Barrier recrossings

This is connnonly known as the transition state theory approximation to the rate constant. Note that all one needs to do to evaluate (A3.11.187) is to detennine the partition function of the reagents and transition state, which is a problem in statistical mechanics rather than dynamics. This makes transition state theory a very usefiil approach for many applications. However, what is left out are two potentially important effects, tiiimelling and barrier recrossing, bodi of which lead to CRTs that differ from the sum of step frmctions assumed in (A3.11.1831. 

T. Komatsuzaki and M. Nagaoka, Study on regularity of barrier recrossing motion, J. Chem. Phys. 105, 10838 (1996). 

E. Dynamical Model for Sn2 Substitution and Central Barrier Recrossing. 152... 

If crossing the central barrier is not rate-controlling in TST, then trapping in the ion-dipole complex must be incorporated into the statistical model and it is more difficult to represent the effect of central barrier recrossings correcting TST with the K factor is not sufficient. The recrossings and presence of both intermolecular and intramolecular complexes are expected to affect the k, kisom, and k rate constants in equation 6. The value for k should be smaller than that of a capture model, and kisom and k 8 should disagree with the predictions of RRKM theory. 

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. 

Since an early stage of the history of ab initio MD study, many cases have been observed in which the calculated trajectories do not support expectation derived from traditional reaction theories, such as RRKM and TST, and thus the applicability or suitability of these theories has been a matter of argument. In this section examples of one of those dynamics-derived phenomena are shown, namely nonstatistical barrier recrossing. 

First of all, liquid-phase studies generally do not obtain data which allows static and dynamic solvent effects to be separated [96,97], Static solvent effects produce changes in activation barriers. Dynamic solvent effects induce barrier recrossing and can lead to modification of rate constants without changing the barrier height. Dynamic solvent effects are temperature and viscosity dependent. In some cases they can cause a breakdown in transition state theory [96]. 

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... 

These examples, although few and preliminary, nonetheless indicate the direction in which time-resolved spectroscopy of reactive species is headed. More detailed examinations of unstable structures between chemical reactants and products will certainly follow. A major goal in this area will be direct observation of coherent wavepacket propagation through local potential maxima (i.e., transition states). Experimental control over wavepacket momentum through potential maxima will be especially important in evaluating solvent effects, barrier recrossing probabilities, and so on. Methods that permit observation and control of transition state production may be anticipated. 

Schork, D. Koppel, H. Barrier recrossing in the vinylidene-acetylene isomerization reaction A five-dimensional ab initio quantum dynamical investigation. J. Chem. Phys. 2001, 115, 7907-9723. 

A more rigorous expression for ki j can be obtained by multiplying the TST expression by a transmission factor that can be calculated easily by running downhill trajectories [3]. However, the corresponding correction which takes into account barrier recrossing is an order of unity for reactions in aqueous solutions and enzymes [4]. 

Over the years, TST has been modified and corrected for kinetic effects of tunneling, barrier recrossing and medium viscosity, yet, developing a theory that will explain such a phenomenon is an on-going challenge. The next section describes attempts to lay a general foundation for such a theory. 

The false sharp barrier limit emerges from the slow variable eqs. (3.41) and (3.45), but not fast variable eqs. (3.50) and (3.51), for the following reason. Comparing Figures 3.2 and 3.6 shows that the slow variable potential W(S v) ignores barrier recrossings due to reflections of the reaction coordinate by the solvent cage that are properly accounted for by... 

CU-CH3CI decomposition MP2/6-31G- [C1-CH3-C1] central barrier recrossing and intrinsic non-RRKM dynamics [121]... 

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... 

In this spirit, we will also briefly describe the basis for some of the microscopic kinetic theories of unimolecular reaction rates that have arisen from nonlinear dynamics. Unlike the classical versions of Rice-Ramsperger-Kassel-Marcus (RRKM) theory and transition state theory, these theories explicitly take into account nonstatistical dynamical effects such as barrier recrossing, quasiperiodic trapping (both of which generally slow down the reaction rate), and other interesting effects. The implications for quantum dynamics are currently an active area of investigation. 

R. E. Gillilan and W. P. Reinhardt, Chem. Phys. Lett., 156,478 (1989). Barrier Recrossing in Surface Diffusion A Phase-Space Perspective. 

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