Solid−Solid Structural Transformations in Lennard-Jones Clusters:  Accurate Simulations versus the Harmonic Superposition Approximation

Abstract

We consider systems undergoing very-low-temperature solid-solid transitions associated with minima of similar energy but different symmetry, and separated by a high potential barrier. In such cases the well-known "broken-ergodicity" problem is often difficult to overcome, even using the most advanced Monte Carlo (MC) techniques, including the replica exchange method (REM). The methodology that we develop in this paper is suitable for the above specified cases and is numerically accurate and efficient. It is based on a new MC move implemented within the REM framework, in which trial points are generated analytically using an auxiliary harmonic superposition system that mimics well the true system at low temperatures. Due to the new move, the low-temperature random walks are able to frequently switch the relevant potential energy funnels leading to an efficient sampling. Numerically accurate results are obtained for a number of Lennard-Jones clusters, including those that have so far been treated only by the harmonic superposition approximation (HSA). The latter is believed to provide good estimates for low-temperature equilibrium properties but is manifestly uncontrollable and is difficult to validate. The present results provide a good test for the HSA and demonstrate its reliability, particularly for estimation of the solid-solid transition temperatures in most cases considered.

Efficient Sampling of Atomic Configurational Spaces

“…For LJ 17 the efficiency gain of nested sampling is a factor of 10 over parallel tempering, while for the larger LJ 25 cluster, as the entropy jump is larger, the efficiency gain is a factor of 100. Our heat capacity curves for the largest clusters (LJ 31 , LJ 36 and LJ 38 ) are consistent with what is reported in the literature [38,42], using computational resources of similar order of magnitude. Note however, that advance knowledge of the global minimum is not required and was not used in the nested sampling simulations.…”

Perspective: Insight into reaction coordinates and dynamics from the potential energy landscape

“…In particular, it provides a framework to circumvent many difficulties associated with sampling problems arising from high potential energy barriers, which often lead to trapping, broken ergodicity, and rare event dynamics. The principal distinction between these methods and the huge variety of alternative approaches to enhanced sampling [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16] and rare events [17][18][19][20] is the use of stationary points of the potential energy to provide an initial coarse-graining. Limits can be defined that permit either high accuracy or systematic approximations to be applied.…”

Metal clusters with hidden ground states: Melting and structural transitions in Al115+, Al116+, and Al117+

“…42 Solid-solid structural transitions are frequently found to precede melting for Lennard-Jones ͑LJ͒ clusters, resulting in two well-resolved peaks in heat capacity. [44][45][46][47][48][49][50] For example, using exchange Monte Carlo simulations Mandelshtam et al found that LJ n clusters with n = 74-78 have two peaks in their heat capacities. 46 The peak at higher temperatures is attributed to a melting transition, and the lower temperature peak is assigned to a solid-to-solid structural transition from the decahedral ground state to an icosahedral geometry.…”