Adiabatic invariance along the reaction coordinate

In a two-dimensional space where a point particle interacts with a diatomic fragment, the action integral Φ pθ dθ (where θ is the angle between the fragment and the line of centers and pθ its conjugate momentum) is an adiabatic invariant. This invariance is thought to be a persistent dynamical constraint. Indeed, its classical Poisson bracket with the Hamiltonian is found to vanish in particular regions of the potential energy surface: asymptotically, at equilibrium geometries, saddle points, and inner turning points, i.e., at remarkable situations where the topography of the potential energy surface is locally simple. Studied in this way, the adiabatic decoupling of the reaction coordinate is limited to disjoint regions. However, an alternative view is possible. The invariance properties of entropy (as defined in information theory) can be invoked to infer that dynamical constraints that are found to operate locally subsist everywhere, throughout the entire reactive process, although with a modified expression. © 2009 American Institute of Physics.