Global Optimization by Basin-Hopping and the Lowest Energy Structures of Lennard-Jones Clusters Containing up to 110 Atoms

TL;DR

This paper introduces a basin-hopping global optimization method that efficiently finds lowest energy structures of Lennard-Jones clusters up to 110 atoms, including some previously undiscovered configurations.

Contribution

The paper presents a novel basin-hopping technique that transforms the energy landscape to improve global minimum search efficiency without altering the true minima.

Findings

Successfully located lowest energy structures for all clusters up to 110 atoms.

Discovered new low-energy configurations not found in previous unbiased searches.

Demonstrated the effectiveness of the method in complex energy landscapes.

Abstract

We describe a global optimization technique using `basin-hopping' in which the potential energy surface is transformed into a collection of interpenetrating staircases. This method has been designed to exploit the features which recent work suggests must be present in an energy landscape for efficient relaxation to the global minimum. The transformation associates any point in configuration space with the local minimum obtained by a geometry optimization started from that point, effectively removing transition state regions from the problem. However, unlike other methods based upon hypersurface deformation, this transformation does not change the global minimum. The lowest known structures are located for all Lennard-Jones clusters up to 110 atoms, including a number that have never been found before in unbiased searches.