Structural and dynamical properties of transition metal clusters

Results of molecular dynamics simulation studies of structural and dynamical properties of 12-, 13-, and 14-atom transition metal clusters are presented. The calculations are carried out using a Gupta-like potential expressed in reduced units. The transformation to absolute units involves two size-dependent parameters which effectively convert the potential into a size-dependent one. The minimum energy geometries of the clusters are obtained through the technique of simulated thermal quenching. A melting-like transition is observed as the energy of the clusters is increased. A novel element of the transition is that it may involve a premelting state.     

Shell structure and response properties of metal clusters

Electronic shell structure, which was first recognized in sodium clusters, has been observed in alkali and noble metals, as well as in divalent and trivalent metals. Shell structure with modifications is expected to be broadly applicable to most metals. Features in the cluster abundance spectra and in the experimental dipole polarizabilities and ionization potentials correlate well with predictions of electronic level filling in spherical and spheroidal potential wells. The lack of precise quantitative agreement between experiment and theory for the response properties indicates necessary refinements in the self-consistent uniform background jellium model for clusters.     

Structural and electronic properties of compound metal clusters

The equilibrium geometries, relative stabilities, and vertical ionization potentials of compound clusters involving Li _n , Na, Mg, and Al atoms have been calculated using ab initio self-consistent field linear combination of atomic orbitals — molecular orbital (SCF-LCAO-MO) method. The exchange energies are calculated exactly using the unrestricted Hartree-Fock (UHF) method whereas the correlation correction is included within the framework of configuration interaction involving pair excitations of valence electrons. While the later correction has no significant effect on the equilibrium geometries of clusters, it is essential for the understanding of relative stabilities. Clusters with even numbers of electrons are found to be more stable than those with odd numbers of electrons regardless of their charge state and atomic composition. The equilibrium geometries of homo-nuclear clusters can be significantly altered by replacing one of its constituent atoms with a hetero-nuclear atom. The role of electronic structure on the geometries and stabilities of compound clusters is discussed.     

General properties of the electronic structure of alkali metal clusters and Ia-IIa mixed clusters

The results of the systematic ab-initio CI investigation of neutral and charged Li _n , Na _n , BeLi _k and MgNa _k clusters are summarized and analyzed. The general characteristic features of the electronic structure are pointed out:a) The participation of the atomic orbitals, which are empty in Ia and IIa metal atoms, allows for a higher valency of these atoms in clusters.b) Jahn-Teller and pseudo-Jahn-Teller effects strongly influence the electronic and geometric structure of clusters.c) Deformations of cluster geometry can lead to biradicaloid structures with higher spin multiplicity in their ground states.d) The peculiarities of the electronic structures of clusters can be deduced from the presence of many “surface” atoms. The theoretical results agree with experimental data presently available and they are useful for interpretation of the experimental findings.     

Chemisorption and chemical reactions on size selected clusters

Low energy ion beam techniques have been used to perform a detailed study of the reactions of Al ₂₅ ⁺ and Si ₂₅ ⁺ with a range of simple molecules (D₂, CH₄, O₂, C₂H₄, CO and N₂). The reactions were studied over a center of mass collision energy range from 0.2eV up to 7eV. Activation barriers for chemisorption onto the clusters were deduced from the experimental results. The activation barriers for chemisorption on Al ₂₅ ⁺ and Si ₂₅ ⁺ are generally similar and show a qualitative correlation with the electronic properties of the reactant molecule. However, the products of the chemical reactions of Al ₂₅ ⁺ and Si ₂₅ ⁺ which result from cluster fragmentation are quite different. Si ₂₅ ⁺ shows a tendency to undergo fission as observed in a number of recent studies of the dissociation of the bare clusters.     

Magnetic properties and EPR spectroscopy of molecular metal clusters

The magnetic properties of molecular metal cluster compounds resemble those of small metal particles in the metametallic size regime. Even-electron metal carbonyl clusters with 10 or more metal atoms are paramagnetic, because their frontier orbital separations of less than 1 eV lead to high-spin electronic configurations. The rhodium cluster [Rh₁₇S₂(CO)₃₂]^3? gives EPR below 200 K withg=2.04, the first example of this type of paramagnetism in an even-electron carbonyl cluster of this 4d metal. Its spectral parameters are compared with those of osmium carbonyl clusters and some significant differences highlighted. Attempts have also been made to generate radical cations from lower-nuclearity, diamagnetic molecular clusters such as Rh₆(CO)₁₆ by chemical oxidation in sulphuric acid. An EPR active species (g=2.09) believed to be [Rh₆(CO)₁₆]⁺ has been obtained.     

