Spikes to Hills: A Continuation of Sticky Hard Sphere Clusters to Long Range Clusters

Energy landscapes for particles with short range interactions are notoriously difficult to explore computationally. To study the sensitivity of these landscapes to parameters of the interaction potential, we start with the most rugged landscape, the set of sticky hard sphere clusters, and use a continuation procedure to evolve the clusters as the range of the potential increases. This procedure captures most local minima of the smoother landscapes, with those missing being mostly high energy clusters. As the potential smoothens, we characterize the merging of clusters by a graph with tree structure. We find these graphs to be insensitive to the interaction strength at short range, but the graphs corresponding to a Lennard-Jones potential vary more than those for a Morse potential at longer range.