Alternative low-symmetry structure for 13-atom metal clusters

Energetic and Kinetic Competition on the Stability of Pd13 Clusters: Ab Initio Molecular Dynamics Simulations

Material stability is the focus on both experiments and calculations, which includes the energetic stability at the static state and the thermodynamic stability at the kinetic state. To show whether energetics or kinetics dominates on material stability, this study focuses on the Pd13 clusters, because of their observable magnetic moment in experiment. Energetically, the CALYPSO searching method and first-principles calculations find that Pd13(C2) is the ground state at 0 K while the static frequency calculations demonstrate that the icosahedron Pd13(Ih) becomes more favorable on free energy as temperature increases. However, their magnetic moments (8 μB) are not in agreement with the experimental value (<5.2 μB). Kinetically, ab initio molecular dynamics simulations reveal that Pd13(C3v) (6 μB) has supreme isomerization temperature and the other 11 low-lying isomers transform to Pd13(C3v) directly or indirectly, demonstrating that Pd13(C3v) has the maximum probability to be observed in experiment. The magnetic moment difference between experiment (<5.2 μB) and this calculation (6 μB) may be due to the spin multiplicities. Our result suggests that the magnetic moment disparity between theory and experiment (in Pd13 clusters) originates from the kinetic stability.

New global minimum conformers for the Pt 19 and Pt 20 clusters: low symmetric species featuring different active sites

CONTEXT

The study of platinum (Pt) clusters and nanoparticles is essential due to their extensive range of potential technological applications, particularly in catalysis. The electronic properties that yield optimal catalytic performance at the nanoscale are significantly influenced by the size and structure of Pt clusters. This research aimed to identify the lowest-energy conformers for Pt18 , Pt19 , and Pt20 species using Density Functional Theory (DFT). We discovered new low-symmetry conformers for Pt19 and Pt20 , which are 3.0 and 1.0 kcal/mol more stable, respectively, than previously reported structures. Our study highlights the importance of using density functional approximations that incorporate moderate levels of exact Hartree-Fock exchange, alongside basis sets of at least quadruple-zeta quality. The resulting structures are asymmetric with varying active sites, as evidenced by sigma hole analysis on the electrostatic potential surface. This suggests a potential correlation between electronic structure and catalytic properties, warranting further investigation.

METHODS

An equivariant graph neural network interatomic potential (NequIP) within the Atomic Simulation Environment suite (ASE) was used to provide initial geometries of the aggregates under study. DFT calculations were performed with the ORCA 5 package, using functional approximations that included Generalized Gradient Approximation (PBE), meta-GGA (TPSS, M06-L), hybrid (PBE0, PBEh), meta-GGA hybrid (TPSSh), and range-separated hybrid ( ω B97x) functionals. Def2-TZVP and Def2-QZVP as well as members of the cc-pwCVXZ-PP family to check basis set convergence were used. QTAIM calculations were performed using the AIMAll suite. Structures were visualized with the AVOGADRO code.

First principles insights into the relative stability, electronic and catalytic properties of core-shell, Janus and mixed structural patterns for bimetallic Pd-X nano-alloys (X = Co, Ni, Cu, Rh, Ag, Ir, Pt, Au)

The three well-known orderings of the two constituting atomic species in a bimetallic nano-alloy - core-shell, Janus and mixed structural patterns - may be interconvertible depending on the synthesis conditions. Using first principles electronic structure calculations in the present work, we look for the microscopic origin for such structural transformation considering eight Pd-related bimetallic nano-alloys. Our analysis shows that it is the change in atom-atom covalency that is responsible for such structural transformation. Our study also reveals that the three patterns are distinctly identified in terms of total orbital hybridization. Finally, we have analyzed the trend in the relative catalytic activity for the three structures of each bimetallic nano-alloy using the d-band model. Our analysis indicates that the trend in the catalytic activity for the bimetallic Pd-X nano-alloys seems to be intermediate to those of the pristine Pd and Pt nano-clusters possessing similar structure and equal number of total atoms. Among the studied binary nano-alloys, the bimetallic Pd-Ni nano-alloy appears as the most suitable binary pair to develop a non-Pt catalyst.

