Thermodynamics and the Global Optimization of Lennard-Jones clusters
Jonathan Doye, David Wales, Mark Miller
Abstract
Theoretical design of global optimization algorithms can profitably utilize recent statistical mechanical treatments of potential energy surfaces (PES's). Here we analyze the basin-hopping algorithm to explain its success in locating the global minima of Lennard-Jones (LJ) clusters, even those such as 38 for which the PES has a multiple-funnel topography, where trapping in local minima with different morphologies is expected. We find that a key factor in overcoming trapping is the transformation applied to the PES which broadens the thermodynamic transitions. The global minimum then has a significant probability of occupation at temperatures where the free energy barriers between funnels are surmountable.
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