Geometric method for large Morse clusters formation

This paper describes a geometrically founded method for constructing the initial configuration of a complete icosahedral structure of an atomic cluster. The method finds a global minimum of the cluster energy as a result of a single local optimization procedure. The method is based on the proposed algorithm for the stratified accommodation of atom centers, that allows one to form structural configurations commonly found among the clusters with global minimum of interatomic interaction energy. This algorithm provides the ability to build a spatial configuration of the dense packing of spheres for the formation of icosahedral and decahedral structures, as well as building complete icosahedrons with a large number of atoms. With the proposed method, we have reached the global minima for large Morse clusters ($N = 817$, $923$, and $1415$), which is a record for Morse clusters with $\rho = 6$.