Testing Different Nonsmooth Formulations of the Lennard-Jones Potential in Atomic Clustering Problems

A cluster is a group of identical molecules or atoms loosely bound by inter-atomic forces. The optimal geometry minimises the potential energy-usually modelled as the Lennard-Jones potential-of the cluster. The minimisation of the Lennard-Jones potential is a very difficult global optimisation problem with extremely many local minima. In addition to cluster problems, the Lennard-Jones potential represents an important component in many of the potential energy models used, for example, in protein folding, protein-peptide docking, and complex molecular conformation problems. In this paper, we study different modifications of the Lennard-Jones potential in order to improve the success rate of finding the global minimum of the original potential. The main interest of the paper is in nonsmooth penalised form of the Lennard-Jones potential. The preliminary numerical experiments confirm that the success rate of finding the global minimum is clearly improved when using the new formulae.