Structure Of Metal Clusters Research Articles

Shell structure of magnesium and other divalent metal clusters

Clusters of the divalent metals magnesium, cadmium, and zinc have been grown in ultracold helium nanodroplets and studied by high-resolution mass spectrometry, with a special emphasis on magnesium. The mass spectra of all materials show similar characteristic features independent of the chosen ionization technique - i.e., electron impact ionization as well as nanosecond and femtosecond multiphoton excitation. In the lower-size range the abundance distributions can be explained by an electronic shell structure. The associated electron delocalization - i.e., metallic bonding - is found to set in at about N=20 atoms. For Mg{sub N} we have resolved crossings of electronic levels at the highest-occupied molecular orbital which result in additional magic numbers compared to the alkali metals: e.g., Mg{sub 40} with 80 electrons. This specific electronic shell structure is also present in the intensity pattern of doubly charged Mg{sub N}. For larger clusters (N{>=}92) a coexistence of electronic shell effects and geometrical packing is observed and a clear signature of icosahedral structure is present beyond N{>=}147.

Trends in the structure and bonding of neutral and charged noble metal clusters

AbstractWe present a systematic study of the electronic and geometric structure of neutral and charged noble metal clusters X (X = Cu, Ag, Au; n ≤ 13; ν = –1,0,+1), obtained from first principles GGA density functional calculations based on norm‐conserving pseudopotentials and a numerical atomic basis set. We determined that the maximum number of atoms forming planar structures with charge ν = (–1,0,+1) are (12, 11, 7) for gold, (5, 6, 5) for silver, and (5, 6, 4) for copper clusters. These results are compared with previous experimental and theoretical estimates. We argue that the tendency to planarity of gold clusters, which is much larger than in copper and silver, is strongly favored by relativistic effects, which decrease the s‐d electron promotion energy and lead to hybridization of the half‐filled 6s orbital with the occupied 5dz2 orbital. Trends for the calculated cohesive energy, average bond lengths, hardness (ionization potential minus electron affinity), and fragmentation energy of the X cluster are presented and discussed in comparison with available experiments and other calculations. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2005

Trends in the structure and bonding of noble metal clusters

We present a systematic study of the electronic properties and the geometric structure of noble metal clusters ${X}_{n}^{\ensuremath{\nu}}$ ($X=\mathrm{Cu}$, Ag, Au; $\ensuremath{\nu}=\ensuremath{-}1,0,+1$; $n\ensuremath{\leqslant}13$ and $n=20$), obtained from first-principles generalized gradient approximation density functional calculations based on norm-conserving pseudopotentials and numerical atomic basis sets. We obtain planar structures for the ground state of anionic $(\ensuremath{\nu}=\ensuremath{-}1)$, neutral $(\ensuremath{\nu}=0)$, and cationic $(\ensuremath{\nu}=1)$ species of gold clusters with up to 12, 11, and 7 atoms, respectively. In contrast, the maximum size of planar clusters with $\ensuremath{\nu}=\ensuremath{-}1,0,+1$ are $n=(5,6,5)$ for silver and (5,6,4) for copper. For ${X}_{20}$ we find a ${T}_{d}$ symmetry for gold and a compact ${C}_{s}$ structure for silver and copper. Our results for the cluster geometries agree partially with previous first-principles calculations, and they are in good agreement with recent experimental results for anionic and cationic gold clusters. The tendency to planarity of gold clusters, which is much larger than in copper and silver, is strongly favored by relativistic effects, which decrease the $s\text{\ensuremath{-}}d$ promotion energy and lead to hybridization of the half-filled $6s$ orbital with the fully occupied $5{d}_{{z}^{2}}$ orbital. That picture is substantiated by analyzing our calculated density matrix for planar and three-dimensional clusters of gold and copper. The trends for the cohesive energy, ionization potentials, electron affinities, and highest accupied and lowest unoccupied molecular orbital gap, as the cluster size increases, are studied in detail for each noble metal and rationalized in terms of two- and three-dimensional electronic shell models. The most probable fragmentation channels for ${X}_{n}^{\ensuremath{\nu}}$ clusters are in very good agreement with available experiments.

Structures of Alkali and Alkaline Earth Metal Clusters with Oxygen Donor Ligands

AbstractFor Abstract see ChemInform Abstract in Full Text.

