Recrossing transmission coefficient

For each MEP, VTST and VTST/OMT calculations are carried out using the progress variable s, along MEP i as the optimized reaction coordinate. (Note that s, is the variable s for ensemble member i.) The improved reaction coordinate for ensemble member i yields a recrossing transmission coefficient r given by... 

For many chemical reactions with high sharp barriers, the required time dependent friction on the reactive coordinate can be usefully approximated as the tcf of the force with the reacting solute fixed at the transition state. That is to say, no motion of the reactive solute is permitted in the evaluation of (2.3). This restriction has its rationale in the physical idea [1,2] that recrossing trajectories which influence the rate and the transmission coefficient occur on a quite short time scale. The results of many MD simulations for a very wide variety of different reaction types [3-12] show that this condition is satisfied it can be valid even where it is most suspect, i.e., for low barrier reactions of the ion pair interconversion class [6],... 

The transmission coefficient k - kET / /4)r measures the departure of the rate constant from its Marcus, TST value and can be directly computed, for different choices of the electronic coupling p, in an MD simulation for the ET reaction [8]. The first important point is that for p = 1 kcal/mol, k is quite close to unity there are few recrossings of the barrier and the Marcus TST Theory is thus an excellent approximation. 

When the coupling is increased to p = 5 kcal/mol and the barrier becomes more rounded, the transmission coefficient is smaller (KEr 0.6) and there are noticeable departures from the Marcus TST theory, although they are not enormous. The the barrier recrossings are found to be restricted to the immediate vicinity of the reaction barrier top. 

Up to moderately high energy ( 179%) of the activation barrier for reactant product in the Are isomerization reaction, the fates of most trajectories can be predicted more accurately by Eq. (11) as the order of perturbation calculation increases, except just in the vicinity of the (approximate) stable invariant manifolds (e.g., see Eig. 5), and that the transmission coefficient K observed in the configurational space can also be reproduced by the dynamical propensity rule without any elaborate trajectory calculation (see Eig. 6). Our findings indicate that almost all observed deviations from unity of the conventional transmission coefficient k may be due to the choice of the reaction coordinate whenever the k arises from the recrossings, and most transitions in chemical... 

Boltzmann s constant. Actually, the TST expression only holds if all molecules which pass from the reactant over the TS go on to product. To allow for recrossings , where a molecule passes over the TS but is refiected back to the reactant side, a transmission coefficient, k, is sometimes introduced. This factor also allows for the quantum mechanical phenomenon of tunnelling, i.e. molecules that have insufficient energy to pass over the TS may tunnel through the barrier and appear on the product side. The transmission coefficient is difficult to calculate, but is usually close to one, and rarely falls outside the range 0.5-2. At low temperatures the tunnelling contribution... 

In transition state theory, dynamic effects are included approximately by including a transmission coefficient in the rate expression [9]. This lowers the rate from its ideal maximum TS theory value, and should account for barrier recrossing by trajectories that reach the TS (activated complex) region but do not successfully cross to products (as all trajectories reaching this point are assumed to do in TS theory). The transmission coefficient can be calculated by activated molecular dynamics techniques, in which molecular dynamics trajectories are started from close to the TS and their progress monitored to find the velocity at which the barrier is crossed and the proportion that go on to react successfully [9,26,180]. It is not possible to study activated processes by standard molecular dynamics because barrier crossing events occur so rarely. One reason for the... 

Inclusion of dynamical effects allows calculation of corrections to simple Transition State Theory, often described by a transmission coefficient k to be multiplied with the TST rate constant (Section 12.1), or used in connection with variational TST (Section 12.3). Classical dynamics allow corrections due to recrossing to be calculated, while a quantum treatment is necessary for including tunnelling effects. Owing to the stringent... 

The transmission coefficient k was calculated from a series of transition-state trajectories by monitoring the recrossings ( = St) that occur as a function of time until each trajectory is finally trapped in the product or reactant well. The normalized reactive flux-correlation function x(t) defined in Eq. 19 was constructed from this set of trajectories 131 the result is shown in Fig. 29. From its initial value, equal to the. transition-state result, ic(<) decreases rapidly until it becomes approximately constant for an extended period. The ra-... 

The value of the transmission coefficient kt is shown for each feature in Table 2. (The value of kt for the last feature is greater than 1 because it includes contributions from higher energy transition states that have not been included in the fit.) Many of the values of the transmission coefficients are very close to unity, suggesting that these features correspond to quantized transition states that are nearly ideal dynamical bottlenecks to the reactive flux. Several of the values of kt deviate from unity this could be the result of the assumption of parabolic effective potential barriers or from recrossing or other multidimensional effects. 

Rosenberg et al. calculated the rate constant for this process, from which the transmission coefficient could be derived. They found that recrossings are quite frequent for this reaction, leading to a transmission coefficient of 0.36 for... 

There are two primary sets of observations we shall discuss here. First, the transmission coefficient was found to be near unity for almost all of the reaction conditions studied.Only when the barrier was reduced to 5 kcal/mol did any of the ensembles display a nonunit transmission coefficient (with the Xe solvent being most effective in causing barrier recrossings even in that case, the transmission coefficient was 0.91). The immediate conclusion that can be drawn from these results is that the solvent does not have much effect on this... 

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