Kramers-Grote-Hynes reaction coordinate

The difference between the Kramers-Grote-Hynes one-dimensional reaction coordinate (KGH) model and the Agmon-Hopfield two-dimensional reaction coordinate (AH) model can be seen clearly by comparing Figs 3.2a and b. 

That is, while numerical accuracy of Kramers Eq. (3.41) would validate the slow variable picture of Eq. (3.29), that of Grote and Hynes Eq. (3.45) does not validate any physical model for the reaction dynamics. Rather, it validates only the accuracy of (a) the partial clamping model [21], used to compute the quantities in Eq. (3.45) and (b) the parabolic barrier approximation U x) U x ) — XjlnKsP y to the gas phase reaction coordinate potential. The accuracy of these, however, requires only that y = x — jc remains small prior to the decision to react. 

We shall present here an equilibrium simulation of the transport of a solute across a liquid-liquid interface, which permits to measure the rate constant. This work has been done with the same rationale than other recent molecular dynamics studies of chemical kinetics /5,6/. The idea is to obtain by simulation, at the same time, a computation of the mean potential as a function of the reaction coordinate and a direct measure of the rate constant. The mean potential can then be used as an input for a theoretical expression of the rate constant, using transition state /7/, Kramers /8/ or Grote-Hynes /9/ theories for instance. The comparaison can then be done in order to give a correct description of the kinetics process. A distinct feature of molecular dynamics, with respect to an experimental testing of theoretical results, is that the numerical simulations have both aspects, theoretical and experimental. Indeed, the computation of mean potentials, as functions of the microscopic models used, is simple to obtain here whereas an analytical derivation would be a heavy task. On the other hand, the computation of the kinetics constant is more comparable to an experimental output. 

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