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.     

A theoretical study of alkali metal atomic clusters: From Lin to Csn (n = 2–8)

A theoretical study of the electronic structure of the first members of the alkali metal atomic clusters series Li_n to Cs_n (n = 2–8) has been done. The geometries of some isomers of the neutral, positive, and negative charged clusters have been determined. Some important properties have also been calculated: atomic binding energies, vertical and adiabatic ionization potentials, vertical and adiabatic electron affinities, static dipole polarizabilities, and energy gaps. Whenever possible they have been compared with experimental values yielding a reasonable agreement which supports some new values as reliable predictions. The data have been discussed in light of the periodic table of elements trends. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2009     

Electronic shell structure in multiply charged silver clusters

Silver clusters are generated by standard laser vaporization technique and ionized via multiphoton ionization. Time-of-flight mass spectrometry reveals singly, doubly and triply charged clusters, Ag _n ^z+ (z=1,2,3). The spectra show, for all charge states, intensity variations, indicating enhanced stabilities for cluster sizes with closed electronic configurations in accord with the spherical jellium model.     

Electron impact ionization of silver clusters Ag n,n≦36

Electron impact ionization of gas phase silver clusters Ag _n ,n≦36 has been achieved in the threshold region. The vertical ionization potentials in this region clearly demonstrate the evidence of shell effects as well as a distinct even-odd oscillation up ton?20. Their general size dependence is somewhat different from that of the alkali metal clusters due to the presence of thed-electrons.     

Ionization energies of cesium and cesium oxide clusters

The vertical ionization potentials of 7 cesium and 86 oxidized cesium clusters were determined using the technique of photoionization mass spectrometry. The spectra were obtained using a tunablecw dye laser for clusters in a mass range 1 to 2024 amu. The vertical ionization potentials (IP) are presented as a function of size and composition. The ionization energies of cesium clusters, Cs_n, decrease with cluster size. Unusually low IP were observed for the enneamer, Cs₉, and for the cesium monoxide Cs₁₁ O. With increasing oxidation of the cesium metal clusters the IP decreases (suboxides) reaches a minimum at Cs(Cs₂O)_n and then increases (superoxides).     

Photoabsorption cross sections of sodium clusters: electronic and geometrical effects

We study the origin of the discrepancy between the photoabsorption cross sections of small jellium spheres calculated by the time dependent local density approximation (TDLDA) and experiments for small metallic clusters. We have specifically studied Na ₂₁ ⁺ . We conclude that both non-local exchange-correlation effects beyond the LDA and geometrical effects beyond the jellium approximation should be taken in the same calculation. We also present local and non-local calculations for Na _n ^? (n=19, 91 and 197) within the framework of the jellium model. The large anions show a fragmentation of the plasmon due to its interference with the ionization threshold. This feature is absent in the TDLDA results.     

Dipole polarizabilities of germanium clusters

Dipole polarizabilities of Ge_n clusters with 2–25 atoms are calculated using finite field (FF) method within density functional theory. The dipole moments and polarizabilities of clusters are sensitively dependent on the cluster geometries and electronic structures. The clusters with low symmetry and large HOMO–LUMO gap prefer to large dipole moments. The polarizabilities of the Ge_n clusters increase rapidly in the size range of 2–5 atoms and then fluctuate around the bulk value. The larger HOMO–LUMO gap may lead to smaller polarizability. As compared with the compact structure and diamond structure, the prolate cluster structure corresponds to a larger polarizability.     

Doubly charged sodium clusters: plasmon response and photoproduction

The optical response of doubly charged sodium clusters Na _n+2 ⁺⁺ was measured for n = 20, 40, and 58 valence electrons, for which the jellium model predicts spherical clusters. A new experimental scheme was developed which allows to separate doubly charged clusters of even mass from the singly charged with half the mass. The optical spectra are dominated by a plasmon-like resonance which is blue shifted and narrower than that of the singly charged clusters. The smallest doubly charged cluster observed was Na ₉ ⁺⁺ . The photo ionization cross section for singly charged clusters was found to be typically 2.6·10^-19cm² per Na atom for photon energies of around 6 eV, which is a factor of 400 smaller than the maximum in the plasmon absorption in the region of hω=2.6 eV.     

Unimolecular dissociation of trivalent metal cluster ions (Al n + , Ga n + , In n + ): evidence for a transition from covalent to metallic bonding

Unimolecular dissociation of aluminum, gallium and indium clusters is investigated. Small sizes dissociate into two channels: either the evaporation of a neutral or a charged monomer. Above a given size n _c, only dissociation of a neutral atom subsists. The evaporation of a charged monomer is characteristic of trivalent metal clusters and is consistent with the size evolution of the ionization potential towards the atomic value. The experiments are interpreted in the framework of the statistical R.R.K. model. For smaller sizes (n < n _c), as two evaporation processes are in competition, we have evaluated cluster relative dissociation energies and ionization potentials. The competition between the two evaporation channels is well mirrored by the evolution of the ionization potentials independently measured by near-threshold photoionization experiments. For gallium, our measurements have revealed that the covalent to metal transition occurs for larger sizes (n = 30–50 atoms) than for aluminum clusters.     