Chemisorption of atomic and molecular oxygen on Au and Ag cluster anions: discrimination of different isomers

Abstract Structures of coinage metal clusters reacted with atomic and molecular oxygen were studied using Ultraviolet Photoelectron Spectroscopy and Density Functional Theory calculations. We show that O 2 partially dissociates on Ag 2 - , and this dissociative chemisorption is a kinetically hindered step. For Au 4 O 2 - , in addition to the previously observed molecularly adsorbed oxygen, we are now able to synthesize a second isomer using atomic oxygen reagents, in which oxygen adsorbs dissociatively. We demonstrate that different isomers can be distinguished by comparative studies of chemisorption of atomic and molecular species on metal clusters, which is otherwise difficult.

Studies of metal exchange reactions: the synthesis and structures of heteronuclear metal clusters containing the indenyl ligand (μ 3-CR)Co 2M(CO) 8(η 5- Ind)(R=H,CH 3,C 6H 5,COOC 2H 5; M=Mo,W)

The novel tetrahedral clusters ( μ 3 -CR)Co 2 M(CO) 8 (η 5 -Ind) (M=Mo,W; R=H, CH 3 , C 6 H 5 , COOC 2 H 5 ) 5 – 12 containing the indenyl ligand were isolated from reactions of tricobalt clusters (μ 3 -CR)Co 3 (CO) 9 (R=H, CH 3 , C 6 H 5 , COOC 2 H 5 ) and K(η 5 -Ind)M(CO) 3 (M=Mo,W) under mild conditions. The cluster complex (μ 3 -CC 6 H 5 )CoMo 2 (CO) 7 (η 5 -Ind)(η 5 -Cp (Cp*=C 5 H 4 C(O)CH 3 ) 16 was obtained via the stepwise metal exchange reaction of complex (μ 3 -CC 6 H 5 )Co 2 Mo(CO) 8 (η 5 -Ind) 9 with Na(η 5 -CpMo(CO) 3 , but the reaction of (μ 3 -CC 6 H 5 )Co 2 Mo(CO) 8 (η 5 -Cp*) 15 with K(η 5 -Ind)Mo(CO) 3 yielded only 9 . The crystal structures of compounds 7 , 9 and 13 were established by single crystal X-ray diffraction methods and show structural evidence for “slippage” of the indenyl ring.

Structures of large transition metal clusters

The present review surveys the results of X-ray diffraction studies of large stoichiometric transition metal clusters containing from 20 to 145 atoms in metal cores surrounded by ligand shells (72 compounds). Structures of such clusters have fragments of close packings (face-centered cubic (f.c.c.), hexagonal close (h.c.p.), and body-centered cubic (b.c.c.) packings) characteristic of crystalline bulk metals as well as mixed packings (f.c.c./h.c.p.), local close packings with pentagonal symmetry, and strongly distorted “amorphous” packings. The observed packing types, their distortions, and the relationship between the atomic structures of metal cores and the atomic radial distribution functions (RDF) are discussed. The structural principles established for the large clusters are applied to analysis of the experimental RDF for metal nanoparticles determined by X-ray diffraction and EXAFS spectroscopy.

Chirality, defects, and disorder in gold clusters

Theoretical and experimental information on the shape and morphology of bare and passivated gold clusters is fundamental to predict and understand their electronic, optical, and other physical and chemical properties. An effective theoretical approach to determine the lowest-energy configuration (global minimum) and the structures of low energy isomers (local minima) of clusters is to combine genetic algorithms and many-body potentials (to perform global structural optimizations), and first-principles density functional theory (to confirm the stability and energy ordering of the local minima). The main trend emerging from structural optimizations of bare Au clusters in the size range of 12−212 atoms indicates that many topologically interesting low-symmetry, disordered structures exist with energy near or below the lowest-energy ordered isomer. For example, chiral structures have been obtained as the lowest- energy isomers of bare Au28 and Au55 clusters, whereas in the size-range of 75−212 atoms, defective Marks decahedral structures are nearly degenerate in energy with the ordered symmetrical isomers. For methylthiol-passivated gold nanoclusters (Au28(SCH3)16 and Au38(SCH3)24), density functional structural relaxations have shown that the ligands are not only playing the role of passivating molecules, but their effect is strong enough to distort the metal cluster structure. In this work, a theoretical approach to characterize and quantify chirality in clusters, based on the Hausdorff chirality measure, is described. After calculating the index of chirality in bare and passivated gold clusters, it is found that the thiol monolayer induces or increases the degree of chirality of the metallic core. We also report simulated high- resolution transmission electron microscopy (HRTEM) images which show that defects in decahedral gold nanoclusters, with size between 1−2 nm, can be detected using currently available experimental HRTEM techniques.

