Thermodynamics and the Global Optimization of Lennard-Jones clusters

TL;DR

This paper explains why the basin-hopping algorithm effectively finds global minima of Lennard-Jones clusters by analyzing how thermodynamic transformations of the potential energy surface facilitate overcoming energy barriers.

Contribution

It provides a theoretical analysis linking statistical mechanics to the success of basin-hopping in complex PES landscapes, especially for multi-funnel topographies.

Findings

Basin-hopping success is due to PES transformations that broaden thermodynamic transitions.

Global minima have high occupation probability at accessible temperatures.

The approach explains overcoming local minima in complex energy landscapes.

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.