Laser photoionization and spectroscopy of gas phase silver clusters

Silver clusters containing up to 40–50 atoms are produced by laser vaporization in a pulsed-nozzle molecular beam source and studied with laser photoionization mass spectroscopy. A variety of Nd:YAG pumped dye laser and UV excimer laser wavelengths are used to achieve ionization. Ionization dynamics are studied by varying the laser wavelength and fluence. Bracketing experiments under single-photon ionization conditions are used to estimate ionization potentials as a function of cluster size. An even-odd ionization potential alternation is observed with odd-numbered clusters (N=3, 5, 7 ...) having lower ionization potentials than adjacent even-numbered species. Shell closings at clusters containing 2, 8 20 and 40 electrons are observed consistent with a one-electron shell model picture of cluster electronic structure. Resonance-enhanced ionization produces a vibrationally resolved spectrum for the trimer, Ag₃, yielding an electronic state assignment and excited state vibrational frequencies. Fragmentation in dimer ionization via theE state at 249 nm establishes the dissociation energy of Ag ₂ ⁺ to be <2.1 eV.     

Theoretical study of the stability of X N n (n=−1, 0, +1, +2; X=Ag,Cu;N≤25) clusters as a function of size using a non-local density functional formalism

The spherical jellium model and self-consistent Weighted Density Approximation (WDA) to density functional theory have been used to study the stability of X _N ⁿ (n=?1, 0, +1, +2; X=Ag, Cu;N≤25) clusters. The calculated magic numbers coincide with the observed ones. The first (IP1) and second (IP2) ionization potentials of Ag _N and Cu _N as a function of size show the typical oscillations induced by the electronic shell-filling effect. IP1 of Cu _N is about 0.5 eV higher than IP1 of Ag _N in the range studied (N≤25). For both Cu _N and Ag _N , IP1 appears to converge well towards the respective experimental values of the work function. The use of WDA allows us to obtain bound negative clusters of small size or with a nearly empty external shell, which is not possible using the Local Density Approximation (LDA) [1, 2]. However the electron affinity of X _N clusters obtained as the difference of energies of the neutral and the negatively charged clusters, becomes negative forN=2, 3 and 8 (very close to zero forN=8), revealing that WDA needs further refinements.     

Small clusters made up of three kinds of neutral alkali atoms

Small clusters made up of three kinds of neutral alkali atoms, i.e. clusters of the form X _? Y _m Z _n , are theoretically studied. These clusters exhibit three series of magic numbers, one for each kind of atoms. That is,?,m, andn independently can be magic numbers rather than their cumulative number?+m+n or, in other words, magic numbers in alkali clusters composed of neutral atoms are due to atoms rather than to delocalized electrons as in jellium model. Of course, if conditions favor delocalization of electrons,?+m+n can be magic but then we have no neutral atoms which are prerequisite for an application of the present model.     

Photoionization mass spectrometry of molecular clusters using synchrotron radiation

The photoionization and dissociative ionization of molecular aggregates using synchrotron radiation is reported. The main objective of the review is to consider the intracluster relaxation processes after ionization. For hydrogen-bonded systems proton transfer is dominant. For small clusters (n<4) appearance potentials, ionization potentials, absolute proton affinities, proton solvation energies and intermolecular bond energies in the ionic clusters are deduced. For van der Waals aggregates proton transfer can also be used to characterize the intermolecular bond in the ionic cluster. Aggregates of CH₄, SiH₄, CH₃F show proton transfer in contrast to simple aromatic compounds, which reveal no proton transfer. From the fragmentation pattern and appearance potentials relaxation by intracluster ion molecule reactions is discussed. In heterogeneous clusters intracluster Penning ionization is observed. The shift of the charge transfer resonances depends on the π-electron density in the aromatic system. The width and spectral position of these resonances are influenced by the cluster size.     

Photoionization studies of transition metal clusters: Ionization potentials of ScnO (n=5−36)

The photoionization efficiency (PIE) spectra and ionization potentials are reported for scandium cluster monoxides (Sc _n O,n=5–36). As found for other transition metal clusters, strong dependence of ionization potential on cluster size is found for small clusters, with the ionization potentials of larger clusters decreasing relatively smoothly with increasing size. The IPs are 0.6–0.8 eV lower than that predicted by conducting spherical droplet model.Performed at Argonne National Laboratory     

Electron detachment and fragmentation in collisions between 50 keV C n − (1 ≤ n ≤ 86) clusters and H2

The destruction cross section for 50 keV negative carbon clusters C _n ^? (1 ≤ n ≤ 88) in collisions with n ₂ is reported. The dominant destruction channel is believed to be electron detachment. The measured cross section values are compared with theoretical values based on a simple geometrical model of the carbon cluster, and structural information is obtained. Fragment spectra of both positive and negative clusters are also recorded and fragmentation patterns are discussed in relation to fragmentation energies and ionization potentials.     