Magnetic properties of free alkali and transition metal clusters

The Stern-Gerlach deflections of small alkali clusters (N<6) and iron clusters (10<N<500) show that the paramagnetic alkali clusters always have a non-deflecting component, while the iron clusters always deflect in the high field direction. Both of these effects appear to be related to spin relaxation however in the case of alkali clusters it is shown that they are in fact caused by avoided level crossing in the Zeeman diagram. For alkali clusters the relatively weak couplings cause reduced magnetic moments where levels cross. For iron clusters however the total spin is strongly coupled to the molecular framework. Consequently this coupling is responsible for avoided level crossings which ultimately cause the total energy of the cluster to decrease with increasing magnetic field so that the iron clusters will deflect in one direction when introduced in an inhomogeneous magnetic field. Experiment and theory are discussed for both cases.     

Synthesis and properties of metal clusters in polymeric matrices

A one-step plasma deposition process is described which allows the uniform dispersion of small metal clusters throughout a thin film polymer matrix. Plasma parameters and plasma gas phase diagnostics relevant to the control of film composition and structure are discussed. Chemical and structural analytical techniques such as I.R. absorption spectroscopy, E.S.C.A., Auger electron spectroscopy, X-ray fluorescence, X-ray and electron diffraction and microscopy are used to characterize the cluster containing films. Changes in cluster size and shape as a function of volume fraction and as a result of post deposition annealing are described. Optical and electrical properties are presented below and above the onset of percolation and are evaluated in terms of contemporary effective medium theories.     

Thermal properties of the valence electrons in alkali metal clusters

The finite-temperature density functional approach is applied for the first time to calculate thermal properties of the valence electron system in metal clusters using the spherical jellium model. Both the canonical and the grand canonical formalism are applied and their differences are discussed. We study the temperature dependence of the total free energyF(N) (including a contribution from the ionic jellium background) for spherical neutral clusters containingN atoms. We investigate, in particular, its first and second differences, Δ₁ F =F (N ? 1) ?F (N) and Δ₂ F =F(N + 1) +F(N ? 1) ? 2F(N), and discuss their possible relevance for the understanding of the mass abundance spectra observed in cluster production experiments. We show that the typical enhancement of magic spherical-shell clusters withN=8, 20, 34, 40, 58, 92, 138, 186, 254, 338, 398, 440, 508, 612..., most of which are well established experimentally, is decreasing rather fast with increasing temperatureT and cluster sizeN. We also present electronic entropies and specific heats of spherical neutral clusters. The Koopmans theorem and related approximations for calculating Δ₁ F and Δ₂ F atT > 0 are discussed.     

Electrical and magnetic properties of thin films containing metal clusters

A large variety of granular polymer thin films can be synthetized in a capacitively coupled coplanar diode radiofrequency (r.f.) discharge system in which an argon-monomer mixture is injected at low pressure (20 mTorr). This approach offers several advantages over the other techniques, e.g. easy control of the metal content in the film from a few % up to 100%. The d.c. electrical properties of gold containing plasma polymerized tetrafluoroethylene (PPTFE) and the magnetic behavior of cobalt containing plasma polymerized propane (PPP) are reported in this paper.     

Formation and properties of metal clusters isolated in helium droplets

The unique conditions forming atomic and molecular complexes and clusters using superfluid helium nanodroplets have opened up an innovative route for studying the physical and chemical properties of matter on the nanoscale. This review summarizes the specific characteristics of the formation of atomic clusters partly generated far from equilibrium in the helium environment. Special emphasis is on the optical response, electronic properties as well as dynamical processes which are mostly affected by the surrounding quantum matrix. Experiments include the optical induced response of isolated cluster systems in helium under quite different excitation conditions ranging from the linear regime up to the violent interaction with a strong laser field leading to Coulomb explosion and the generation of highly charged atomic fragments. The variety of results on the outstanding properties in the quantum size regime highlights the peculiar capabilities of helium nanodroplet isolation spectroscopy.     