DFT Investigations of Aun Nano-Clusters Supported on TiO2 Nanotubes: Structures and Electronic Properties

TiO₂ nanotubes (TiO₂NTs) are beneficial for photogenerated electron separation in photocatalysis. In order to improve the utilization rate of TiO₂NTs in the visible light region, an effective method is to use Au_n cluster deposition-modified TiO₂NTs. It is of great significance to investigate the mechanism of Au_n clusters supported on TiO₂NTs to strengthen its visible-light response. In this work, the structures, electronic properties, Mulliken atomic charge, density of states, band structure, and deformation density of Au_n (n = 1, 8, 13) clusters supported on TiO₂NTs were investigated by DMOL3. Based on published research results, the most stable adsorption configurations of Au_n (n = 1, 8, 13) clusters supported with TiO₂NTs were obtained. The adsorption energy increased as the number of Au adatoms increased linearly. The Au_n clusters supported on TiO₂NTs carry a negative charge. The band gaps of the three most stable structures of each adsorption system decreased compared to TiO₂NTs; the valence top and the conduction bottom of the Fermi level come mainly from the contribution of 5d and 6s-Au. The electronic properties of the 5d and 6s impurity orbitals cause valence widening and band gap narrowing.

Thermal Stability of Ag13- Clusters Studied by Ab Initio Molecular Dynamics Simulations

Identification of the geometric structures of silver clusters is of great importance in future nanotechnologies due to their superior properties. Nevertheless, some ground-state structures are still in academic debate, partly because the experiments and theoretical calculations are not performed at the same temperatures. For example, silver clusters usually have compact configurations. However, a combined experimental and theoretical study proposed that the most stable structure of Ag₁₃^- had a two-coordinated atom. By using the CALYPSO approach for the global minima search followed by first-principles calculations, we discovered that a more compact trilayer Ag₁₃^- cluster was the ground state, in accordance with another three works published recently. In addition, its O₂ adsorption structure is also energetically favored. By tracing characteristic bond changes in ab initio molecular dynamics (MD) simulations, we confirmed that, compared with other isomers, this trilayer structure and its O₂ adsorption structure also had the highest thermal stability. This work emphasized the thermal stability concept in theoretical calculations, which may be a necessary supplement to explain the experimental observations on cluster science.

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.

Largely Enhanced Ferromagnetism in Bare CuO Nanoparticles by a Small Size Effect

Magnetic properties of fully oxygenated bare CuO nanoparticles have been investigated using magnetization, X-ray diffraction, neutron diffraction, and Raman scattering measurements. The Langevin field profile is clearly revealed in the isothermal magnetization of 8.8 nm CuO nanoparticle assembly even at 300 K, revealing a 172 times enhancement of the ferromagnetic responses over that of bulk CuO. Surface magnetization of 8.8 nm CuO reaches 18% of the core magnetization. The Cu spins in 8.8 nm CuO order below 400 K, which is 1.7 times higher than the 231 K observed in bulk CuO. A relatively simple magnetic structure that may be indexed using a modulation vector of (0.2, 0, 0.2) was found for the 8.8 nm CuO, but no magnetic incommensurability was observed in bulk CuO. The Cu spins in 8.8 nm CuO form spin density waves with length scales of 5 chemical unit cells long along the crystallographic a- and c-axis directions. Considerable amounts of electronic charge shift from around the Cu lattice sites toward the interconnecting regions of two neighboring Cu-Cu ions, resulting in a stronger ferromagnetic direct exchange interaction for the neighboring Cu spins in 8.8 nm CuO.

Influences of MgO(001) and TiO2(101) Supports on the Structures and Properties of Au Nanoclusters

Due to the unique structures, photoelectric properties, good catalytic activity, and broad potential applications, gold nanoclusters (Au n ) received extensive attention in catalysis, bioengineering, environmental engineering, and so on. In the present work, the structures and properties of Au n adsorbed on the MgO(001) and TiO 2 (101) surfaces were investigated by density functional theory. The results showed that the catalytic properties of Au n will be enhanced when Au n is adsorbed on certain supports. Because the difference of the outer electronic structure of metals in supports, the direction of the charge transfer was different, thus inducing the different charge distribution on Au n . When Au n was adsorbed on MgO(001) [TiO 2 (101)] surface, Au n will have negative [positive] charges and thus higher catalytic activity in oxidation [reduction] reaction. The variation of surface charges caused by the support makes Au n possess different catalytic activity in different systems. Moreover, the electronic structure of the support will make an obvious influence on the s and d density of states of Au n , which should be the intrinsic reason that induces the variations of its structure and properties. These results should be an important theoretical reference for designing Au n as the photocatalyst applied to the different oxidation and reduction reactions.

