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.     

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.     

The Breit interaction in external magnetic fields

The Breit energy of a system, which is shown to depend on the external magnetic vector potential, is exactly transformed, by applying Gordon decompositions, to a form explicitly exhibiting some of the field dependence. The result is used to derive the leading Breit contributions to NMR chemical shifts and atomic g factors.     

The Morse oscillator under time-dependent external fields

A method to solve the equations for the Morse oscillator under intense time-dependent external fields is presented. Exact analytical formulas for the dipole matrix elements are calculated by the use of the hypergeometric algebra. The continuum is described by an expansion using Laguerre functions. The full algorithm for the calculation of wave functions can be controlled by the convergence of series and by the errors of a first order integration method. We apply our technique to the selective preparation of high overtones by femtosecond laser pulses. The population of the target state is optimized as a function of the intensity and frequency. Introducing a second simultaneous laser, we study the effects of relative frequency and phase over the target state population and dissociation channels. The calculations exhibit a rich interference pattern showing the enhancement and the suppression of the target population by varying the laser parameters.     

The structure-averaged jellium model for metal clusters

We present an extension of the jellium model for alkali clusters which allows a selfconsistent determination of the jellium background in addition to the Kohn-Sham solution of the electron dynamics. It includes the volume and the surface energy of the ionic distribution. We discuss applications to the shape of clusters and to the position and width of the plasmon resonances.     

Binary metal alloy clusters

Binary alloy clustersA _n B _m (A,B: Bi, Sb, Pb, Ag, in different compositions) have been generated by simultaneous inert gas condensation of the two vapours. Under suitable condensation conditions the adsorption of single atomsA to clustersB _m can be studied. The adsorption probabilities are found to vary with cluster size. The cluster reactivities depend on the number of absorbed foreign atoms. Lead and bismuth clusters are found to be highly reactive in cracking the strongly bound Sb₄-tetrahedron. One single interaction channel is found for Pb _n /Sb₄ (symmetrical dissociation) and three interaction channels are found for Bi _n /Sb₄ (symmetrical and nonsymmetrical dissociation). Pb- and Bi-clusters have different onset thresholds for dissociative reactivity.     

The collective response of deformed sodium clusters

We employ the structure-averaged jellium model (SAJM) to obtain the selfconsistent LDA Kohn-Sham ground state of axially deformed sodium clusters with broken leftright symmetry, and calculate the dipole-response of the low-energy isomers using the local RPA (LRPA) scheme in the range 7 < Z ≤ 59. We choose the multipole operators r ^P Y _LM (p=1,...,10; L=1,...,4, M=0,1) as coupled intrinsic modes of the electron system. The collective spectra are compared with recent measurements of the dipole absorption cross section performed by Meibom et al., and we find very good agreement of the positions and strengths of the leading collective modes in the measured range 47 < Z ≤ 59.     

Ionization and Coulomb explosion of small group 10 transition metal oxide clusters in strong light fields

The ionization properties of small group 10 metal oxide clusters are explored using ultrafast pulses centered at 624 nm. Maximum atomic charge states resulting from Coulomb explosion were observed to be Ni(3+), Pd(3+), Pt(5+), and O(2+) species with similar ionization potentials ～30-35 eV. Ion signal as a function of laser intensity of each charge state of Ni, Pd, Pt, and O resulting from Coulomb explosion was mapped and compared to that predicted from semi-classical tunneling theory using sequential ionization potentials to quantify observed enhancements in ionization. The saturation intensity (I(sat)) of each charge state is measured and compared to previous studies on group 5 transition metal oxides. The atomic charge states of nickel showed a large enhancement in ionization compared to palladium and platinum, reflective of the differing bonding properties of each metal with oxygen. Results indicate that nickel oxide clusters undergo a greater extent of ionization enhancement as a result of multiple ionization mechanisms. The ionization enhancement behavior of each metal oxide species is explored herein.     

Electronic structure of metal clusters

Photoemission spectra of valence electrons in metal clusters, together with threshold ionization potential measurements, provide a coherent picture of the development of the electronic structure from the isolated atom to the large metallic cluster. An insulator-metal transition occurs at an intermediate cluster size, which serves to define the boundary between small and large clusters. Although the outer electrons may be delocalized over the entire cluster, a small cluster remains insulating until the density of states near the Fermi level exceeds 1/kT. In large clusters, with increasing cluster size, the band structure approaches that of the bulk metal. However, the bands remain significantly narrowed even in a 1000-atom cluster, giving an indication of the importance of long-range order. The core-electron binding-energy shifts of supported metal clusters depend on changes in the band structure in the initial state, as well as on various final-state effects, including changes in core hole screening and the coulomb energy of the final-state charge. For cluster supported on amorphous carbon, this macroscopic coulomb shift is often dominant, as evidenced by the parallel shifts of the core-electron binding energy and the Fermi edge. Auger data confirm that final-state effects dominate in cluster of Sn and some other metals. Surface atom core-level shifts provide a valuable guide to the contributions of initial-state changes in band structure to cluster core-electron binding energy shifts, especially for Au and Pt. The available data indicate that the shift observed in supported, metallic clusters arise largely from the charge left on the cluster by photoemission. As the metal-insulator transition is approached from above, metallic screening is suppressed and the shift is determined by the local environment.     

