Properties of Kinetic Transition Networks for Atomic Clusters and Glassy Solids

TL;DR

This paper investigates the network properties of minima and transition states in atomic clusters and glassy solids, revealing small-world features in clusters but not in glass formers, and analyzing their structural implications.

Contribution

It constructs and analyzes kinetic transition networks for atomic clusters and compares them with glassy systems, highlighting differences in network topology.

Findings

Clusters exhibit small-world network properties.

Glass systems do not show small-world characteristics.

Networks are not scale-free, as degree distributions do not follow a power law.

Abstract

A database of minima and transition states corresponds to a network where the minima represent nodes and the transition states correspond to edges between the pairs of minima they connect via steepest-descent paths. Here we construct networks for small clusters bound by the Morse potential for a selection of physically relevant parameters, in two and three dimensions. The properties of these unweighted and undirected networks are analysed to examine two features: whether they are small-world, where the shortest path between nodes involves only a small number or edges; and whether they are scale-free, having a degree distribution that follows a power law. Small-world character is present, but statistical tests show that a power law is not a good fit, so the networks are not scale-free. These results for clusters are compared with the corresponding properties for the molecular and atomic structural glass formers ortho-terphenyl and binary Lennard-Jones. These glassy systems do not show small-world properties, suggesting that such behaviour is linked to the structure-seeking landscapes of the Morse clusters.