Lennard-Jones Clusters

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: Our work on N<110 has been published in See also the quantum Lennard-Jones clusters database entry. The inclusion of the zero-point energy can cause some of the global minima to change.
A table of global minima for N=151-309 and N=1001-1610 is available at Xuegang Shao's web site
If you can improve on any of the results given in these pages email me, and I will update the database.
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Jonathan Doye © 1997