Magic numbers for classical Lennard-Jones cluster heat capacities

Abstract

Heat capacity curves as functions of temperature for classical atomic clusters bound by pairwise Lennard-Jones potentials were calculated for aggregate sizes 4≤N≤24 using Monte Carlo methods. J walking (or jump walking) was used to overcome convergence difficulties due to quasiergodicity in the solid-liquid transition region. The heat capacity curves were found to differ markedly and nonmonotonically as functions of cluster size. Curves for N=4, 5, and 8 consisted of a smooth, featureless, monotonic increase throughout the transition region, while curves for N=7 and 15–17 showed a distinct shoulder in this region; the remaining clusters had distinguishable transition heat capacity peaks. The size and location of these peaks exhibited ‘‘magic number’’ behavior, with the most pronounced peaks occurring for magic number sizes of N=13, 19, and 23. This is consistent with the magic numbers found for many other cluster properties, but there are interesting differences for some of the other cluster sizes. Further insight into the transition region was obtained by comparing rms bond length fluctuation behavior with the heat capacity trends. A comparison of the heat capacities with other cluster properties in the solid-liquid transition region that have been reported in the literature indicates partial support for the view that, for some clusters, the solid-liquid transition region is a coexistence region demarcated by relatively sharp, but separate, melting and freezing temperatures; some discrepancies, however, remain unresolved.