From canyons to valleys: Numerically continuing sticky hard sphere clusters to the landscapes of smoother potentials

TL;DR

This paper investigates how energy landscapes of small particle clusters evolve as the interaction range increases, revealing cluster merging behaviors and the influence of potential type on cluster configurations.

Contribution

It introduces a numerical continuation method to track local minima of particle clusters across different interaction ranges and potential types, highlighting cluster merging mechanisms.

Findings

Clusters merge as interaction range increases.

Short to medium ranges yield nearly identical clusters across potentials.

Longer ranges cause significant cluster variation and rearrangements.

Abstract

We study the energy landscapes of particles with short-range attractive interactions as the range of the interactions increases. Starting with the set of local minima for $6\leq N\leq12$ hard spheres that are "sticky", i.e. they interact only when their surfaces are exactly in contact, we use numerical continuation to evolve the local minima (clusters) as the range of the potential increases, using both the Lennard-Jones and Morse families of interaction potentials. As the range increases, clusters merge, until at long ranges only one or two clusters are left. We compare clusters obtained by continuation with different potentials and find that for short and medium ranges, up to about 30\% of particle diameter, the continued clusters are nearly identical, both within and across families of potentials. For longer ranges the clusters vary significantly, with more variation between families of potentials than within a family. We analyze the mechanisms behind the merge events, and find that most rearrangements occur when a pair of non-bonded particles comes within the range of the potential. An exception occurs for nonharmonic clusters, those that have a zero eigenvalue in their Hessian, which undergo a more global rearrangement.