Thermodynamics and the Global Optimization of Lennard-Jones clusters

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 \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 transitions. The global minimum then has a significant probability of occupation at temperatures where the free energy barriers between funnels are surmountable.

arXiv comment13 pages, 13 figures, revtex

References in corpus (10)

• Global Optimization by Basin-Hopping and the Lowest Energy Structures of Lennard-Jones Clusters Containing up to 110 Atoms
• Simulated Tempering: A New Monte Carlo Scheme
• Molecular geometry optimization with a genetic algorithm
• Generalized Simulated Annealing
• Event-based relaxation of continuous disordered systems
• Diffusive Dynamics of the Reaction Coordinate for Protein Folding Funnels
• Traveling through potential energy landscapes of disordered materials: the activation-relaxation technique
• On the Thermodynamics of Global Optimization
• Topology of amorphous tetrahedral semiconductors on intermediate lengthscales
• Simulated Annealing with Tsallis Weights - A Numerical Comparison

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