Parallel tempering Monte Carlo combined with clustering Euclidean metric analysis to study the thermodynamic stability of Lennard-Jones nanoclusters.

A basic requirement for an atom-level understanding of nanoclusters is the knowledge of their atomic structure. This understanding is incomplete if it does not take into account temperature effects, which play a crucial role in phase transitions and changes in the overall stability of the particles. Finite size particles present intricate potential energy surfaces, and rigorous descriptions of temperature effects are best achieved by exploiting extended ensemble algorithms, such as the Parallel Tempering Monte Carlo (PTMC). In this study, we employed the PTMC algorithm, implemented from scratch, to sample configurations of LJ (n=38, 55, 98, 147) particles at a wide range of temperatures. The heat capacities and phase transitions obtained with our PTMC implementation are consistent with all the expected features for the LJ nanoclusters, e.g., solid to solid and solid to liquid. To identify the known phase transitions and assess the prevalence of various structural motifs available at different temperatures, we propose a combination of a Leader-like clustering algorithm based on a Euclidean metric with the PTMC sampling. This combined approach is further compared with the more computationally demanding bond order analysis, typically employed for this kind of problem. We show that the clustering technique yields the same results in most cases, with the advantage that it requires no previous knowledge of the parameters defining each geometry. Being simple to implement, we believe that this straightforward clustering approach is a valuable data analysis tool that can provide insights into the physics of finite size particles with few to thousand atoms at a relatively low cost.