On the involvement of d-electrons in superatomic shells: the group 3 and 4 transition metals

The geometries and electronic structures of small M₇^C (M = Sc, Y, La, Ti, Zr, Hf; C = 0, ±1, ±2) clusters have been calculated at a range of multiplicities at each cluster charge, using density functional theory methods. These clusters conform to the existing superatom model, with some contextual differences. There are a range of states which are populated by the outermost s and d-electrons of the constituent atoms, with an irregular Aufbau rule for the states formed from the atomic d-electrons. The states comprised of d-electrons present themselves as two states of P-symmetry and two states of F-symmetry, which are nearly degenerate, followed by states of D-symmetry, a shell ordering which arises due to the symmetry, and favourable overlap, of the contributing states. The effect of exact exchange in modulating the localisation of these states is also discussed. In addition, this study shows pseudo-superatomic states which arise due to the 5-fold symmetry of the clusters, materialising as either a ring or plane of electron density. In summary, these observations allow for an expansion of the role that early transition metals have within the existing superatom framework.

Au60-: The Smallest Gold Cluster with the High-Symmetry Icosahedral Core Au13

Among coinage metal nanoclusters with 55 atoms, only Ag₅₅^- and Cu₅₅^- are the geometric magic-number clusters, as both exhibit icosahedral symmetry. Au₅₅^-, however, exhibits much lower symmetry due largely to the strong relativistic bonding effect. In this study, we collect a much larger population (>10,000 isomers) of low-energy isomers of Au₅₅^- to Au₆₀^- by using the combined density-functional theory and basin-hopping global optimization method. We also include the spin-orbit effect in the density-functional theory computation to achieve simulated photoelectron spectra in quantitative fashion. Remarkably, we uncover that the Au₁₃ core with the highest icosahedral ( I_h) symmetry emerges at the size of Au₆₀^-. Stability analysis suggests that Au₅₇^- with 58 valence electrons, an electronic magic number, is the relatively more stable cluster in the size range considered. Overall, in this size range we reveal a compromise between the trend toward having a perfect icosahedral 13-atom core and the strong relativistic bonding effect.

Structural properties of sub-nanometer metallic clusters

At the nanoscale, the investigation of structural features becomes fundamental as we can establish relationships between cluster geometries and their physicochemical properties. The peculiarity lies in the variety of shapes often unusual and far from any geometrical and crystallographic intuition clusters can assume. In this respect, we should treat and consider nanoparticles as a new form of matter. Nanoparticle structures depend on their size, chemical composition, ordering, as well as external conditions e.g. synthesis method, pressure, temperature, support. On top of that, at finite temperatures nanoparticles can fluctuate among different structures, opening new and exciting horizons for the design of optimal nanoparticles for advanced applications. This article aims to overview geometrical features of transition metal clusters and of their various rearrangements.

Structural determination of neutral Co n clusters (n = 4-10,13) through IR-UV two-color vibrational spectroscopy and DFT calculations

We recorded IR spectra for neutral cobalt clusters via two-color IR-UV ionization, using the Free Electron Laser for intracavity experiments (FELICE). Well-resolved IR spectra are presented for [Formula: see text] (n  =  4-10, 13) and analyzed with the help of Density Functional Theory calculations using two different correlation exchange functionals: the revisited Tao-Perdew-Staroverov-Scuseria (revTPSS) and the frequently used Perdew-Burke-Ernzerhof (PBE) approaches. Although we have not performed an extensive structure search, we tentatively assign the spectra for all cluster sizes except for n  =  7, and n  =  10. We find that neither of the two functionals chosen clearly outperforms the other in predicting IR spectra, and that relatively low scaling factors of 0.82 (PBE) and 0.8 (revTPSS) are required. In contrast to the magnetic moments, the calculated electric dipole moments fluctuate strongly as a function of cluster size and could therefore be used as an indirect probe to the cluster structure.

Stability of small cationic platinum clusters

The relative stability of small cationic platinum clusters is investigated by photofragmentation experiments and density functional theory calculations.

