Trajectory studies recrossing

A number of MD studies on various unimolecular reactions over the years have shown that there can sometimes be large discrepancies (an order of magnitude or more) between reaction rates obtained from molecular dynamics simulations and those predicted by classical RRKM theory. RRKM theory contains certain assumptions about the nature of prereactive and postreactive molecular dynamics it assumes that all prereactive motion is statistical, that all trajectories will eventually react, and that no trajectory will ever recross the transition state to reform reactants. These assumptions are apparently not always valid otherwise, why would there be discrepancies between trajectory studies and RRKM theory Understanding the reasons for the discrepancies may therefore help us learn something new and interesting about reaction dynamics. 

Angle-dependent barriers to reaction provide physical insight into the steric effect Whether they accurately reflect the anisotropy of the potential for reaction is not yet clear. For early barrier reactions and when the approach motion is rapid the orientation at reaction, probably is reasonably related to the experimental by the ADLCM model. Recrossing and other dynamical effects have not been included yet in the ADLCM on a profound physical basis. So far in the present study then-effects on the deduced barrier appear to be minor and intuitive. Trajectory studies such as those of Schechter et al. [26] and others [27] will provide more guidelines for interpretation of steric data. 

A potentially very significant finding from the trajectory studies is the trapping of trajectories in the central-barrier region of the potential energy surface, with concomitant recrossings of the barrier. The former suggests... 

Trajectory Studies of Sn2 Nucleophilic Substitution. II. Nonstatistical Central Barrier Recrossing in the CD -I- CH3CI System. 

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. 

The MP2/6-31G direct dynamics simulation study was later extended to cover the dynamics from the central barrier for the SN2 reaction of Cl I C2H5CI.104 The majority of the trajectories starting from the saddle point moved off the central barrier to form the Cl- C2H5CI complex. The results were different from those obtained previously for the CH3C1 reaction, in which extensive recrossing was observed. The reaction of C2H5CI was, in this sense, consistent with the prediction by the RRKM theory. However, some of the... 

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... 

In addition to the classical trajectory calculations, a variety of other theoretical studies have been done. Accurate quantum mechanical scattering results for zero total angular momentum have been reported for reaction (40). The reaction has also been studied by using transition-state theory (TST). Transition-state theory overestimates (compared to experiment) the thermal rate by a factor of about two. This may be caused by errors in the PES or to recrossings , that is, trajectories which pass through the transition state but quickly return to reactants rather than going on to form products (TST incorrectly counts these as reactive events). Studies are also being done to understand the spectroscopy of the transition state of this reaction. ... 

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