The jellium model of simple metal clusters has enjoyed remarkable empirical success, leading to many theoretical questions. In this review, we first survey the hierarchy of theoretical approximations leading to the model. We then describe the jellium model in detail, including various extensions. One important and useful approximation is the local-density approximation to exchange and correlation effects, which greatly simplifies self-consistent calculations of the electronic structure. Another valuable tool is the semiclassical approximation to the single-particle density matrix, which gives a theoretical framework to connect the properties of large clusters with the bulk and macroscopic surface properties. The physical properties discussed in this review are the ground-state binding energies, the ionization potentials, and the dipole polarizabilities. We also treat the collective electronic excitations from the point of view of the cluster response, including some useful sum rules.

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The physics of simple metal clusters: self-consistent jellium model and semiclassical approaches

A density-functional formalism comparable to the theory of Hohenberg, Kohn and Sham is developed for electronic systems subject to time-dependent external fields. The formalism leads to a set of time-dependent Kohn-Sham equations which, in addition to the external potential, contain a time-dependent Hartree term and a local time-dependent exchange-correlation potential. Rigorous properties and explicit approximations of the latter are discussed in detail. Generalizations of the basic formalism to incorporate the nuclear motion and to deal with magnetic effects are described. Within the regime of linear-response theory, the time-dependent Kohn-Sham equations lead to a formally exact representation of the frequency-dependent linear density response. Applications within the linear-response regime include the computation of photoabsorbtion cross sections, the determination of van der Waals forces and the calculation of excitation energies. The latter is based on the fact that the frequency-dependent linear density response has poles at the true excitation energies of the interacting many-body system. The time-dependent Kohn-Sham formalism then leads to a simple additive correction of the Kohn-Sham single-particle excitation energies. Beyond the linear-response regime, the time-dependent Kohn-Sham scheme is applied to atoms in strong femto-second laser pulses to describe multi-photon ionization and harmonic generation in a non-perturbative way.

Density functional theory of time-dependent phenomena

The field of cluster research can trace its origins back to the mid-nineteenth century when early studies of colloids, aerosols, and nucleation phenomena were reported. The field underwent a resurgence of interest several decades ago when well-defined clusters were observed in supersonic expansions that could be investigated using mass spectrometers. The advent of the laser provided a new dimension, enabling detailed spectroscopic observations through the probing of systems of varying size and degree of solvation. Modern interest derives from recognition that interrogating clusters provides a way of studying the energetics and dynamics of intermediate states of matter as cluster systems evolve from the gas toward the condensed state. Herein, we endeavor to highlight some of the significant advances which have been made during the past several decades that have led to a nearly explosive growth of interest in the field of cluster science. Finally, we conclude that the field will continue to expand through i...

Clusters: Structure, Energetics, and Dynamics of Intermediate States of Matter

Shells of atoms

Recently, films produced by depositing pre-formed mass-selected atomic clusters in the size range 1–10 nm have generated a great deal of attention. The ability to control the size, density and in some cases the morphology of the deposited particles allows unprecedented flexibility in the creation of new types of nanostructure. The technique enables research on the fundamental behaviour of matter at mesoscopic length scales and in addition has enormous potential in the creation of new materials whose properties can be widely varied. This review will describe the technology used to produce the particles and deposit them, and discuss the details of the landing on the surface and subsequent surface kinetics. The equilibrium structures and morphologies of the particles will be reviewed as also how the organisation of the particle assemblies is influenced by the particle–surface and inter-particle interactions. As a result of the reduced average atomic coordination, the quantum size effect and the modified screening response in nanoscale systems, the clusters display novel electronic and magnetic properties and these will be described for a range of elements including transition metals, noble and simple metals, and rare-earths. In addition to the native properties, the effect of the interaction with the substrate and other deposited particles will be explored. Finally, the work on coated particles and particles embedded in matrices will be reviewed and the potential to create new materials and devices will be discussed.

Nanoclusters deposited on surfaces

Collective excitation in closed-shell potassium cluster ions

Unimolecular dissociation channels of mass-selected doubly charged sodium clusters ${\mathrm{Na}}_{\mathit{n}}^{++}$ have been determined for cluster sizes near and above the critical size, ${\mathit{n}}_{\mathit{c}}$=27, from which doubly charged clusters are detectable in mass spectra. On a time scale of 50 \ensuremath{\mu}s with respect to ionization, doubly charged clusters of size n=${\mathit{n}}_{\mathit{c}}$ are found to fission asymmetrically. For cluster sizes above ${\mathit{n}}_{\mathit{c}}$, however, evaporation of a neutral monomer is the dominant channel for delayed dissociation. An estimation of the height of the Coulombic barrier is given for ${\mathrm{Na}}_{\mathit{n}}^{++}$ near the critical size, using the framework of statistical theory.

Asymmetric fission of Nan++ around the critical size of stability.

Morphology control of the supported islands grown from soft-landed clusters

Formation and evolution of fragmentation instabilities in fractal islands, obtained by deposition of silver clusters on graphite, are studied. The fragmentation dynamics and subsequent relaxation to the equilibrium shapes are controlled by the deposition conditions and cluster composition. Sharing common features with other materials' breakup phenomena, the fragmentation instability is governed by the length-to-width ratio of the fractal arms.

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F. Carlier

Papers

Collective excitation in closed-shell potassium cluster ions

Asymmetric fission of Nan++ around the critical size of stability.

Morphology control of the supported islands grown from soft-landed clusters

Instability driven fragmentation of nanoscale fractal islands.

Photoionization of mass-selected Kn+ ions: A test for the ionization scaling law.