Barriers Grote-Hynes model

These and similar results have been interpreted as confirmations of the Grote-Hynes model as a valid physical theory of liquid phase reactions, and, relatedly, of frequency-dependent friction as a valid concept for liquid phase chemistry. This interpretation is spurious. Actually the result Kgh( ) Kmd(T ) shows only that for the systems of Table III the decision to react is made near the barrier top. 

In order for the reaction to take place with the mechanism in the Grote-Hynes theory as well as in the Kramers theory, the reactant must surmount over the transition-state barrier only by diffusional Brownian motions regulated by solvent fluctuations. In the two-step mechanism of the Sumi-Marcus model, on the other hand, surmounting over the transition-state barrier is accomplished as a result of sequential two steps. That is, the barrier is climbed first by diffusional Brownian motions only up to intermediate heights, from which much faster intramolecular vibrational motions take the reactant to the transition state located at the top of the barrier. 

In the previous sections a model of the frequency-dependent collisional friction has been derived. Because the zero-frequency friction for a spherical particle in a dense fluid is well modeled by the Stokes-Einstein result, even for particles of similar size as the bath particles, there has been considerable interest in generalizing the hydrodynamic approach used to derive this result into the frequency domain in order to derive a frequency-dependent friction that takes into account collective bath motions. The theory of Zwanzig and Bixon, corrected by Metiu, Oxtoby, and Freed, has been invoked to explain deviation from the Kramers theory for unimolec-ular chemical reactions. The hydrodynamic friction can be used as input in the Grote-Hynes theory [Eq. (2.35)] to determine the reactive frequency and hence the barrier crossing rate of the molecular reaction. However, the use of sharp boundary conditions leads to an unphysical nonzero high-frequency limit to Ib(s). which compromises its utility. 

In the second section the calculation of the rate constant was discussed from the classical mechanics viewpoint. Voth, Chandler, and Miller derived a quantum mechanical expression for the rate constant based on a path integral formalism. Using this expression as a starting point, Voth and O Gormani derived an effective barrier model to allow the calculation of the barrier tunneling contribution to the quantum mechanical rate constant for reactions in dissipative baths. The spirit of their derivation is quite similar to that which treats Grote-Hynes theory o as transition state theory for a parabolic barrier in a harmonic bath. 

In this chapter, we give an account of our recent MD and theoretical analysis of electron transfer" (ET) and SnI ionization" reactions in RTILs. Specifically, we consider the unimolecular ET of a model diatomic reaction complex in l-butyl-3-methyldicyanamide (BMI" DCA ) and ionization of 2-chloro-2-methylpropane in 1-ethyl-3-methylimidazolium hexafluorophosphate (EMI+PEg ). The influence of the RTIL environment on free energetics and dynamics of these reactions is described with attention paid to its similarities to and differences from the conventional polar solvents. The MD results for barrier crossing dynamics on reaction kinetics are analyzed via the Grote-Hynes (GH) theory and compared with the transition state theory (TST) and Kramers theory predictions. 

Kramers [67], Northrup and Hynes [103], and also Grote and Hynes [467] have considered the less extreme case of reaction in the liquid phase once the reactants are in collision where such energy diffusion is not rate-limiting. Let us suppose we could evaluate the (transition state) rate coefficient for the reaction in the gas phase. The conventional transition state theory needs to be modified to include the effect of the solvent motion on the motion of the reactants as they approach the top of the activation barrier. Kramers [67] used a simple model of the... 

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. 

Grote euid Hynes (1980) have reinvestigated the Kramers model in order to include non-MarkovicUi response. Indeed, for sharp barriers, the... 

---