MoS2-supported gold nanoparticle for CO hydrogenation

Employing dispersion-corrected density functional theory, we examine the geometry, electronic structure, and reactivity of 13-atom Au nanoparticle supported on defect-laden single-layer MoS₂. The planar structure of Au₁₃ favored in isolated phase, transforms into the three-dimensional structure when supported on MoS₂. We find that charge is transferred from MoS₂ to Au₁₃, and that the electron density is also distributed away from the Au₁₃/MoS₂ interfacial region-making Au sites away from the interface catalytically active. Owing to effect of the support, the Au d states become narrower, and the frontier states appear close to the Fermi level. Consequently, in contrast to the reactivity of Au₁₃/TiO₂ toward methanol decomposition, Au₁₃/MoS₂ offers excellent activity toward methanol synthesis, as demonstrated here, via CO hydrogenation.

Evolution of the structural, energetic, and electronic properties of the 3d, 4d, and 5d transition-metal clusters (30 TMn systems for n = 2–15): a density functional theory investigation

Subnanometric transition-metal (TM) clusters have attracted great attention due to their unexpected physical and chemical properties, leastwise compared to their bulk counterparts.

Geometrical and electronic structures of small Co–Mo nanoclusters

The geometries, energetics and electronic structures of Co₁₃, Mo₁₃, Co₁₂Mo and Mo₁₂Co clusters are systematically investigated by using the first principles method combined with a genetic algorithm.

Relative edge energy in the stability of transition metal nanoclusters of different motifs

When a structure is reduced to a nanometer scale, the proportion of the edge atoms increases significantly, which can play a crucial role in determining both their geometric and electronic properties, as demonstrated by the recently established generalized Wulff construction principle [S. F. Li, et al., Phys. Rev. Lett., 2013, 111, 115501]. Consequently, it is of great interest to clarify quantitatively the role of the edge atoms that dominate the motifs of these nanostructures. In principle, establishing an effective method valid for determining the absolute value of the surface energy and particularly the edge energy for a given nanostructure is expected to resolve such a problem. However, hitherto, it is difficult to obtain the absolute edge energy of transition metal clusters, particularly when their sizes approach the nanometer regime. In this paper, taking Ru nanoclusters as a prototypical example, our first-principles calculations introduce the concept of relative edge energy (REE), reflecting the net edge atom effect over the surface (facet) atom effect, which is fairly powerful to quasi-quantitatively estimate the critical size at which the crossover occurs between different configurations of a given motif, such as from an icosahedron to an fcc nanocrystal. By contrast, the bulk effect should be re-considered to rationalize the power of the REE in predicting the relative stability of larger nanostructures between different motifs, such as fcc-like and hcp-like nanocrystals.

Insights into the geometries, electronic and magnetic properties of neutral and charged palladium clusters

We performed an unbiased structure search for low-lying energetic minima of neutral and charged palladium Pd_n^Q (n = 2–20, Q = 0, + 1 and –1) clusters using CALYPSO method in combination with density functional theory (DFT) calculations. The main candidates for the lowest energy neutral, cationic and anionic clusters are identified, and several new candidate structures for the cationic and anionic ground states are obtained. It is found that the ground state structures of small palladium clusters are more sensitive to the charge states. For the medium size Pd_n^0/+/– (n = 16–20) clusters, a fcc-like growth behavior is found. The structural transition from bilayer-like structures to cage-like structures is likely to occur at n = 14 for the neutral and cationic clusters. In contrast, for the anionic counterparts, the structural transition occurs at Pd₁₃^–. The photoelectron spectra (PES) of palladium clusters are simulated based on the time-dependent density functional theory (TD-DFT) method and compared with the experimental data. The good agreement between the experimental PES and simulated spectra provides us unequivocal structural information to fully solve the global minimum structures, allowing for new molecular insights into the chemical interactions in the Pd cages.

Development of Ferromagnetic Superspins in Bare Cu Nanoparticles by Electronic Charge Redistribution

We report on the results of investigating the ferromagnetic properties of bare Cu nanoparticles. Three sets of bare Cu nanoparticle assemblies with mean particle diameters of 6.6, 8.1, and 11.1 nm were fabricated, employing the gas condensation method. Curie-Weiss paramagnetic responses to a weak driving magnetic field were detected, showing the appearance of particle superspins that overcomes the diamagnetic responses from the inner core. The isothermal magnetization displays a Langevin field profile together with magnetic hysteresis appearing even at 300 K, demonstrating the existence of ferromagnetic superspins in the Cu nanoparticles. Shifting of a noticeable amount of electronic charge from being distributed near the lattice sites in bulk form toward their neighboring ions in nanoparticles was found. The extended 3d and 4s band mixture are the main sources for the development of localized 3d holes for the development of ferromagnetic particle superspins in Cu nanoparticles.

