The structural properties of free nanoclusters are reviewed. Special attention is paid to the interplay of energetic, thermodynamic, and kinetic factors in the explanation of cluster structures that are actually observed in experiments. The review starts with a brief summary of the experimental methods for the production of free nanoclusters and then considers theoretical and simulation issues, always discussed in close connection with the experimental results. The energetic properties are treated first, along with methods for modeling elementary constituent interactions and for global optimization on the cluster potential-energy surface. After that, a section on cluster thermodynamics follows. The discussion includes the analysis of solid-solid structural transitions and of melting, with its size dependence. The last section is devoted to the growth kinetics of free nanoclusters and treats the growth of isolated clusters and their coalescence. Several specific systems are analyzed.

We review in this article the current theoretical understanding of collective and single particle diffusion on surfaces and how it relates to the existing experimental data. We begin with a brief survey of the experimental techniques that have been employed for the measurement of the surface diffusion coefficients. This is followed by a section on the basic concepts involved in this field. In particular, we wish to clarify the relation between jump or exchange motion on microscopic length scales, and the diffusion coefficients which can be defined properly only in the long length and time scales. The central role in this is played by the memory effects. We also discuss the concept of diffusion under nonequilibrium conditions. In the third section, a variety of different theoretical approaches that have been employed in studying surface diffusion such as first principles calculations, transition state theory, the Langevin equation, Monte Carlo and molecular dynamics simulations, and path integral formalism are presented. These first three sections form an introduction to the field of surface diffusion. Section 4 contains subsections that discuss surface diffusion for various systems which have been investigated both experimentally and theoretically. The focus here is not so much on specific systems but rather on important issues concerning diffusion measurements or calculations. Examples include the influence of steps, diffusion in systems undergoing phase transitions, and the role of correlation and memory effects. Obviously, the choice of topics here reflects the interest and expertise of the authors and is by no means exhaustive. Nevertheless, these topics form a collection of issues that are under active investigation, with many important open questions remaining.

The energetics of nanoclusters is investigated for five different metals (Ag, Cu, Au, Pd, and Pt) by means of quenched molecular dynamics simulations. Results are obtained for two different semiempirical potentials. Three different structural motifs are considered: icosahedra (Ih), decahedra (Dh), and truncated octahedra (TO). The crossover sizes among structural motifs are directly calculated, considering cluster up to sizes $\text{N≃40\hspace{0.05em}000.}$ For all the systems considered, it is found that icosahedra are favored at small sizes, decahedra at intermediate sizes, and truncated octahedra at large sizes. However, the crossover sizes depend strongly on the metal: in Cu, the icosahedral interval is rather large, and it is followed by a very wide decahedral window; on the contrary, in Au, the icosahedral interval is practically absent, and the decahedral window is narrow. The other metals display intermediate behaviors, Ag being close to Cu, and Pd and Pt being close to Au. A simple criterion, which is based on the ratio between the bulk modulus and the cohesive energy per atom, is developed to account for the differences among the metals.

A new family of magic cluster structures is found by genetic global optimization, whose results are confirmed by density functional calculations. These clusters are Ag-Ni and Ag-Cu nanoparticles with an inner Ni or Cu core and an Ag external shell, as experimentally observed for Ag-Ni, and present a polyicosahedral character. The interplay of the core-shell chemical ordering with the polyicosahedral structural arrangement gives high-symmetry clusters of remarkable structural, thermodynamic, and electronic stability, which can have high melting points (they melt higher than pure clusters of the same size), large energy gaps, and (in the case of Ag-Ni) nonzero magnetic moments.

We show by molecular dynamics simulations on three systems ($B/A=\mathrm{P}\mathrm{d}/\mathrm{A}\mathrm{g}$, $\mathrm{C}\mathrm{u}/\mathrm{A}\mathrm{g}$, and $\mathrm{N}\mathrm{i}/\mathrm{A}\mathrm{g}$) that three-shell metallic nanoparticles made by a core of a metal $A$, an intermediate shell of metal $B$ and an external shell of metal $A$ ($A\mathrm{\text{−}}B\mathrm{\text{−}}A$ nanoparticles) can be grown by deposition of $B$ atoms onto an $A$ core. The growth of the intermediate $B$ shell is triggered by the fact that the most favorable positions for isolated $B$ impurities inside $A$ clusters are located just one layer below the cluster surface.