Structures of metallic clusters: Mono- and polyvalent metals

We present detailed numerical results on the ground state structures of metallic clusters. The Gupta-type many-body potential is used to account for the interactions between atoms in the cluster. Both the genetic algorithm technique and the basin hopping method have been applied to search for the global energy minima of clusters. The excellent agreement found in both schemes for the global energy minima gives credence to the optimized energy values obtained. For four monovalent and one polyvalent metals studied in this work and within the accuracy of the energies presented here, we find that the global energy minima predicted by the basin hopping method are the same as those values obtained by the genetic algorithm. Our calculations for the ground state energies of alkali metallic clusters show regularities in the energy differences, and the cluster growth pattern manifested by this same group of clusters is generally icosahedral, which is quite different from the close-packed and decahedral preferentially exhibited by the tetravalent lead clusters. Considering the inherent disparities in the electronic properties and the bulk structures in these metals (body-centered cubic for alkali metals and face-centered cubic for the lead metal), it is not unreasonable to conjecture that the valence electrons do play a subtle role in the conformation of metallic clusters.

Probing the electronic structure of polynuclear metal clusters with total electron spin S > 1/2 and significant zero-field splitting; Application to the clusters of the nitrogenase MoFe-proteinElectronic supplementary information (ESI) available: Spectral simulations of P. furiosus ferredoxin, of the alternative nitrogenase FeV-cofactor signal and for the FeMo-cofactor from K. pneumoniae under turn-over conditions. See http://www.rsc.org/suppdata/cp/b1/b110486c/

We present a systematic approach to the simulation of EPR spectra of several different spin systems with spin S > 1/2 at arbitrary microwave frequencies and various zero-field splittings (zfs) using direct diagonalization of the complete spin energy matrix. With this method effective simulations can be obtained for systems at every microwave energy irrespective of the zfs interactions and it is therefore also expected to work for systems in the ‘low field limit’ at low microwave frequencies when the zfs energy dominates and where perturbation approaches fail. Here we have used metal complexes in biological systems with substantial zfs interactions, especially the nitrogenase ‘super-clusters’, in order to test the simulation routine. The nitrogenase MoFe-protein contains two types of very complex clusters, FeMo-cofactor and the P-cluster, that can be prepared in several different paramagnetic, oxidation states. It is therefore an ideal system for probing the usefulness of the method. Good spectral simulations were obtained for the FeMo-cofactor signal, with total spin S = 3/2, and the P-cluster signals, with total spins S = 7/2 and S = 9/2 and probably S = 5/2, from the nitrogenase MoFe-protein of Klebsiella pneumoniae (Kp1) at various oxidation levels. The simulations of the S = 3/2 FeMo-cofactor signal reproduces both the ΔMS = 1 transitions generating a strongly rhombic signal from transitions between the MS = ±1/2 spin levels and the ΔMS = 3 transition within the MS = ±3/2 Kramers doublet that gives rise to a signal at g = 6.0. Ferricyanide-oxidised Kp1 gives us the rare opportunity to observe signals from both S = 7/2 and an earlier putatively assigned S = 9/2 spin state from a cluster in a biological environment. In contrast to earlier measurements on the thionine oxidised protein, the experimentally measured S = 7/2 and S = 9/2 states are observed simultaneously for ferricyanide oxidised Kp1 and the individual spectra have been simulated.

Structure and properties of small sodium clusters

We have investigated structure and properties of small metal clusters using all-electron ab initio theoretical methods based on the Hartree-Fock approximation and density functional theory, perturbation theory and compared results of our calculations with the available experimental data and the results of other theoretical works. We have systematically calculated the optimized geometries of neutral and singly charged sodium clusters having up to 20 atoms, their multipole moments (dipole and quadrupole), static polarizabilities, binding energies per atom, ionization potentials and frequencies of normal vibration modes. Our calculations demonstrate the great role of many-electron correlations in the formation of electronic and ionic structure of small metal clusters and form a good basis for further detailed study of their dynamic properties, as well as structure and properties of other atomic cluster systems.

