Cooperativity and localization

Cooperativity and localization are very exciting 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' otherwise. Examples of cooperative and uncooperative rearrangements can be found here.

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. Interestingly, it turns out that cooperativity and barrier height are related. We discovered that cooperative rearrangements have the smallest barriers.

Average barrier as a function of localization and cooperativity indices calculated for LJ75 pathway database. The darkest shading corresponds to the highest barriers. Outlying points are connected to illustrate the boundaries of the data area.

It is not known if cooperative pathways are as ubiquitous as uncooperative ones for realistic systems. We know, however, that for LJ₁₃ system, where it is possible to database all the elementary rearrangements, cooperative rearrangements are abundant.

This work was described in detail in: S. A. Trygubenko and D. J. Wales, `Analysis of cooperativity and localization for atomic rearrangements', J. Chem. Phys., 121, 6689-6697 (2004). [JCP Online] [arXiv]