From Sticky-Hard-Sphere to Lennard-Jones-Type Clusters

Abstract

A relation ${\mathcal{M}}_{\mathrm{SHS}\to \mathrm{LJ}}$ between the set of non-isomorphic 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 $V_{mn}^{\mathrm{LJ}}(r)=\frac{\epsilon }{n-m}[m{r}^{-n}-n{r}^{-m}]$ 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 non-injective and non-surjective, 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 unfavourable 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.

10 pages

References in corpus (6)

• Sticky-sphere clusters
• Structure and dynamics of model colloidal clusters with short-range attractions
• Free energy of singular sticky-sphere clusters
• Properties of Kinetic Transition Networks for Atomic Clusters and Glassy Solids
• Nucleation and structural growth of cluster crystals
• Modeling aggregation processes of Lennard-Jones particles via stochastic networks

Cited by in corpus (8)

• The Lennard Jones Potential Revisited -- Analytical Expressions for Vibrational Effects in Cubic and Hexagonal Close-Packed Lattices
• Morphometric approach to many-body correlations in hard spheres
• Brownian dynamics simulations of hard rods in external fields and with contact interactions
• The Gregory-Newton Problem for Kissing Sticky Spheres
• From canyons to valleys: Numerically continuing sticky hard sphere clusters to the landscapes of smoother potentials
• Geometric constraints in protein folding
• Distinguishing failure modes at the molecular level by examining heterogeneity in local structures and dynamics
• Instability of the Body-Centered Cubic Lattice within the Sticky Hard Sphere and Lennard-Jones Model obtained from Exact Lattice Summations