Photoionization of alkali metal clusters

The photoionization cross section for spherical alkali metal clusters is predicted to oscillate as a function of the photon wavenumber with a frequency determined by the diameter of the cluster. The oscillations and other principal features of the photo cross section can be worked out analytically using semiclassical techniques. An accurate numerical calculation with different cluster potentials confirms these results qualitatively. Quantitative details depend sensitively on the actual potential. Hence, properties of the true cluster potential can be inferred from the experimental cross section. This might turn out to be useful for improving theoretical cluster potentials.     

Time-resolved analysis of strong-field induced plasmon oscillations in metal clusters by spectral interferometry with few-cycle laser fields

We propose a scheme for ultrafast real-time imaging of laser-induced collective electron oscillations (Mie plasmons) in gas phase metal clusters by interferometrically stable scanning of two intense few-cycle optical laser pulses. The feasibility of our nonlinear spectral interferometry method with experimentally accessible observables is tested in a theoretical case study on simple-metal clusters (Na(147)). The results show that the plasmon period and lifetime as well as the phase and relative amplitude of the collective electron motion can be extracted with sub-fs resolution. The access to nonlinear response effects, as the demonstrated increase of the plasmon lifetime with laser intensity due to ionization-induced contraction of the electron cloud, opens up vast opportunities for interrogating ultrafast many-particle dynamics in nanosystems under strong laser fields with unprecedented resolution.     

Bridges between trinuclear metal clusters

Our research on trinuclear Os and Ru carbonyl clusters linkedvia inorganic and organic bridges is reviewed in the context of the nature of the interaction between the linked clusters. The component clusters can behave as essentially independent entities (TYPE A). The component trinuclear species may fuse to form new higher nuclearity clusters in which the indentities of the components are lost (TYPE B). Alternatively, the cluster units retain their identities but for electronic reasons there is long-range metal-metal bonding between them (TYPE C).     

Multiply charged anionic metal clusters

The stability and decay channels of multiply charged anionic metal clusters are studied using the uniform jellium background model and the local density approximation, with self-interaction corrections when necessary. Shell effects are introduced using an adaptation of the nuclear Strutinsky method. Singly charged anions are stable for all sizes, but multiply charged negative ions are stable against spontaneous electron decay only above certain critical sizes. Below the border of stability, the anions are metastable against electron tunneling through a Coulombic barrier. Lifetimes for such decay processes are estimated. Fission channels may compete with the electron autodetachment and are studied for the case of doubly charged anions.     

Plasmons in fissioning metal clusters

We study the plasmon response of Na₁₈ ⁺⁺ along its two most favorable (symmetric and asymmetric) fission paths. Strong symmetry breaking and unusually large difference between the ion and electron distribution give rise to strong Landau fragmentation of the resonance spectra which has not been observed in normal configurations near the cluster ground state. This carries forth in the multiplasmon regime to a strong dissipation with large spectral noise. Furthermore, we find a low-lying resonance peak as indicator of the pre-scission stage of the electron cloud.     

Pairing effects in metal clusters

Motivated by the experimental finding of oddeven alternations in the mass spectra and ionization potentials of metal clusters, we have investigated the possibility of interpreting these results as evidence for pairing correlations among the electrons. For the present exploratory calculations, we have used a spherical BCS model which we have applied, as an example, to some Al clusters. Additional model calculations have been carried out for Na _N with 34<N<100 in order to illustrate a possible systematics.     

Theory of fragmentation of metal clusters

The theory of shell correction developed for discussing fissing of heavy nuclei is applied to symmetric fragmentation of charged metal clusters. Assuming the effective potential of an anisotropic harmonic oscillator, we calculate the shell correction. We also calculate the energy of deformed charged droplets in the two-dimensional parameter space describing the deformation of droplets such as elongation and neck formation. The symmetric fragmentation of microclusters of alkali and noble metals is discussed.     

Nonlinear optics of metal fractal clusters

Linear and nonlinear optical properties of metal fractal clusters are studied. Experimental evidence is presented proving that clusters possess unique optical nonlinearities, characterized by rapid response, broadbandness and enormously high values of nonlinear susceptibility. A 10⁶ times enhancement of the DFWM signal has been observed experimentally in silver particles aggregated into clusters. For the first time frequency-and polarization-selective photomodification of fractal silver clusters has been realized.     

Near-IR luminescence of monolayer-protected metal clusters

Visible-near-IR luminescence spectra of gold MPCs that are similar, irrespective of the number of core atoms (all <2 nm diameter) and different monolayers, are reported. The luminescence can be quantitatively invoked by introducing polar ligands into nonpolar MPC monolayers and by galvanic exchange of metal atoms on the MPC core surface with different metals. The observed emissions are believed to result from surface-localized states that depend on both the core metal of the nanoparticle and the ligands attached to the metal surface.     

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.