Collective hyperspherical coordinates for polyatomic molecules and clusters

For n-body dynamics an analysis is made of the properties of configuration space within a symmetric hyperspherical framework. Coordinates are conveniently broken up into spatial (or external) rotations, kinematic invariants (related to the inertia moments) and kinematic (or internal) rotations. Their usefulness is demonstrated for the study of constrained intramolecular motions and of concerted reactions and for collective modes of polyatomic molecules and clusters. For a fixed hyperradius, which is a measure of total inertia, the space of kinematic invariants is the surface of a right spherical triangle that leads to the tetrahedral (for n = 4) or octahedral (for n S 5) tessellation of the sphere. Alternative parametrizations are discussed, including the proper one to deal with the umbrella inversion motion of ammonia.