Statistical theories of chemical reactions. Distributions in the transition region

Abstract

The distribution of states in the transition region is considered for chemical reactions occurring with reactants in thermal equilibrium. It is argued that when products are absent the distribution in the transition region is identical to an equilibrium distribution except that states originating from products are missing. The phenomenon is illustrated with classical trajectory calculations for three collinear systems with widely different potential energy surfaces: (a) intersecting rectangular channels of different elevation, (b) a smooth curve of parabolic cross section, and (c) a surface for the endothermic reaction H, + J---'H + HI. For purely classical reactants in an equilibrium distribution a "bobsled noneffect" is found. The use of a conversion coefficient ~ in place of the usual transmission coefficient K in transition state theory is shown to correct for the nonequilibrium distribution in the transition region. The equivalence of the combined phase space/trajectory method and the conventional trajectory method is demonstrated for the three examples.

Reactivity of the β-AlF3(100) surface: defects, fluorine mobility and catalysis of the CCl2F2 dismutation reaction

“…The effects of quantum tunnelling are not included, although for high barriers this effect is very small. It does not include the effects of dynamical recrossings of the transition state, that is, it assumes that every barrier crossing event proceeds directly to the products, and hence the rate constant may be over-estimated [48][49][50] .…”

Elaborating Transition Interface Sampling Methods

“…The transition state theory (TST) rate constant is then related to the probability to be at the maximum of the free energy barrier. This rate is only an approximation and the second part of the reactive flux methods computes the correction, the transmission coefficient, by starting many fleeting trajectories from the top of the barrier [6,7,8,9]. However, the success of this method depends strongly on the choice of reaction coordinate.…”

“…The time-scale problem is traditionally solved by a two-step reactive flux method [6,7,8,9]. One first calculates the free energy as a function of a reaction coordinate describing the process.…”

Communication: κ-dynamics—An exact method for accelerating rare event classical molecular dynamics

“…The overestimation of the TST rate can also be calculated from the recrossings of trajectories initiated at the TS. 10,11 This so-called dynamical correction factor, or transmission coefficient, κ ∈ [0, 1], is the ratio of the true rate to the TST rate,…”