Characterizing the network topology of the energy landscapes of atomic clusters

TL;DR

This paper analyzes the network structure of energy landscapes in atomic clusters, revealing small-world and scale-free properties influenced by potential energy differences, with implications for understanding cluster dynamics.

Contribution

It introduces a network-based characterization of energy landscapes for Lennard-Jones clusters, highlighting the influence of energy heterogeneity on network topology.

Findings

Networks exhibit small-world and scale-free characteristics.

Low-energy minima serve as network hubs.

Network structure reflects spatial embedding and energy heterogeneity.

Abstract

By dividing potential energy landscapes into basins of attractions surrounding minima and linking those basins that are connected by transition state valleys, a network description of energy landscapes naturally arises. These networks are characterized in detail for a series of small Lennard-Jones clusters and show behaviour characteristic of small-world and scale-free networks. However, unlike many such networks, this topology cannot reflect the rules governing the dynamics of network growth, because they are static spatial networks. Instead, the heterogeneity in the networks stems from differences in the potential energy of the minima, and hence the hyperareas of their associated basins of attraction. The low-energy minima with large basins of attraction act as hubs in the network.Comparisons to randomized networks with the same degree distribution reveals structuring in the networks that reflects their spatial embedding.