Distance as coordinate: A distance geometry study on isomerizations of small Lennard-Jones and Au₆⁺ clusters

Abstract

Atomic clusters generally do not have a clear skeletal structure, and proper representation of their geometry is problematic. Bearing in mind the interactions, one can consider that a set of interatomic distances is a natural choice to represent the structure. However, for large degrees of freedom, redundancy is often a problem. Here, we report the analysis of cluster rearrangements in the metric space. The Cayley-Menger determinant plays a crucial role in overcoming the redundancy and controlling the collective changes of multiple atoms only with few variables. As examples, we discuss atomic rearrangements in the Lennard-Jones and Au₆⁺ clusters.