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 convenie ntly broken up into spatial (or external) rotations, kinematic invariants ( related to the inertia moments) and kinematic (or internal) rotations. Thei r usefulness is demonstrated for the study of constrained intramolecular mo tions and of concerted reactions and for collective modes of polyatomic mol ecules and clusters. For a fixed hyperradius, which is a measure of total i nertia, the space of kinematic invariants is the surface of a right spheric al triangle that leads to the tetrahedral (for n = 4) or octahedral (for n greater than or equal to 5) tessellation of the sphere. Alternative paramet rizations are discussed, including the proper one to deal with the umbrella inversion motion of ammonia.