Global optimization of Morse clusters by potential energy transformations

The Morse potential is a simple model for the potential energy of atoms with a single parameter ρ that determines the width of the potential well and allows a wide variety of materials to be modeled. Morse clusters are particularly important for applications, but their global optimization is also an extremely hard problem, highly relevant to methods that are to be applied to find the optimal configuration of a biomolecule. In particular, large ρ values are very challenging and, until now, no unbiased global-optimization method has been able to detect all the (putative) global minima at ρ = 14 for clusters with up to N = 80 atoms. In this paper we introduce some techniques for transforming the original Morse potential that allow us to increase considerably the efficiency in locating the known global minima and also to discover some new optimal clusters. These methods are promising candidates for application to the optimization of biomolecules.