Trends in magnetism of free Rh clusters via relativistic ab-initio calculations

A fully relativistic ab-initio study on free Rh clusters of 13-135 atoms is performed to identify general trends concerning their magnetism and to check whether concepts which proved to be useful in interpreting magnetism of 3d metals are applicable to magnetism of 4d systems. We found that there is no systematic relation between local magnetic moments and coordination numbers. On the other hand, the Stoner model appears well-suited both as a criterion for the onset of magnetism and as a guide for the dependence of local magnetic moments on the site-resolved density of states at the Fermi level. Large orbital magnetic moments antiparallel to spin magnetic moments were found for some sites. The intra-atomic magnetic dipole Tz term can be quite large at certain sites but as a whole it is unlikely to affect the interpretation of x-ray magnetic circular dichroism experiments based on the sum rules.

An insight into the structures, stabilities, and bond character of B(n)Pt (n=1∼6) clusters

We perform a systematical investigation on the geometry, thermodynamic/kinetic stability, and bonding nature of low-lying isomers of BnPt (n=1-6) at the CCSD(T)/[6-311+G(d)/LanL2DZ]//B3LYP/[6-311+G(d)/LanL2DZ] level. The most stable isomers of BnPt (n=1-6) adopt planar or quasi-planar structure. BnPt (n=2-5) clusters can be generated by capping a Pt atom on the B-B edge of pure boron clusters. However, For B6Pt with non-planar structure, a single doped Pt atom significantly affects the shape of the host boron cluster. The dopant of the Pt atom can improve the stability of pure boron clusters. The valence molecular orbital (VMO), electron localization function (ELF), and Mayer bond order (MBO) are applied to gain insight into the bonding nature of BnPt (n=2-6) isomers. The aromaticity for some isomers of BnPt (n=2-6) is analyzed and discussed in terms of VMO, ELF, adaptive natural density partitioning (AdNDP), and nucleus-independent chemical shift (NICS) analyses. Results obtained from the energy and cluster decomposition analyses demonstrate that B2Pt and B4Pt exhibits as highly stable. Importantly, some isomers of BnPt (n=2-5) are stable both thermodynamically and kinetically, which are observable in future experiment.

Structural and electronic study of neutral, positive, and negative small rhodium clusters [Rh(n), Rh(n)(+), Rh(n)(-) ; n = 10-13]

We have carried out a systematic study for the determination of the structure and the fundamental state of neutral and ionic small rhodium clusters [Rhn, Rhn(+), Rhn(-); n = 10-13] using ab initio Hartree-Fock methods with a LANL2DZ basis set. A range of spin multiplicities is investigated for each cluster. We present the bond lengths, angles, and geometric configuration adopted by the clusters in its minimum energy conformation showing the differences when the clusters have different number of unpaired electrons. Also we report the vertical ionization potential and the adiabatic one calculated by the Koopmans' theorem.

Large orbital magnetic moment in Pt₁₃ clusters

We present an extensive study of Pt₁₃ clusters embedded in a Na-Y zeolite, by comparing calculations for isolated clusters to experimental data. We perform structural refinements for various geometries involving the isolated clusters and calculate the corresponding x-ray absorption and magnetic circular dichroism spectra, from the joint perspective of pseudopotential plane wave calculations and real space multiple scattering theory. Taking into account the spin-orbit coupling significantly improves the previous scalar relativistic predictions of magnetic properties. The ensemble of embedded Pt₁₃ is found to be dominated by a non-magnetic cuboctahedral geometry. One of the implications is that the ground state of Pt₁₃ clusters in the zeolite environment is different from that of isolated particles. We investigate several isomers that yield a magnetic signature. Furthermore, their abundance was estimated by direct comparison with experiment. We found that one third of the magnetic moment of Pt₁₃ comes from the orbital contribution, in agreement with the experimental value. We therefore provide theoretical proof of the extraordinary orbital magnetization in Pt13 clusters.

