Discrete Optimal Global Convergence of an Evolutionary Algorithm for Clusters under the Potential of Lennard Jones

A review of the properties that bond the particles under Lennard Jones Potential allow to states properties and conditions for building evolutive algorithms using the CB lattice with other different lattices. The new lattice is called CB lattice and it is based on small cubes, such the number of its vertices in a region is always greater than the number of the particles of a cluster or a region of a lattice inside of the same size region of the CB lattice. Moreover, the estimation of a putative optimal cluster of the Lennard Jones can be done theoretically in short time but, the proof, for such cluster to be the global optimal cannot be determining in efficient time. The proof of the global optimality for a cluster is related to the binomial coefficient (