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

The femtosecond optical response of noble metal nanoparticles and its connection to the ultrafast electron dynamics are discussed in light of the results of high-sensitivity femtosecond pump−probe experiments. The physical origins of the nonlinear responses in the vicinity of the surface plasmon resonance and interband transition threshold are analyzed using extension of the theoretical models used in the bulk materials. These responses contain information on the electron interaction processes (electron−electron and electron−phonon scattering) that can thus be directly investigated in the time domain. Their size and environment dependences are discussed, and the results are compared to the ones in the bulk materials. Time-resolved techniques also permit direct study of the vibrational modes of metal nanoparticles and, in particular, the determination of their damping, which is a sensitive probe of the nature of the surrounding matrix and of the interface quality.

Ultrafast Electron Dynamics and Optical Nonlinearities in Metal Nanoparticles

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

We report a joint experimental and theoretical study of the electronic and atomic structures of small gold clusters with up to 14 atoms. Well-resolved photoelectron spectra were obtained for AuN- (N = 1−14) at several photon energies. Even−odd alternations were observed, where the even-sized clusters (except Au10-) exhibit an energy gap between the lowest binding energy peak and the rest of the spectrum, indicating that all the neutral even-sized clusters have closed shells. The Au10- spectrum reveals the existence of isomers, with the ground-state cluster exhibiting an extremely high electron binding energy. Evidence of multiple isomers was also observed in the spectra of N = 4, 8, 12, and 13. The structures of the gold cluster anions in the range N = 4−14 were investigated using first-principles simulations. A striking feature of the anionic clusters in this range is the occurrence of planar ground-state structures, which were predicted in earlier theoretical studies (Hakkinen, H.; et al. Phys. Rev. Let...

On the Electronic and Atomic Structures of Small AuN- (N = 4−14) Clusters: A Photoelectron Spectroscopy and Density-Functional Study

Empirical relations are established between the cohesive energy, surface tension, and melting temperature of different bulk solids. An expression for the size-dependent melting for low-dimensional systems is derived on the basis of an analogy with the liquid-drop model and these empirical relations, and compared with other theoretical models as well as the available experimental data in the literature. The model is then extended to understand (i) the effect of substrate temperature on the size of the deposited cluster and (ii) the superheating of nanoparticles embedded in a matrix. It is argued that the exponential increase in particle size with the increase in deposition temperature can be understood by using the expression for the size-dependent melting of nanoparticles. Superheating is possible when nanoparticles with a lower surface energy are embedded in a matrix with a material of higher surface energy in which case the melting temperature depends on the amount of epitaxy between the nanoparticles and the embedding matrix. The predictions of the model show good agreement with the experimental results. A scaling for the size-dependent melting point suppression is also proposed.

Liquid-drop model for the size-dependent melting of low-dimensional systems

We investigate the unimolecular dissociation dynamics of energy‐rich sodium cluster ions, Na+n (5≤n≤40) by measuring the time evolution of their sequential monomer or dimer evaporative cooling The experimental technique, tandem time‐of‐flight mass spectroscopy, measures the relative rate of competing dissociation channels from metastable ion clusters selected during an initial sampling time interval immediately following the creation of the ion cluster ensemble Pulsed laser UV photoionization converts the distribution of neutral clusters emerging from a free‐jet expansion to the distribution of ion clusters from which the initial selection takes place For the smaller clusters, 3≤n≤14, we compare the measured dissociation rates with those calculated from a modified version of the RRK theory of unimolecular dissociation In applying the theory we use monomer and dimer binding energies determined from theoretical calculation For larger clusters, 15≤n≤40, the binding energies are not known, and we invert 

Dynamics of unimolecular dissociation of sodium cluster ions

Collective excitation in closed-shell potassium cluster ions

The unimolecular dissociation of energy rich lithium cluster ions shows that Li+n dissociate by sequential atom or dimer loss. The binding energies of Li+n (n=4–42) generated in an evaporative ensemble are determined from unimolecular decay, within a well defined time window, and energy constraint. They present a sawtooth behavior vs cluster size less pronounced that it should be from a simple metal model. Odd–even alternation is superimposed on the sawtooth behavior, with odd sized cluster ions being more stable. Cohesive energies per atom of Li+n are deduced from these dissociation energies up to n=40 and from extended photo‐induced measurements up to n=95. Cohesive energies per atom of neutral clusters Lin are derived by combining these ionic cohesive energies with the literature ionization potentials. The linearity of the neutral cluster cohesive energy vs the cluster surface to volume ratio permits a volume and a surface energy to be deduced. These values are compared to the bulk values.

Dissociation pathways and binding energies of lithium clusters from evaporation experiments

Multistep photon absorption has been used to measure the collective excitation of free lithium clusters having up to 1500 atoms. The blueshift of the Mie resonance energy, as cluster size increases, probes the surface erects. Its absolute value is consistent with the dielectric constants of the bulk down to a 100 atom cluster. The comparison with calculations in random-phase approximation in the local approximation demonstrates that the jellium model is no longer valid for lithium clusters

Optical response of large lithium clusters: Evolution toward the bulk.

The absorption cross-section profile of large charged clusters is measured by a new procedure based on multistep photoabsorption experiments. Comparison is done with the predictions of classical and quantum treatments. In light of these results, size trends in the optical properties of alkali clusters are discussed.

J. Leygnier

Papers

Dynamics of unimolecular dissociation of sodium cluster ions

Collective excitation in closed-shell potassium cluster ions

Dissociation pathways and binding energies of lithium clusters from evaporation experiments

Optical response of large lithium clusters: Evolution toward the bulk.

Collective resonance in large free potassium cluster ions.