Scanning the potential energy surface of iron clusters: A novel search strategy

A new methodology for finding the low-energy structures of transition metal clusters is developed. A two-step strategy of successive density functional tight binding (DFTB) and density functional theory (DFT) investigations is employed. The cluster configuration space is impartially searched for candidate ground-state structures using a new single-parent genetic algorithm [I. Rata et al., Phys. Rev. Lett. 85, 546 (2000)] combined with DFTB. Separate searches are conducted for different total spin states. The ten lowest energy structures for each spin state in DFTB are optimized further at a first-principles level in DFT, yielding the optimal structures and optimal spin states for the clusters. The methodology is applied to investigate the structures of Fe4, Fe7, Fe10, and Fe19 clusters. Our results demonstrate the applicability of DFTB as an efficient tool in generating the possible candidates for the ground state and higher energy structures of iron clusters. Trends in the physical properties of iron clusters are also studied by approximating the structures of iron clusters in the size range n=2–26 by Lennard-Jones-type structures. We find that the magnetic moment of the clusters remains in the vicinity of 3μB/atom over this entire size range.

Synthesis, structure and electrochemistry of acetylide-bridged mixed metal cluster [Fe 2(CO) 6(μ 3-S) 2W{(η 5-C 5H 5)W(CO) 3(CCPh)} 2

Abstract Thermolysis of a toluene solution containing [Fe2W(CO)10(μ3-S)2] (1) and [(η5-C5H5)W(CO)3(CCPh)] (2), at 80°C yields the mixed metal cluster [Fe2(CO)6(μ3-S)2W{(η5-C5H5)W(CO)3(CCPh)}2] (3). Structure of 3 has been established crystallographically. It consists of a triangular Fe2W unit, each face of which is capped by a sulfido ligand. Each Fe atom bears three carbonyl groups. Two separate molecules of [(η5-C5H5)W(CO)3(CCPh)] are attached to the W atom of the Fe2W core through the acetylide groups.

Prediction of the lowest-energy structures of rare-earth metallic clusters with a Möbius inversion pair potential

The M\"obius inversion pair potential has been employed, in combination with genetic algorithms, to predict the lowest-energy structures of the rare-earth metallic clusters ${\mathrm{La}}_{N},$ ${\mathrm{Ce}}_{N},$ and ${\mathrm{Pr}}_{N}$ $(N=3--20).$ Results are given for the symmetries, binding energies, nearest-neighbor distances of these clusters, and lowest-energy configurations of ${\mathrm{Ce}}_{N}$ clusters. Also, the calculated second finite difference of the total energy shows that for three species elements, the 13-atom clusters with ${I}_{d}$ symmetry are particularly stable. Some minor peaks are also found at size $N=4,$ 6, 11, and 15, which indicates that the corresponding clusters are relatively stable in structure. Present work points out a route to studying clusters.

Structure and Bonding of Gold Metal Clusters, Colloids, and Nanowires Studied by EXAFS, XANES, and WAXS

The structure and bonding of a series of gold clusters and gold nanomaterials stabilized by ligands or confined within nanoporous alumina have been investigated using EXAFS, XANES, and WAXS. Two gold clusters stabilized by two different ligands, Au-55(PPh3)(12)Cl-6 and AU(55)(T-8-OSS - SH)(12)Cl-6 were confirmed to be of face-centered cubic structure type with metal-metal distances of 2.785 and 2.794 Angstrom, respectively, shorter than in bulk gold. Colloidal gold of 180 Angstrom diameter stabilized by sulfonated phosphine ligands had structural and electronic properties very similar to those of bulk gold but smaller Debye-Waller factors. The cluster Au-55(PPh3)(12)Cl-6 adsorbed into nanoporous alumina membrane was found to retain its integrity inside the membrane but with slightly longer Au-Au bonds due to some aggregation. The same cluster thermally transformed into colloidal gold within the alumina membrane was found to be almost identical structurally and electronically to the bulk. Gold nanowires electrochemically grown within the nanoporous alumina were found to be composed on average of 120 Angstrom diameter crystallites. These have the same structure as the bulk, but with smaller Debye-Waller factors, indicating either a better crystallinity or that the gold atoms are more tightly held than in the bulk. The difference of area method L-3 - kL(2) was used to quantify the d orbital occupancy. The two ligand-stabilized Au-55 clusters both had a smaller value (2.7) than the bulk material (4.1). The nanomaterials inside the membrane also showed smaller L-3 - kL(2) values. The geometrical and electronic structures of these gold materials how a very clear pattern of buildup as the number of gold atoms increases from Au-55 clusters through Au colloids and nanowires to the bulk metal.

