The heat capacity and isomer distributions of the 38-atom Lennard-Jones cluster have been calculated in the canonical ensemble using parallel tempering Monte Carlo methods. A distinct region of temperature is identified that corresponds to equilibrium between the global minimum structure and the icosahedral basin of structures. This region of temperatures occurs below the melting peak of the heat capacity and is accompanied by a peak in the derivative of the heat capacity with temperature. Parallel tempering is shown to introduce correlations between results at different temperatures. A discussion is given that compares parallel tempering with other related approaches that ensure ergodic simulations.

Clusters of polycyclic aromatic hydrocarbon (PAH) molecules are modeled using explicit all-atom potentials using a rigid-body approximation. The considered range of PAHs goes from pyrene (C10H8) to circumcoronene (C54H18) and clusters containing between 2 and 32 molecules are investigated. In addition to the usual repulsion-dispersion interactions, electrostatic point-charge interactions are incorporated, as obtained from density functional theory calculations. The general electrostatic distribution in neutral or singly charged PAHs is reproduced well using a fluctuating-charges analysis, which provides an adequate description of the multipolar distribution. Global optimization is performed using a variety of methods, including basin-hopping and parallel tempering Monte Carlo. We find evidence that stacking the PAH molecules generally yields the most stable motif. A structural transition between one-dimensional stacks and three-dimensional shapes built from multiple stacks is observed at larger sizes, and the threshold for this transition increases with the size of the monomer. Larger aggregates seem to evolve toward the packing observed for benzene in bulk. Difficulties met in optimizing these clusters are analyzed in terms of the strong anisotropy of the molecules. We also discuss segregation in heterogeneous clusters and vibrational properties in the context of astrophysical observations.

We examine in detail the causes of the structural transitions that occur for those small LennardJones clusters that have a non-icosahedral global minima. Based on the principles learned from these examples we develop a method to construct structural phase diagrams that show in a coarse-grained manner how the equilibrium structure of large clusters depends on both size and temperature. The method can be augmented to account for anharmonicity and quantum effects. Our results illustrate that the vibrational entropy can play a crucial role in determining the equilibrium structure of a cluster.

We study the 38-atom Lennard-Jones cluster with parallel tempering Monte Carlo methods in the microcanonical and molecular dynamics ensembles. A new Monte Carlo algorithm is presented that samples rigorously the molecular dynamics ensemble for a system at constant total energy, linear and angular momenta. By combining the parallel tempering technique with molecular dynamics methods, we develop a hybrid method to overcome quasiergodicity and to extract both equilibrium and dynamical properties from Monte Carlo and molecular dynamics simulations. Several thermodynamic, structural, and dynamical properties are investigated for LJ 38 , including the caloric curve, the diffusion constant and the largest Lyapunov exponent. The importance of insuring ergodicity in molecular dynamics simulations is illustrated by comparing the results of ergodic simulations with earlier molecular dynamics simulations.

We show that the vibrational entropy can play a crucial role in determining the equilibrium structure of clusters by constructing structural phase diagrams showing how the structure depends upon both size and temperature. These phase diagrams are obtained for example rare gas and metal clusters.PACS numbers: 61.46.+w,36.40.Mr,36.40.Ei Much of the interest in clusters or nanoparticles derives from the insights they can provide into how properties emerge and evolve on going between the atomic and molecular and bulk limits. Cluster structure provides a particular interesting example of this size evolution. At large enough sizes the clusters must display the bulk crystalline structure, but this limit may sometimes only be achieved at very large sizes (e.g. at least 20 000 atoms for sodium clusters [1]) and before that limit is reached unusual structural forms are often observed. For example, many clusters bound by van der Waals or metallic forces exhibit structures with five-fold axes of symmetry, a possibility that is forbidden in bulk crystalline materials. For these clusters the dominant structural motif typically changes from icosahedral ( Fig. 1(b)) to decahedral ( Fig. 1(c)) to face-centred-cubic (fcc) ( Fig. 1(a)) as the size increases.For many materials these structural changes occur at sizes that are too large for global optimization to be feasible. Therefore, the typical theoretical approach to systematically investigating the size evolution of cluster structure is to compare the energies of stable sequences of structures, such as the forms shown in Fig. 1. 'Crossover sizes' are then identified where the sequence with lowest energy changes. At this crossover the most common equilibrium structure is expected to change. This technique has been applied to rare gas [2,3,4], metal [5,6,7,8] and molecular clusters [9].The above approach is certainly valid at zero temperature, since the equilibrium structure then corresponds to the one with lowest energy. At other temperatures, however, the structure with lowest free energy needs to be found. However, perhaps through an expectation that entropic effects are unlikely to be important or are too complicated to take into account, size is usually the only variable that is considered both experimentally [10,11,12] and theoretically [2,3,4,5,6,7,8].In this paper we consider the role that entropy plays in the size evolution of cluster structure, and show that temperature can be a key variable in determining the equi- [14]. These clusters have the optimal shape for the three main types of regular packing seen in clusters: face-centred cubic, icosahedral and decahedral, respectively. The latter two structural types cannot be extended to bulk because of the five-fold axes of symmetry.librium structure of a cluster. A clue to this result can be garnered from the growing number of examples of solidsolid transitions in clusters where the structure changes from fcc or decahedral to icosahedral as the temperature increases [15,16,17,18,19]. The most well-investigated example...