Density functional theory study of the structures,electronic states and stabilities of Al n Pt (n = 1–15) clusters

The binding energy, dissociation energy, ionization potentials, electron affinities, gap and stability of small Al _n Pt (n = 1–15) clusters, in comparison with pure aluminum clusters have been systematically investigated by means of density functional calculations at the B3LYP level. The growth patten for Al _n Pt clusters is that the Pt atom substituted the surface atom of the Al _{n + 1} clusters for n < 13. Starting from n = 13, the Pt atom completely falls into the center of the Al-frame. The Pt atom substituted the center atom of the Al _{n + 1} clusters to form the Pt-encapsulated Aln geometries for n > 13. We also find that the impurity Pt atom causes local structural distortion due to different atomic radii and different bonding characteristics. The clusters with total atom numbers of 2, 7, and 11 exhibit high stability.     

Threshold photoionization behaviour of (Li2O)Lin clusters produced by a laser vaporization source

We report on the production of small and medium size lithium and lithium oxide clusters by a laser vaporization cluster source. The isotopomeric distribution of natural lithium allowed to identify Li_kO clusters as the most abundant components in the mass spectrum. Photoionization efficiency curves of Li_kO clusters with photon energies from 3.4 to 4.7 eV were measured for 8 ≤ k ≤ 27. Using linear extrapolation of the increase in photoionization efficiency with photon energy, ionization potentials were extracted. With the chemical bond of the O^2- anion to two Li atoms, leaving n = k-2 valence electrons in the (Li₂O)Li_n clusters, clear shell closure effects are present at n = 8 and n = 20.     

Theoretical study of the stability of small triply charged carbon clusters Cn3+ (n = 3–12)

Using density functional theory, coupled cluster and multireference methods, dissociation energies and 3rd ionization potentials for, respectively, triply charged and neutral carbon clusters have been evaluated. The results show that the smaller C_n³⁺ clusters are metastable, i.e., they present a fragmentation channel with negative dissociation energy. The lowest dissociation channel always corresponds to evaporation of a singly charged carbon atom. Good agreement with available experimental data is found for most two-fragment channels. The third ionization potential of the corresponding neutral species decreases with cluster size.     

Ionization dynamics of van-der-Waals clusters

The ionization process of homogeneous and heterogeneous van-der-Waals clusters has been investigated using various ionization methods (electron bombardment, charge exchange, photoionization methods), and different analyzing techniques. Direct and indirect ionization processes can be distinguished in the experiments from the shape of the ionization curve which depends on the type of cluster. These features appear differently in homogeneous and heterogeneous systems: Homogeneous systems exhibit characteristic ionization efficiency curves where the direct ionization path appears as a sudden increase in the ionization efficiency while the indirect transition gives rise to a long drawn out tail extending to the true ionization threshold. In heterogeneous clusters the indirect ionization path proceeds via excited states of the component with the larger ionization potential and subsequent energy transfer to the other component. These transitions are shifted and broadened depending on the type of internal interaction. Conclusions are drawn concerning the geometry and the interaction potential inside the cluster. The resolution of the TEPICO (Threshold Electron Photo Ion Coincidence) experiments makes it possible to determine the kinetic energy release of the fragments. It is shown that the results are related to the stabilities of the cluster ions involved in the fragmentation chain. Results are presented for pure rare gas clusters (Ar _n , Kr _n , Xe _n ) and for mixed systems (Ar _n O_2m , Ar _n Xe, Kr _n Xe, (CH₄) _n Ne).     

Geometries and stabilities of Ag n v (v?=?±1, 0; n?=?21–29) clusters

We performed a systematical study on the lowest-energy structures of the medium-sized silver clusters Ag _n (n?=?21?C29) by using a genetic algorithm coupled with a tight-binding method, and the DFT calculations with Perdew?CWang generalized-gradient approximation. The corresponding cluster ions were also searched based on the neutral cluster structures. It is found that the Ag_21?C23 prefer icosahedron or double-icosahedron as core structures. Ag _n (n?=?24?C27) favor a bulk-like fcc stacking motif. Ag₂₈ and Ag₂₉ tend to high symmetrical structures. The relative stabilities, the ionization potentials and electronic affinities of silver clusters analyzed in the paper are consistent with the experimental data. It is interesting to find that the experimental spectra fit reasonable well the optical absorption spectra obtained with the structures calculated by us.