Cluster optimization simplified by interaction modification

Abstract

Even when interactions are known exactly, it is generally very difficult to determine the lowest-energy configuration (a global potential energy minimum) for clusters with more than very few atoms or molecules. In mathematical parlance this is an NP-complete problem. A nonlinear optimization strategy, the ‘‘ant–lion method,’’ has been proposed to accelerate the search for global minima, and works by adroitly deforming the potential surface to produce overwhelming dominance by global minimum potential energy basins. This strategy is illustrated by application to clusters of 13 noble gas atoms. Monte Carlo results demonstrate that reduction of p in the pair potential 4(r−2p−r−p) below the ‘‘physical’’ value 6 produces a dramatic rise to essentially unity in probability of random encounter with the global minimum basins (icosahedral clusters).