Stacking principle and magic sizes of transition metal nanoclusters based on generalized Wulff construction

Nanoclusters with extra stability at certain cluster sizes are known as magic clusters with exotic properties. The classic Wulff construction principle, which stipulates that the preferred structure of a cluster should minimize its total surface energy, is often invoked in determining the cluster magicity, resulting in close-shelled Mackay icosahedronal clusters with odd-numbered magic sizes of 13, 55, 147, etc. Here we use transition metal clusters around size 55 as prototypical examples to demonstrate that, in the nanometer regime, the classic Wulff construction principle needs to be generalized to primarily emphasize the edge atom effect instead of the surface energy. Specifically, our detailed calculations show that nanoclusters with much shorter total edge lengths but substantially enlarged total surface areas are energetically much more stable. As a consequence, a large majority of the nanoclusters within the 3d-, 4d-, and 5d-transition metal series are found to be fcc or hcp crystal fragments with much lower edge energies, and the widely perceived magic size of 55 is shifted to its nearby even numbers.

Spin polarization and quantum spins in Au nanoparticles

The present study focuses on investigating the magnetic properties and the critical particle size for developing sizable spontaneous magnetic moment of bare Au nanoparticles. Seven sets of bare Au nanoparticle assemblies, with diameters from 3.5 to 17.5 nm, were fabricated with the gas condensation method. Line profiles of the X-ray diffraction peaks were used to determine the mean particle diameters and size distributions of the nanoparticle assemblies. The magnetization curves M(H_a) reveal Langevin field profiles. Magnetic hysteresis was clearly revealed in the low field regime even at 300 K. Contributions to the magnetization from different size particles in the nanoparticle assemblies were considered when analyzing the M(H_a) curves. The results show that the maximum particle moment will appear in 2.4 nm Au particles. A similar result of the maximum saturation magnetization appearing in 2.3 nm Au particles is also concluded through analysis of the dependency of the saturation magnetization M_P on particle size. The M_P(d) curve departs significantly from the 1/d dependence, but can be described by a log-normal function. Magnetization can be barely detected for Au particles larger than 27 nm. Magnetic field induced Zeeman magnetization from the quantum confined Kubo gap opening appears in Au nanoparticles smaller than 9.5 nm in diameter.

A strategy to find minimal energy nanocluster structures

An unbiased strategy to search for the global and local minimal energy structures of free standing nanoclusters is presented. Our objectives are twofold: to find a diverse set of low lying local minima, as well as the global minimum. To do so, we use massively the fast inertial relaxation engine algorithm as an efficient local minimizer. This procedure turns out to be quite efficient to reach the global minimum, and also most of the local minima. We test the method with the Lennard-Jones (LJ) potential, for which an abundant literature does exist, and obtain novel results, which include a new local minimum for LJ13 , 10 new local minima for LJ14 , and thousands of new local minima for 15≤N≤65. Insights on how to choose the initial configurations, analyzing the effectiveness of the method in reaching low-energy structures, including the global minimum, are developed as a function of the number of atoms of the cluster. Also, a novel characterization of the potential energy surface, analyzing properties of the local minima basins, is provided. The procedure constitutes a promising tool to generate a diverse set of cluster conformations, both two- and three-dimensional, that can be used as an input for refinement by means of ab initio methods.

A density functional study of Rh13

A density functional study was performed for the Rh13 cluster using the linear combination of Gaussian-type orbitals density functional theory (LCGTO-DFT) approach. The calculations employed both the local density approximation (LDA) as well as the generalized gradient approximation (GGA) in combination with a quasi-relativistic effective core potential (QECP). Initial structures for the geometry optimization were taken along Born–Oppenheimer molecular dynamics (BOMD) trajectories. The BOMD trajectories were performed at different temperatures and considered different potential energy surfaces (PES). As a result, several hundred isomers of the Rh13 cluster in different spin multiplicities were optimized with the aim to determine the lowest energy structures. All geometry optimizations were performed without any symmetry restriction. A vibrational analysis was performed to characterize these isomers. Structural parameters, relative stability energy, harmonic frequencies, binding energy, and most relevant Kohn–Sham (KS) molecular orbitals are reported. The obtained results are compared with available data from the literature. This study predicts a low symmetry biplanarlike structure as the ground-state structure of Rh13 with 11 unpaired electrons. This isomer was first noticed by inspection of first-principle Born–Oppenheimer molecular dynamics (BOMD) simulations between 300 and 600 K. This represents the most extensive theoretical study on the ground-state structure of the Rh13 cluster and underlines the importance of BOMD simulations to fully explore the PES landscapes of complicated systems.

