Thermodynamics and the global optimization of Lennard-Jones clusters
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 LJ38 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.
|Journal||J. Chem. Phys.|
Doye, J. P. K, Wales, D. J, & Miller, M. A. (1998). Thermodynamics and the global optimization of Lennard-Jones clusters. J. Chem. Phys., 109, 8143–8153.