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

TLDR

The method exploits landscape features identified as essential for efficient relaxation to the global minimum. The study presents a basin‑hopping technique that transforms the potential energy surface into interpenetrating staircases. The technique maps each configuration to its local minimum via geometry optimization, thereby eliminating transition state regions. The transformation preserves the global minimum, and the method discovers the lowest known structures for all Lennard‑Jones clusters up to 110 atoms, including previously unknown ones.

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.