Coordinates which diagonalize the kinetic energy of relative motion

The most general sets of coordinates which diagonalize the relative kinetic energy of an N particle system are derived. These include reaction coordinates which are symmetric with respect to both the reactants and products. The angle of skewing of an idealized potential energy surface determines whether a molecular collision is adiabatic or leads to an exchange reaction. The shape of the potential energy surface leads to vibrationally excited diatomic molecules as products in hydrogen-halogen reactions.