Cooperativity and Localization
Cooperativity and localization are properties of the rearrangement pathways.
Rearrangement is called 'localized' if a small fraction of the atoms participates in it, and 'delocalized' in the opposite limit. Rearrangement is called 'cooperative' if most of the atoms that participate move simultaneously, and 'uncooperative' if atoms move sequentially.
Any pathway can be broken down into elementary (or single-step) rearrangement paths that feature no intermediate minima. Among single-step rearrangements, delocalized uncooperative ones are the most difficult to find. It turns out that cooperativity and barrier height are related: cooperative rearrangements have the smallest barriers.
Rearrangements of LJ75 Cluster Localized on Two Atoms
While studying cooperativity and localization properties of rearrangement pathways we sampled and analysed a large number of them for LJ75—a 75-atom cluster bound by Lennard-Jones intermolecular pair potential.
The potential energy surface for LJ75 is rich in stationary points, and using cooperativity measure as a guide we saw why some pathways are easy to find with aggressive, approximate optimisers while others are excruciatingly hard.
Here we present two rearrangements of LJ75—the most cooperative and the most uncooperative ones we have found at the time of study. They illustrate the issues one will face when coming up with sampling and optimisation techniques that are both unbiased in terms of construction of initial guesses and robust so that they can work well with numerical optimisers.