  We propose new measures of localization and cooperativity for the analysis of
atomic rearrangements. We show that for both clusters and bulk material
cooperative rearrangements usually have significantly lower barriers than
uncooperative ones, irrespective of the degree of localization. We also find
that previous methods used to sample stationary points are biased towards
rearrangements of particular types. Linear interpolation between local minima
in double-ended transition state searches tends to produce cooperative
rearrangements, while random perturbations of all the coordinates, as sometimes
used in single-ended searches, has the opposite effect.
