Using Clusters To Relate Topography And Dynamics Of Multidimensional Potentials

Striking results obtained recently for(KCl)32indicate that clusters undergoing cooling can find their way to regular structures under statistically unfavorable odds as large as1012:1even when all energy is removed in only about 25 vibrational periods.1,2To understand what characteristics of potential surfaces are responsible for such “focusing” character, we have undertaken a series of statistical analyses of a moderately complex system, the van der Waals cluster of 19 atoms held by pairwise Lennard–Jones forces. The analysis can be done hierarchically, first in terms of the distributions of minima and of saddles, then of pairs of successive wells and intervening saddles, and then in terms of whole sequences of pathways to different basins. The goals are an interpretation of what make a complex surface “focusing” or glass-forming, and a means to quantify the optimal cooling schedule to achieve either a structure of a selected (and physically attainable) type, or an arbitrary, presumably amorphous structure.