THERMODYNAMICS AND THE GLOBAL OPTIMIZATION OF LENNARD-JONES CLUSTERS

Theoretical design of global optimization algorithms can profitably ut ilize recent statistical mechanical treatments of potential energy sur faces (PES's). Here we analyze the basin-hopping algorithm to explain its success in locating the global minima of Lennard-Jones (LJ) cluste rs, even those such as LJ(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 tra nsitions. The global minimum then has a significant probability of occ upation at temperatures where the free energy barriers between funnels are surmountable. (C) 1998 American Institute of Physics. [S0021-9606 (98)50143-2].