Global view of classical clusters: the hyperspherical approach to structure and dynamics

Hyperspherical and related approaches to the dynamics of few particles have been extensively exploited in nuclear, atomic and molecular physics in order to successfully deal with demanding quantum mechanical problems, such as few-nucleon structures and triatomic chemical reactions. In this work, we explore the use of these tools for the study of the structure and dynamics of atomic clusters, for which an ample phenomenology is being accumulated from a classical mechanics perspective. The invariants associated to the inertia tensor were examined for known absolute minimum energy structures of Lennard-Jones clusters up to a number of particles N = 150, while for N less than or equal to 12 the structures of all relative minima were determined and studied in relationship with their symmetries. Morse clusters and a realistic interaction model for argon clusters were also briefly considered. In order to deal with cluster dynamics the concept of grand angular momentum is formulated in classical mechanics as a sum of external, deformation and internal ( or kinematic) angular momenta. A similar decomposition, of prospective use for the analysis of molecular dynamics simulations, is proposed for the classical kinetic energy. The example of a classical trajectory analysis is given for the isomerization by pseudorotation of an N = 5 cluster.