  The transition states and dividing surfaces used to find rate constants for
bimolecular reactions are shown to undergo qualitative changes, known as Morse
bifurcations, and to exist for a large range of energies, not just immediately
above the critical energy for first connection between reactants and products.
Specifically, we consider capture between two molecules and the associated
transition states for the case of non-zero angular momentum and general
attitudes. The capture between an atom and a diatom, and then a general
molecule are presented, providing concrete examples of Morse bifurcations of
transition states and dividing surfaces. The reduction of the $n$-body systems
representing the reactions is discussed and reviewed with comments on the
difficulties associated with choosing appropriate charts and the global
geometry of the reduced spaces.
