On the subtleties of cluster construction when defining crystalline nuclei in atomistic simulations

Molecular dynamics is routinely used to investigate crystal nucleation rates via computer simulations. According to classical nucleation theory, the size of the largest cluster should be the best approximation of the reaction coordinate. In Lennard-Jones melts, the sixth-order ten Wolde criterion [ten Wolde et al., Faraday Disc. 104, 93-110 (1996)] is often used to determine particles within solid environments, which are then grouped together based on proximity to define solid clusters. However, the resulting descriptor can sometimes poorly represent the nucleation process. Here, we investigate the effect of cluster construction methods on observed committor behavior. In the first part of the paper, we construct clusters based on (i) proximity only or (ii) proximity and the presence of an oriented "bond" between particles. In the second part of the paper, we vary the internal cutoffs used to compute the relevant order parameters. We find that, although a cluster construction method can have a large effect on the scale of a single nucleus, aggregate properties over ensembles of nuclei remain similar. In contrast, varying internal cutoffs can have a significant effect on both physical and committor properties. The results from both investigations support using a reaction coordinate of crystallinity times the size of the largest cluster rather than the size of the largest cluster alone.