Andrés Aguado

Melting and Freezing of Metal Clusters

Recent developments allow heat capacities to be measured for size-selected clusters isolated in the gas phase. For clusters with tens to hundreds of atoms, the heat capacities determined as a function of temperature usually have a single peak attributed to a melting transition. The melting temperatures and latent heats show large size-dependent fluctuations. In some cases, the melting temperatures change by hundreds of degrees with the addition of a single atom. Theory has played a critical role in understanding the origin of the size-dependent fluctuations, and in understanding the properties of the liquid-like and solid-like states. In some cases, the heat capacities have extra features (an additional peak or a dip) that reveal a more complex behavior than simple melting. In this article we provide a description of the methods used to measure the heat capacities and provide an overview of the experimental and theoretical results obtained for sodium and aluminum clusters.

Structures and stabilities of Aln+, Aln, and Aln− (n=13–34) clusters

Putative global minima of neutral (Al(n)) and singly charged (Al(n) (+) and Al(n) (-)) aluminum clusters with n=13-34 have been located from first-principles density functional theory structural optimizations. The calculations include spin polarization and employ the generalized gradient approximation of Perdew, Burke, and Ernzerhof to describe exchange-correlation electronic effects. Our results show that icosahedral growth dominates the structures of aluminum clusters for n=13-22. For n=23-34, there is a strong competition between decahedral structures, relaxed fragments of a fcc crystalline lattice (some of them including stacking faults), and hexagonal prismatic structures. For such small cluster sizes, there is no evidence yet for a clear establishment of the fcc atomic packing prevalent in bulk aluminum. The global minimum structure for a given number of atoms depends significantly on the cluster charge for most cluster sizes. An explicit comparison is made with previous theoretical results in the range n=13-30: for n=19, 22, 24, 25, 26, 29, 30 we locate a lower energy structure than previously reported. Sizes n=32, 33 are studied here for the first time by an ab initio technique.

Structural and Electronic Properties of Small Neutral (MgO) n Clusters

Ab initio perturbed ion calculations are reported for neutral stoichiometric (MgO) n (n<13) clusters. A great number of isomer structures are identified and studied. For the isomers of (MgO)n (n<7) clusters, a full geometrical relaxation is considered. Correlation corrections are included for all cluster sizes using the Coulomb-Hartree-Fock model proposed by Clementi @IBM J. Res. Dev. 9 ,2 ~1965!#. The results obtained compare favorably with the experimental data and other previous theoretical studies. The inclusion of correlation is crucial in order to achieve a good description of these systems. We find a number of important isomers that allow us to interpret the experimental magic numbers without the assumption of structures based on (MgO)3 subunits. Finally, as an electronic property, the variations in the cluster ionization potential with the cluster size are studied and related to the structural isomer properties. @S0163-1829~97!00236-1#

Orbital-free molecular dynamics simulations of melting in Na8 and Na20: Melting in steps

The melting-like transitions of Na8 and Na20 are investigated by ab initio constant energy molecular dynamics simulations using a variant of the Car–Parrinello method which employs an explicit electronic kinetic energy functional of the density, thus avoiding the use of one-particle orbitals. Several melting indicators are evaluated in order to determine the nature of the various transitions, and are compared with other simulations. Both Na8 and Na20 melt over a wide temperature range. For Na8, a transition is observed to begin at ∼110 K, between a rigid phase and a phase involving isomerizations among the different permutational isomers of the ground state structure. The “liquid” phase is completely established at ∼220 K. For Na20, two transitions are observed: the first, at ∼110 K, is associated with isomerization transitions among those permutational isomers of the ground state structure which are obtained by interchanging the positions of the surface-like atoms; the second, at ∼160 K, involves a struc...

Structure and bonding in small neutral alkali halide clusters

restricted structural relaxation criterion. A trend of competition between rocksalt and hexagonal ringlike isomers is found and discussed in terms of the relative ionic sizes. The main conclusion is that an approximate value of r C /r A50.5 ~where r C and r A are the cationic and anionic radii! separates the hexagonal from the rocksalt structures. The classical electrostatic part of the total energy at the equilibrium geometry is enough to explain these trends. The magic numbers in the size range studied are n54, 6, and 9, and these are universal since they occur for all alkali halides and do not depend on the specific ground-state geometry. Instead those numbers allow for the formation of compact clusters. Full geometrical relaxations are considered for (LiF) n (n53 ‐ 7) and (AX)3 clusters, and the effect of Coulomb correlation is studied in a few selected cases. These two effects preserve the general conclusions achieved thus far. @S0163-1829~97!01848-1#

Photoelectron spectroscopy of cold aluminum cluster anions: Comparison with density functional theory results

Photoelectron spectra of cold aluminum cluster anions Al(n)(-) have been measured in the size range n=13-75 and are compared to the results of density functional theory calculations. Good agreement between the measured spectra and the calculated density of states is obtained for most sizes, which gives strong evidence that the correct structures have been found. In particular the results confirm the occurrence of rather different structural motifs in this size range, from fcc-like stacks over fragments of decahedrons to disordered structures. An analysis of the density of states of representatives of the different structural motifs shows that the electronic structure is strongly influenced by the cluster geometry, and that a clear jelliumlike electron shell structure is present only in some exceptional cases.