Structural patterns of unsupported gold clusters

The structure of metal clusters is essential to predict many of their physical and chemical properties. Using first principles density functional calculations it was recently found that even ‘magic’ cluster sizes, for which very compact and symmetric structures exist, have lower-energy ‘disordered’ structures. The origin of these structures was shown to lie in the non-pairwise metallic interactions; while the compact ordered geometries are very stable for pair potentials, they are de-stabilized by the tendency of metallic bonds to contract at the surface. Here we identify important patterns of the resulting ‘amorphous’ structures, showing why they are optimal for the metallic potential, and how they can be used to predict structures for other cluster sizes.

Size Effect on the Atomistic Structure of Metallic Atom Clusters

The atomistic structure of metallic atom clusters is discussed based on the experimental results with the following conclusions: (1) When ultrafine particles of metals become smaller than the critical sizes corresponding to the nucleus size of the crystals, they behave as atom clusters and their atomistic structure changes as a function of the number of constituent atoms, i.e., the many-body potential. (2) Icosahedrons are formed first and change to the cuboctahedral structure before such atom clusters take the final crystal structures. (3) The phonon mode of these atomistic structures is very much softened, and thus the zigzag atom-chains are formed dynamically around the average position of atoms even in the cuboctahedral structure. (4) The hybrid orbital corresponding to the final crystal structure is formed when atom clusters grow to the critical size. As a result, the binding strength sufficiently increases along a certain crystal axis such as the 〈110〉 in the fcc structure and the 〈111〉 in the bcc one, so that atomic rearrangement can occur within the ultrafine particles, including disappearance of multi-twin in Au particles, to take the bonding state of crystals.

Modular design of icosahedral metal clusters

The concept of crystalline “module,” that is, an unambiguously isolated, repeated quasi-molecular element, is introduced. This concept is more general than the concept of crystal lattice. The generalized modular approach allows extension of the methods and principles of crystallography to quasi-crystals, clusters, amorphous solids, and periodic biological structures. Principles of construction of aperiodic, nonequilibrium regular modular structures are formulated. Limitations on the size of icosahedral clusters are due to the presence of spherical shells with non-Euclidean tetrahedral tiling in their structure. A parametric relationship between the structures of icosahedral fullerenes and metal clusters of the Chini series was found.

Simulation of ab initio results for palladium and rhodium clusters by tight-binding calculations

The study of metal clusters is nowadays a very active field of research using both experimental and theoretical techniques. Regular trends as well as unexpected behaviors have been observed regarding size-dependent properties such as ionization potentials and atomization energies. Palladium and rhodium clusters of small size have been extensively studied at various semiempirical and ab initio levels of the theory, but the achievement and the interpretation of these calculations are generally difficult to be performed because of the incomplete shell structure of transition metal clusters. So we have tried to mimic the most important conclusions of the ab initio results available for Pd and Rh clusters by means of tight-binding calculations, in the original Wolfsberg–Helmholz form, with appropriate parametrized repulsion terms. The occupation numbers of the one-electron energy levels have been determined by taking into account some predictions of the graph theory. This enables us to study the variation of the atomization energies per atom for these clusters and to derive a bond-energy systematics for Pd–Pd, Rh–Rh, and Pd–Rh linked atoms. Magic clusters with 13 atoms are considered. © 2001 John Wiley & Sons, Inc. Int J Quant Chem 82: 26–33, 2001

Parallelizing generalized LSD calculations on real space grids: application to the spin structure of transition metal clusters

First results and performance of a parallel implementation of generalized LSD calculations on real space grids are discussed on the example of Ni3 for which a structure closer to experimental data than previous work is found.