Adiabatic decoupling of the reaction coordinate

Abstract

ABSTRACT:When 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 ionmolecule reaction, the action integral ͗P ͘ ϭ ͑1/2͒͛P d is an adiabatic invariant. The Poisson bracket of ͗P ͘ 2 with Hamiltonians corresponding to a great variety of longrange 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.

The Role of Long-Range Forces in the Determination of Translational Kinetic Energy Release. Loss of C4H4+ from the Benzene and Pyridine Cations

“…As pointed out by Bates 61 and by Schlier, 62 the cyclic action integral Ip θ dθ, where p θ is an angular momentum, is an adiabatic invariant of the problem; that is, the reaction coordinate is adiabatically decoupled from rotation. Recent research 63,64 has shown that the Poisson bracket of the adiabatic invariant is proportional to p r µ r -3 for the ion-dipole interaction and to p r Q r -4 for the ion-quadrupole case. This short-range behavior of the Poisson bracket implies that the quality of the adiabatic approximation is expected to be quite good, at least at asymptotically large values of r. However, because it also increases linearly with the translational momentum p r , the validity of the adiabatic separation becomes questionable at high translational energies.…”

“…When the reaction coordinate is adiabatically decoupled from the bath, the dynamics is equivalent to a one-dimensional motion along the reaction coordinate in an effective potential. [62][63][64] The equation of motion obeys Jacobi's form of the least-action principle, which is particularly simple when the dynamics is one-dimensional. [63][64][65] This principle asserts 57,66 that the actual trajectory between two points r 1 and r 2 minimizes the integral ∫ r1 r 2 ε 1/2 dr.…”

“…[62][63][64] The equation of motion obeys Jacobi's form of the least-action principle, which is particularly simple when the dynamics is one-dimensional. [63][64][65] This principle asserts 57,66 that the actual trajectory between two points r 1 and r 2 minimizes the integral ∫ r1 r 2 ε 1/2 dr. This accounts [63][64][65] for the fact that, for both reactions 1.1 and 1.2, the dynamical constraint to be used in the MEM is ε 1/2 , in conformity with the experimental findings at low internal energy (metastable domain, Figures 1 and 2).…”

“…When the reaction coordinate is adiabatically decoupled from the bath, the dynamics is equivalent to a one-dimensional motion along the reaction coordinate in an effective potential. − The equation of motion obeys Jacobi’s form of the least-action principle, which is particularly simple when the dynamics is one-dimensional. − This principle asserts , that the actual trajectory between two points r 1 and r 2 minimizes the integral ∫ r 1 r 2 ε 1/2 d r . This accounts − for the fact that, for both reactions and , the dynamical constraint to be used in the MEM is ε 1/2 , in conformity with the experimental findings at low internal energy (metastable domain, Figures and ).…”

The Elimination of Redundant Constraints in Surprisal Analysis of Unimolecular Dissociation and Other Endothermic Processes

“…Simple model computations are reviewed in ref ; see also refs − . Propensity rules relating states and channels are discussed in refs and and references therein with important earlier work by Troe and Quack …”