Global optimization of binary Lennard–Jones clusters

Abstract

In this paper we present our experience with the optimization of atomic clusters under the binary Lennard–Jones potential. This is a generalization of the single atom type Lennard–Jones model to the case in which atoms of two different types (and ‘sizes’) interact within the same cluster. This problem has a combinatorial structure which increases complexity and requires strategies to be revised in order to take into account such new aspects. Our approach has been a very effective one: we have been able not only to confirm most putative optima listed in the Cambridge Cluster Database, but also to find 95 improved solutions.

Keywords:

• binary Lennard–Jones cluster
• optimization
• Cambridge cluster database
• population basin hopping
• Morse potential

Acknowledgements

The research reported in this paper has been partially supported by project PRIN ‘Innovative Problems and Models in Nonlinear Optimization’ and by project PRIN ‘Nonlinear Optimization, Variational Inequalities and Equilbrium Problems’.