Adiabatic decoupling of the reaction coordinate

Abstract

AbstractWhen the dynamics is constrained by adiabatic invariance, a reactive process can be described as a one‐dimensional motion along the reaction coordinate in an effective potential. This simplification is often valid for central potentials and for the curved harmonic valley studied in the reaction path Hamiltonian model. For an ion–molecule reaction, the action integral 〈Pθ〉 = (1/2π)∮Pθ dθ is an adiabatic invariant. The Poisson bracket of 〈Pθ〉2 with Hamiltonians corresponding to a great variety of long‐range electrostatic interactions is found to decrease with the separation coordinate r, faster than the corresponding potential. This indicates that the validity of the adiabatic approximation is not directly related to the shape of the potential energy surface. The leading role played by the translational momentum is accounted for by Jacobi's form of the least action principle. However, although the identification of adiabatic regions by this procedure is limited to a specific range of coordinate configurations, equivalent constraints must persist all along the reaction coordinate and must operate during the entire reaction, as a result of entropy conservation. The study of the translational kinetic energy released on the fragments is particularly appropriate to detect restrictions on energy exchange between the reaction coordinate and the bath of internal degrees of freedom. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2008