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:

Pictures of Global minima
Tables of Global minima:
- N=3-150
- N=310-561 (provided by Xueguang Shao)
- N=562-1000 (provided by Xueguang Shao)
Points files for each minimum are accessible from this Table.

Our work on N<110 has been published in

D.J. Wales and J.P.K. Doye, J. Phys. Chem. A, 101, 5111-5116 (1997)
Global optimization by basin-hopping and the lowest energy structures of Lennard-Jones clusters containing up to 110 Atoms

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.

Return to The Cambridge Cluster Database.