Classification of Shapes and Deformations of Large Systems by Invariant Coordinates

The use of hyperspherical coordinates is widespread in reactive scattering studies, allowing for a symmetric representation of the quantum dynamics of reactive processes. Indeed, among the variants of hyperspherical coordinates, the so called “symmetric” ones are “democratic” with respect to the asymptotic channels and so are the corresponding basis sets, since basis functions can be symmetrized with respect to particle exchange, acting on just a reduced subset of coordinates. Applications to scattering problems are limited to few-atom systems, due to computational cost. An extension of the representation to many-body classical dynamics is possible and has been proposed in a series of papers, where different aspects have been investigated. Here we recall the possibility of defining shape coordinates invariant with respect to the remaining degrees of freedom, which are suitable for systematic classification of structures of clusters and large biomolecules. The definition of shape parameters and to provide examples of their application are the purposes of the present paper.