Symmetry and deformations of cluster and biomolecules by invariant shape coordinates

The hyperspherical coordinate systems have been extensively adopted in the study of few-body quantum scattering problems in nuclear and molecular physics. The hyperangular momenta are the dynamical quantities used in this representation and the hyperspherical harmonics are the corresponding basis functions. Such a representation, initially developed for few-body systems, was extended to cluster and large molecules by providing definitions of the hyperangular momenta and related invariant dynamical quantities in the framework of classical mechanics. Here, the hyperspherical shape coordinates, invariant with respect to rotations and kinematic rotations, are proposed as a tool for classifying deformations of cluster and molecules in the the static analysis of the geometry of minimum energy structures.