Structure determination in 55-atom Li–Na and Na–K nanoalloys

The structure of 55-atom Li-Na and Na-K nanoalloys is determined through combined empirical potential (EP) and density functional theory (DFT) calculations. The potential energy surface generated by the EP model is extensively sampled by using the basin hopping technique, and a wide diversity of structural motifs is reoptimized at the DFT level. A composition comparison technique is applied at the DFT level in order to make a final refinement of the global minimum structures. For dilute concentrations of one of the alkali atoms, the structure of the pure metal cluster, namely, a perfect Mackay icosahedron, remains stable, with the minority component atoms entering the host cluster as substitutional impurities. At intermediate concentrations, the nanoalloys adopt instead a core-shell polyicosahedral (p-Ih) packing, where the element with smaller atomic size and larger cohesive energy segregates to the cluster core. The p-Ih structures show a marked prolate deformation, in agreement with the predictions of jelliumlike models. The electronic preference for a prolate cluster shape, which is frustrated in the 55-atom pure clusters due to the icosahedral geometrical shell closing, is therefore realized only in the 55-atom nanoalloys. An analysis of the electronic densities of states suggests that photoelectron spectroscopy would be a sufficiently sensitive technique to assess the structures of nanoalloys with fixed size and varying compositions.

Molecular dynamics simulations of the liquid–vapor interface of a molten salt. I. Influence of the interaction potential

Molecular dynamics simulations are used to calculate the surface tension γ and study the structural properties of the liquid–vapor interface of the simple molten salt KI. The focus of the present paper is the effect on the calculated surface tension of different terms in the interionic potential and of the way that long-ranged interactions are treated. Specifically, we analyze the dependence of γ on: (a) boundary conditions employed in the Ewald summations of Coulomb interactions; (b) truncation of dispersion interactions; (c) inclusion of polarization effects. Our results show that (a) the use of vacuum boundary conditions in the direction perpendicular to the interface helps to maintain the mechanical equilibrium of the interface; (b) an Ewald summation of dispersion interactions is necessary to avoid substantial truncation effects; (c) polarization tends to decrease γ by significant amounts, and improves the agreement with experiment. In all cases, a reduction of γ comes with a corresponding increase o...

First-principles determination of the structure of NaN and NaN− clusters with up to 80 atoms

We have performed an extensive computational search for the global minimum (GM) structures of both neutral and anionic sodium clusters with up to 80 atoms. The theoretical framework combines basin hopping unbiased optimizations based on a Gupta empirical potential (EP) and subsequent reoptimization of many candidate structures at the density functional theory level. An important technical point is that the candidates are selected based on cluster shape descriptors rather than the relative stabilities of the EP model. An explicit comparison of the electronic density of states of cluster anions to experimental photoemission spectra suggests that the correct GM structures have been identified for all but two sizes (N = 47 and 70). This comparison validates the accuracy of the proposed methodology. Furthermore, our GM structures either match or improve over the results of previous works for all sizes. Sodium clusters are seen to accommodate strain very efficiently because: (a) many structures are based on polyicosahedral packing; (b) others are based on Kasper polyhedra and show polytetrahedral order; (c) finally, some (N + 1)-atom structures are obtained by incorporating one adatom into the outermost atomic shell of a compact N-atom cluster, at the cost of increasing the bond strain. GM structures of neutrals and anions differ for most sizes. Cluster stabilities are analyzed and shown to be dominated by electron shell closing effects for the smaller clusters and by geometrical packing effects for the larger clusters. The critical size separating both regimes is around 55 atoms. Some implications for the melting behavior of sodium clusters are discussed.

Activation of Dinitrogen by Solid and Liquid Aluminum Nanoclusters: A Combined Experimental and Theoretical Study

Cross sections for chemisorption of N2 onto Al44(+/-) cluster ions have been measured as a function of relative kinetic energy and the temperature of the metal cluster. There is a kinetic energy threshold for chemisorption, indicating that it is an activated process. The threshold energies are around 3.5 eV when the clusters are in their solid phase and drop to around 2.5 eV when the clusters melt, indicating that the liquid clusters are much more reactive than the solid. Below the melting temperature the threshold for Al44(-) is smaller than for Al44(+), but for the liquid clusters the anion and cation have similar thresholds. At high cluster temperatures and high collision energies the Al44N2(+/-) chemisorption product dissociates through several channels, including loss of Al, N2, and Al3N. Density functional calculations are employed to understand the thermodynamics and the dynamics of the reaction. The theoretical results suggest that the lowest energy pathway for activation of dinitrogen is not dynamically accessible under the experimental conditions, so that an explicit account of dynamical effects, via molecular dynamics simulations, is necessary in order to interpret the experimental measurements. The calculations reproduce all of the main features of the experimental results, including the kinetic energy thresholds of the anion and cation and the dissociation energies of the liquid Al44N2(+/-) product. The strong increase in reactivity on melting appears to be due to the volume change of melting and to atomic disorder.