Lennard-Jones clusters have become a much-studied test system for global optimization methods designed for configurational problems. Our application of the `basin-hopping' algorithm is one of the most successful methods in the size regime N<110.
Most of the global minima have structures based upon the Mackay icosahedron. The exceptions, which are based on a face-centred-cubic truncated octahedron (N=38) and Marks decahedra (N=75-77,102-104), provide a stiff test for any putative global optimization algorithm. The basin-hopping and genetic algorithms are the only unbiased global optimization methods which have found the decahedral global minima.More information about the global minima can be accessed from the following pages: