The optimal geometry of Lennard-Jones clusters: 148–309

Abstract

This paper deals with the global optimization problem of determining the n-atom cluster configuration that yields the minimum Lennard-Jones potential energy. To approach this problem we propose a genetic algorithm combined with a stochastic search procedure on icosahedral lattices. Although the potentials obtained with our method for n=148,…,309 are in fact only upper bounds for the global minima, we believe that most of these upper bounds are tight. We provide a geometrical description of the optimal configurations found, whose structures are either icosahedral or Marks decahedral in character. Also, we were able to discover a novel morphology – called FD here – for Lennard-Jones atomic clusters.