Electronic properties of large metal clusters in jellium and pseudo-jellium models

The energy-density functional approach and jellium-like models are used to examine two important electronic properties of metal (Li, Na, K) clusters: their shell and supershell structures, and the behaviour of plasmon energies with increasing cluster sizes. A comparative study is made between predictions of the usual jellium model and those of the pseudo-jellium model where pseudohamiltonians are used.     

Argon solvent effects on optical properties of silver metal clusters

Argon gas at a high pressure (～80 bar) has been expanded using a miniaturized pulsed valve at room temperature, producing a supersonic beam of cold, large argon droplets. Atoms of silver are subsequently embedded into the droplet using the pick-up technique. The resulting Ag(n)Ar(droplet) distribution was analyzed using multiphoton laser ionization time-of-flight mass spectrometry. Besides bare metal clusters, snowballs of silver monomers and dimers encapsulated in up to 50 argon atoms have been observed. The influence of the solvent on the optical absorption of the solute was studied for embedded Ag(8) using resonant two-photon ionization in the ultraviolet. A redshift and broadening of the Ag(8)Ar(droplet) optical spectrum compared to that measured in pure [Federmann et al., Eur. Phys. J. D 1999, 9, 11] and Ar-doped helium droplets [Diederich et al., J. Chem. Phys.2002, 116, 3263] was observed, which is attributed to the interaction with the larger Ar matrix environment.     

Rotational effects on the magnetic properties of an ensemble of free metal clusters

The magnetization of an ensemble of free magnetic metal clusters in an inhomogeneous external magnet field is calculated. In particular we have investigated the effects of the combined lattice anisotropy and cluster rotation on the magnetic properties. If weak anisotropy is present, almost superparamagnetic behavior is obtained. For stronger anisotropies deviations from this are calculated as a consequence of spin resonance due to the anisotropy field and the cluster rotation. This was proposed recently by de Heer et al. to explain his experimental data as generally expected, since a rotating cluster in a static magnetic field should behave similarly than a nonrotating one in an oscillating magnetic field. The magnetization depends also sensitively on the relaxation times.     

Simple metal clusters

The response of alkali cluster ions to an optical excitation is investigated for two different photon energy domains. Below the ionization potential giant resonances in the photoabsorption cross-section are observed for closed shell species. Above the ionization potential, the ionization process competes with the photofragmentation process. The number of valence electrons determines both the behavior of the photoabsorption spectrum and the evolution of the ionization cross-section with the cluster size. The stability of the clusters against an excess of charge is examined through the observation of an asymmetric fission of Na _n ⁺⁺ . Experimental results are discussed in term of an electrostatic model giving an estimate of the critical size of stability and of the height of the coulombic barrier.     

On the phase of metal clusters

Metal clusters of about 1,000 atoms formed in condensing flows of pure vapors are predicted to remain liquid in high vacuum since evaporation cooling essentially terminates before solidification is achieved. Radiation cooling does not contribute considerably in times comparable to the usual cluster flight times.     

High nuclearity metal clusters: Miniature bulk of unusual structures and properties?

Recent developments in cluster synthesis have produced many high nuclearity metal clusters of discretesize andshape approaching that of small particles. Some of these clusters have metal arrangements resemblingfragments of metallic lattices and thus may be considered as aminiature bulk. Some are related to the quasicrystalline phase. Yet others have little or no structural features in common with that of the bulk. These metal clusters of definitivesize andshape provide an opportunity for the study of the evolution of band structure fromatomic tomolecular to thebulk. The focus of this review is on the unusual structures and properties of well-defined high nuclearity metal clusters and their possible relations or variant to the bulk state. Specifically, interesting electronic, optical, and magnetic properties of metal clusters in the quantum-size regime are described. Structural systematics of high nuclearity metal clusters, ranging from thecluster-of-clusters to thelayer-by-layer growth sequence, are discussed. It is hoped that further studies of the structures and properties of large metal cluster compounds of discretesize andshape will shed light on how, when, and why metallic or other bulk behavior begins and ends.     

Alkali metal clusters and the jellium model

The application of the jellium model and the resulting quantum shell structure for metal clusters is examined in the light of theoretical calculations and experimental observations. Objections to the jellium model by Kappes, Schar, Rädi and Schumacher appear to be based on misunderstandings of the model and on inadequate experiments.