PERFORMANCE OF THE SHIFT METHOD OF GLOBAL MINIMIZATION IN SEARCHES FOR OPTIMUM STRUCTURES OF CLUSTERS OF LENNARD-JONES ATOMS

The optimal geometry of a finite cluster of atoms is difficult to find because the number of minima of the potential energy is huge for larger clusters. Until now, the only deterministic procedure designed to find the lowest-energy structures of such clusters was the diffusion equation method, which performed well for large clusters but sometimes failed for smaller ones. In the present paper we propose the so-called shift method (also deterministic), which deforms the original potential energy hypersurface by shifting the atom-atom Lennard-Jones potential. As a result, the whole system collapses into a single point. Then, by using the reversing procedure, the original potential is gradually restored while optimizing the structure for each step. This results in a kind of big bang, because the atoms emerge from the collapse point and the cluster geometry evolves to the final one corresponding to the original undeformed potential. The procedure applied to the clusters containing up to 19 atoms turned out to produce in all cases under study the structures of the lowest energy.