A relation ${\mathcal{M}}_{\mathrm{SHS}\to \mathrm{LJ}}$ between the set of nonisomorphic sticky-hard-sphere clusters ${\mathcal{M}}_{\mathrm{SHS}}$ and the sets of local energy minima ${\mathcal{M}}_{LJ}$ of the $(m,n)$-Lennard-Jones potential $V_{mn}^{\mathrm{LJ}}\left(r\right)=\frac{\varepsilon }{n-m}[m{r}^{-n}-n{r}^{-m}]$ is established. The number of nonisomorphic stable clusters depends strongly and nontrivially on both $m$ and $n$ and increases exponentially with increasing cluster size $N$ for $N\gtrsim 10$. While the map from ${\mathcal{M}}_{\mathrm{SHS}}\to {\mathcal{M}}_{\mathrm{SHS}\to \mathrm{LJ}}$ is noninjective and nonsurjective, the number of Lennard-Jones structures missing from the map is relatively small for cluster sizes up to $N=13$, and most of the missing structures correspond to energetically unfavorable minima even for fairly low $(m,n)$. Furthermore, even the softest Lennard-Jones potential predicts that the coordination of 13 spheres around a central sphere is problematic (the Gregory-Newton problem). A more realistic extended Lennard-Jones potential chosen from coupled-cluster calculations for a rare gas dimer leads to a substantial increase in the number of nonisomorphic clusters, even though the potential curve is very similar to a (6,12)-Lennard-Jones potential.

• Received 1 February 2018

DOI:https://doi.org/10.1103/PhysRevE.97.043309