cleaves a Ni-Ni bond of Ni4, binding to all Ni atoms. Inclusion of the impurity atom leads to a partial oxidation of the metal atoms and, in the most stable structures, reduces the spin polarization of the cluster compared to bare Ni4. An H impurity interacts mainly with the Ni 4s orbitals, whereas the Ni 3d orbitals participate strongly in the bonding with O and C impurity atoms. For these impurity atoms, Ni 3d contributions dominate the character of the HOMO of the ligated cluster, in contrast to the HOMO of bare Ni4 where Ni 4s orbitals prevail. We also discuss a simple model which relates the effect of a H impurity on the magnetic state of metal clusters to the spin character (minority or majority) of the LUMO or HOMO of the bare metal cluster.

Homonuclear transition-metal trimers

Density-functional theory has been used to determine the ground-state geometries and electronic states for homonuclear transition-metal trimers constrained to equilateral triangle geometries. This represents the first application of consistent theoretical methods to all of the ten 3d block transition-metal trimers, from scandium to zinc. A search of the potential surfaces yields the following electronic ground states and bond lengths: Sc3(2A1',2.83 A), Ti3(7E',2.32 A), V3(2E",2.06 A), Cr3(17E',2.92 A), Mn3(16A2',2.73 A), Fe3(11E",2.24 A), Co3(6E",2.18 A), Ni3(3A2",2.23 A), Cu3(2E',2.37 A), and Zn3(1A1',2.93 A). Vibrational frequencies, several low-lying electronic states, and trends in bond lengths and atomization energies are discussed. The predicted dissociation energies DeltaE(M3-->M2+M) are 49.4 kcal mol(-1)(Sc3), 64.3 kcal mol(-1)(Ti3), 60.7 kcal mol(-1)(V3), 11.5 kcal mol(-1)(Cr3), 32.4 kcal mol(-1)(Mn3), 61.5 kcal mol(-1)(Fe3), 78.0 kcal mol(-1)(Co3), 86.1 kcal mol(-1)(Ni3), 26.8 kcal mol(-1)(Cu3), and 4.5 kcal mol(-1)(Zn3).

Broken-symmetry unrestricted hybrid density functional calculations on nickel dimer and nickel hydride

In the present work we investigate the adequacy of broken-symmetry unrestricted density functional theory for constructing the potential energy curve of nickel dimer and nickel hydride, as a model for larger bare and hydrogenated nickel cluster calculations. We use three hybrid functionals: the popular B3LYP, Becke's newest optimized functional Becke98, and the simple FSLYP functional (50% Hartree-Fock and 50% Slater exchange and LYP gradient-corrected correlation functional) with two basis sets: all-electron (AE) Wachters+f basis set and Stuttgart RSC effective core potential (ECP) and basis set. We find that, overall, the best agreement with experiment, comparable to that of the high-level CASPT2, is obtained with B3LYP/AE, closely followed by Becke98/AE and Becke98/ECP. FSLYP/AE and B3LYP/ECP give slightly worse agreement with experiment, and FSLYP/ECP is the only method among the ones we studied that gives an unacceptably large error, underestimating the dissociation energy of Ni(2) by 28%, and being in the largest disagreement with the experiment and the other theoretical predictions. We also find that for Ni(2), the spin projection for the broken-symmetry unrestricted singlet states changes the ordering of the states, but the splittings are less than 10 meV. All our calculations predict a deltadelta-hole ground state for Ni(2) and delta-hole ground state for NiH. Upon spin projection of the singlet state of Ni(2), almost all of our calculations: Becke98 and FSLYP both AE and ECP and B3LYP/AE predict (1)(d(A)(x(2)-y(2)d(B)(x(2)-y(2)) or (1)(d(A)(xy) (d)(B)(xy)) ground state, which is a mixture of (1)Sigma(g) (+) and (1)Gamma(g). B3LYP/ECP predicts a (3)(d(A)(x(2)-y(2))d(B)(xy) (mixture of (3)Sigma(g) (-) and (3)Gamma(u)) ground state virtually degenerate with the (1)(d(A)(x(2)-y(2)d(B)(x)(2)-y(2)/(1)(d(A)(xy)D(B)(xy) state. The doublet delta-hole ground state of NiH predicted by all our calculations is in agreement with the experimentally predicted (2)Delta ground state. For Ni(2), all our results are consistent with the experimentally predicted ground state of 0(g) (+) (a mixture of (1)Sigma(g) (+) and (3)Sigma(g) (-)) or 0(u) (-) (a mixture of (1)Sigma(u) (-) and (3)Sigma(u) (+)).

Structural stability and electronic state of transition metal trimers

Ground state geometries were searched for transition metal trimers Sc3, Y3, La3, Lu3, Ti3, Zr3, and Hf3 by density functional methods. For all the studied trimers, our calculation indicates that the ground state geometries are either equilateral triangle (Zr3 and Hf3) or near equilateral triangle (Ti3, Sc3, Y3, La3, and Lu3). For rare earth trimers Sc3, Y3, La3, and Lu3, isosceles triangle (near equilateral triangle) at quartet state is the ground state. Isosceles triangle at doublet state is the competitive candidate for the ground state. For Zr3 and Hf3, equilateral triangle at singlet state is the most stable. For Ti3, isosceles triangle (near equilateral triangle) at quintet state gives the ground state. For Sc3, Zr3, and Hf3, where experimental results are available, the predicted geometries are in agreement with experiment in which the ground state is equilateral triangle (Zr3) or fluxional (Sc3 and Hf3). For Y3, the calculated geometry is in agreement with experimental observation and previous theoretical study that Y3 is a bent molecule for the ground state. For La3, our calculation is in excellent agreement with previous theoretical study based on density functional methods.

Orbital magnetism in transition-metal clusters: from Hund's rules to bulk quenching

The local and average orbital moments <L> of transition-metal (TM) clusters are determined bridging the gap between atomic Hund's rules and solid-state quenching. A remarkable enhancement of <L> is revealed in agreement with recent measurements. In small Ni(N) (N< or =10), <L> represents (20-40)% of the total magnetization and is therefore crucial for the comparison between theory and experiment. Larger clusters (N> or =150) show nearly bulklike quenching at the interior but retain a considerable surface enhancement. Trends for different TM's are discussed.