A computational study of 13-atom Ar–Kr cluster heat capacities

Abstract

Heat capacity curves as functions of temperature were calculated using Monte Carlo methods for the series of Ar 13−n Kr n clusters (0 ≤ n ≤ 13). The clusters were modeled classically using pairwise additive Lennard-Jones potentials.J-walking (or jump-walking) was used to overcome convergence difficulties due to quasiergodicity present in the solid-liquid transition regions, as well as in the very low temperature regions where heat capacity anomalies arising from permutational isomers were observed. Substantial discrepancies between the J-walking results and the results obtained using standard Metropolis Monte Carlo methods were found. Results obtained using the atom-exchange method, another Monte Carlo variant designed for multi-component systems, were mostly similar to the J-walker results. Quench studies were also done to investigate the clusters' potential energy surfaces; in each case, the lowest energy isomer had an icosahedral-like symmetry typical of homogeneous thirteen-atom rare gas clusters, with an Ar atom being the central atom.

Magic number behavior for heat capacities of medium-sized classical Lennard-Jones clusters

“…Ar 52 and Ar 53 have some isomers having closely spaced potential energies only slightly above the lowest-energy isomer, and then very few isomers until ∆V min ≈ 2.5. This type of isomer energy distribution is similar to the distributions seen for binary Ar-Kr clusters, where many mixed isomer configurations had energies similar to the lowest-energy isomer, 24 and the quench results are similar too, with the low-lying isomer quench curves showing plateaus throughout much of the solid-like temperature region. However, neither Ar 52 nor Ar 53 exhibited the small, very low temperature heat capacity peaks that were evident in the binary cluster curves.…”

“…Peaks in heat capacity curves have typically been associated with cluster phase changes, particularly solid-liquid changes. 20,25,32,33,35,39 However, peaks can arise from other circumstances as well, such as mixing anomalies 23,24 and premelting effects, which can make the assignment of the cluster melting temperatures difficult. Calvo and Spiegelmann defined the melting temperatures of the sodium clusters they studied whose heat capacity curves had multiple peaks, as the temperature associated with the highest peak.…”

“…This poor convergence is a consequence of quasiergodicity, or the incomplete sampling of configuration space. 18 Various methods have been developed in recent years to reduce the systematic errors resulting from quasiergodicity, including histogram methods, 20 jumpwalking methods (J-walking), [21][22][23][24][25][26][27][28] smart walking methods (S-walking), 29 and parallel tempering methods. [30][31][32] Many of these methods are based on the coupling of configurations obtained from ergodic higher-temperature simulations to the quasiergodic lower-temperature simulations.…”

Composition-induced structural transitions in mixed rare-gas clusters

“…17 The multiple-funnel structure of these energy landscapes makes it especially hard to locate the most stable structures (global minima) or to simulate the finite-temperature behavior of these clusters in an ergodic way. The effects of mixing different rare-gas atoms on cluster structure and thermodynamics have been studied for the specific size 13 by Frantz on the examples of Ar-Kr mixtures 18 as well as Ne-Ar mixtures. 19 Fanourgakis et al have also investigated these latter compounds.…”

Taming the rugged landscape: Techniques for the production, reordering, and stabilization of selected cluster inherent structures

“…Utilizing the above-outlined methods, researchers have produced a relatively coherent picture of the relationship between the nature of underlying potential energy surface ͑PES͒ and the physical properties of the associated systems. For example, from the studies by Berry et al, [22][23][24][25] the single component studies of Wales et al, [13][14][15] the mixed LennardJones ͑LJ͒ cluster studies of Jordan et al 26 as well as the research of others, [27][28][29][30] we have begun to understand the nature of systems for which the lowest inherent structures can or cannot be readily located.…”