Structural, electronic and magnetic properties of transition metal binary alloy clusters with isoelectronic components: case study with MnmTcn, TimZrn and MnmRen

With the goal of achieving an understanding of the properties of bimetallic alloy clusters having atoms of two isoelectronic elements, we have studied the structural, electronic and magnetic properties of MnmTcn, MnmRen and TimZrn clusters with m + n = 13 (n = 0, 1, 4, 6, 9, 12, 13), using first-principles density functional calculations. MnmTcn and MnmRen represent clusters of isoelectronic series with a half-filled d shell, while TimZrn represents an isoelectronic cluster series of early transition metals. Mn-rich alloy clusters are found to prefer compact structures and isoelectronic Tc-rich or Re-rich alloy clusters are found to adopt open structures. In contrast, TimZrn clusters are all found to stabilize in compact structures, irrespective of being Ti-rich or Zr-rich. This change in behavior between two isoelectronic series is found to be driven by differences in hybridization effects, due to differences in the evolution of the relative energy positions of the d level with respect to the s and p levels upon moving from 3d to 4d or 5d elements. This effect further competes with the magnetization effect to decide the morphology of the alloy clusters. Focusing on the magnetic properties of the studied clusters, we find that the single Tc atom substituted alloy cluster exhibits markedly improved magnetic properties compared to that of pure Mn clusters.

Ab initio random structure search for 13-atom clusters of fcc elements

The 13-atom metal clusters of fcc elements (Al, Rh, Ir, Ni, Pd, Pt, Cu, Ag, Au) were studied by density functional theory calculations. The global minima were searched for by the ab initio random structure searching method. In addition to some new lowest-energy structures for Pd13 and Au13, we found that the effective coordination numbers of the lowest-energy clusters would increase with the ratio of the dimer-to-bulk bond length. This correlation, together with the electronic structures of the lowest-energy clusters, divides the 13-atom clusters of these fcc elements into two groups (except for Au13, which prefers a two-dimensional structure due to the relativistic effect). Compact-like clusters that are composed exclusively of triangular motifs are preferred for elements without d-electrons (Al) or with (nearly) filled d-band electrons (Ni, Pd, Cu, Ag). Non-compact clusters composed mainly of square motifs connected by some triangular motifs (Rh, Ir, Pt) are favored for elements with unfilled d-band electrons.

Spin fluctuations of paramagnetic Rh clusters revealed by x-ray magnetic circular dichroism

The magnetic moment induced on Rh atoms, forming 1.6 nm average diameter clusters, embedded in an Al(2)O(3) matrix, has been determined using x-ray magnetic circular dichroism measurements. The magnetic moment varies linearly with the applied magnetic field. At 2.3 K and under 17 T, the spin magnetic moment amounts to 0.067(2) μ(B)/Rh atom. The orbital moment does not exceed 2% of the spin moment. The susceptibility is highly temperature dependent. This is in agreement with a prediction due to Moriya and Kawabata, that in itinerant electron systems, close to the onset of magnetism, the renormalization of the magnetic susceptibility by electron correlations, leads to a Curie-like behavior.

Magnetostructural effects in ligand stabilized Pd13 clusters: a density functional theory study

We show computationally that ligation allows tuning of the magnetostructural properties of the Pd(13) cluster. The bare, phosphine and thiol capped clusters were investigated at the density functional level. The most stable conformers of the bare cluster are of high spin, septet and nonet and of distorted C(3v), C(s) and I(h) geometries. Ligation stabilizes the I(h) geometry and quenches the high spin states, down to a triplet for Pd(13)(PH(3))(12) and to a quintet for Pd(13)(SCH(3))(12).The influence of the two capping systems on the magnetostructural properties of the ligated clusters is analyzed in connection with their different bonding properties. The mixed ligand species Pd(13)(SCH(3))(6)(PH(3))(6) is also characterized. Due to the multiple energetically accessible spin states, unusual thermal behaviour of the average magnetic moment is predicted for these clusters.