Aims. The competition between the formation and destruction of coronene clusters under interstellar conditions is investigated theoretically. Methods. The unimolecular nucleation of neutral clusters is simulated with an atomic model combining an explicit classical force field and a quantum tight-binding approach. Evaporation rates are calculated in the framework of the phase space theory and are inserted in an infrared emission model and compared with the growth rate constants. Results. It is found that, in interstellar conditions, most collisions lead to cluster growth. The time evolution of small clusters (containing up to 312 carbon atoms) was specifically investigated under the physical conditions of the northern photodissociation region of NGC 7023. These clusters are found to be thermally photoevaporated much faster than they are reformed, thus providing an interpretation for the lowest limit of the interstellar cluster size distribution inferred from observations. The effects of ionizing the clusters and density heterogeneities are also considered. Based on our results, the possibility that PAH clusters could be formed in PDRs is critically discussed.

We investigate the thermodynamic behavior of quantum many-body systems using several methods based on classical calculations. These approaches are compared for the melting of Lennard-Jones ͑LJ͒ clusters, where path-integral Monte Carlo ͑PIMC͒ results are also available. First, we examine two quasiclassical approaches where the classical potential is replaced by effective potentials accounting for quantum corrections of low order in ប. Of the Wigner-Kirkwood and Feynman-Hibbs effective potentials, only the latter is found to be in quantitative agreement with quantum simulations. However, both potentials fail to describe even qualitatively the low-temperature regime, where quantum effects are strong. Our second approach is based on the harmonic superposition approximation, but with explicit quantum oscillators. In its basic form, this approach is in good qualitative agreement with PIMC results, and becomes more accurate at low temperatures. By including anharmonic corrections in the form of temperature-dependent frequency shifts, the agreement between the quantum superposition and the PIMC results becomes quantitative for the caloric curve of neon clusters. The superposition method is then applied to larger clusters to study the influence of quantum delocalization on the melting and premelting of LJ 19 , LJ 31 , LJ 38 , and LJ 55. The quantum character strongly affects the thermodynamics via changes in the ground state structure due to increasing zero-point energies. Finally, we focus on the lowest temperature range, and we estimate the Debye temperatures of argon clusters and their size variation. A strong sensitivity to the cluster structure is found, especially when many surface atoms reorganize as in the anti-Mackay/Mackay transition. In the large size regime, the Debye temperature smoothly rises to its bulk limit, but still depends slightly on the growth sequence considered.

The thermodynamics of sodium clusters is investigated by means of a classical empirical potential and a simple quantal tight-binding model. Neutral and singly charged clusters of sizes ranging from 8 to 147 atoms are considered. A very particular attention is paid to the optimization and sampling problems. We determine the lowest-energy structures (global minima) with the “basin-hopping” technique, and the finite-temperature simulations are improved by using the “q-jumping” method and put together with the multiple histogram method. The clusters geometries may be very different on the model used, but also on the ionic charge, up to the size of about 40 atoms. The thermodynamical analysis is performed near the solid–liquid transition by calculating the complete calorific curves (heat capacities) as well as some microscopic parameters to probe the dynamics on the energy landscapes, including the spectra of isomers found by periodic quenching, isomerization indexes and the Lindemann parameter δ. Up to the largest sizes, we find that the heat capacity generally displays several features within the two models, although structural differences in the lowest-energy isomers usually induce different calorific curves. These premelting phenomena are characteristic of isomerizations taking place in a limited part of the configuration space. The thermodynamics appears to be directly related to the lowest-energy structure, and melting by steps is favored by the presence of defects on its surface. We estimate the melting temperatures Tmelt(n) and latent heats of melting L(n), and we observe two very different behaviors of their variations with the size n. Below about 75 atoms, both Tmelt and L exhibit strong non-monotonic variations typical of geometric size effects. This “microscopic” behavior is caused by the dominating premelting effects, and is replaced by a more “macroscopic” behavior for sizes larger than about 93 atoms. The premelting phenomena become there less important, and the melting process is much like the bulk solid–liquid phase transition rounded by size effects. The continuous variations displayed by the melting temperature are the only remains of cluster size effects. The models used are discussed and criticized on the basis of the similarities and discrepancies between their predictions and the experimental data.