Reaction dynamics RRKM theory

Extensions of this statistical thermodynamical approach to estimating reaction rates include the RRK and RRKM theories of unimolecular decay rates, and the information theoretic formulation of reaction dynamics. These theories are remarkably successful, although generally more successful at interpreting experimental data and correlating results than at deriving results a priori. 

The existence of the polyad number as a bottleneck to energy flow on short time scales is potentially important for efforts to control molecnlar reactivity rising advanced laser techniqnes, discussed below in section Al.2.20. Efforts at control seek to intervene in the molecnlar dynamics to prevent the effects of widespread vibrational energy flow, the presence of which is one of the key assumptions of Rice-Ramsperger-Kassel-Marcns (RRKM) and other theories of reaction dynamics [6]. 

A situation that arises from the intramolecular dynamics of A and completely distinct from apparent non-RRKM behaviour is intrinsic non-RRKM behaviour [9], By this, it is meant that A has a non-random P(t) even if the internal vibrational states of A are prepared randomly. This situation arises when transitions between individual molecular vibrational/rotational states are slower than transitions leading to products. As a result, the vibrational states do not have equal dissociation probabilities. In tenns of classical phase space dynamics, slow transitions between the states occur when the reactant phase space is metrically decomposable [13,14] on the timescale of the imimolecular reaction and there is at least one bottleneck [9] in the molecular phase space other than the one defining the transition state. An intrinsic non-RRKM molecule decays non-exponentially with a time-dependent unimolecular rate constant or exponentially with a rate constant different from that of RRKM theory. 

One example of non-IRC trajectory was reported for the photoisomerization of cA-stilbene.36,37 In this study trajectory calculations were started at stilbene in its first excited state. The initial stilbene structure was obtained at CIS/6-31G, and 2744 argon atoms were used as a model solvent with periodic boundary conditions. In order to save computational time, finite element interpolation method was used, in which all degrees of freedom were frozen except the central ethylenic torsional angle and the two adjacent phenyl torsional angles. The solvent was equilibrated around a fully rigid m-stilbene for 20 ps, and initial configurations were taken every 1 ps intervals from subsequent equilibration. The results of 800 trajectories revealed that, because of the excessive internal potential energy, the trajectories did not cross the barrier at the saddle point. Thus, the prerequisites for common concepts of reaction dynamics such TST or RRKM theory were not satisfied. 

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... 

The RRKM theory is a ubiquitous tool for studying dissociation or isomerization rates of molecules as a function of their vibrational energy. Still highly active in the theoretical field, Marcus has tackled such issues as the semiclassical theory for inelastic and reactive collisions, devising reaction coordinates, new tunneling paths, and exploring solvent dynamics effects on unim-olecular reactions in clusters. 

Rice et al. [99] developed a global potential energy surface based on the Mowrey et al. [103] results and performed extensive classical trajectory calculations to study the dynamics of the CH2NN02 dissociation reactions. They calculated rates for reactions (III) and (IV) with classical barriers of 35 and 37 kcal/mol, respectively. They found that N-N bond fission dominates at low energy but that HONO elimination is competitive. Chakraborty and Lin [104] predict the opposite on the basis of their ab initio barriers and RRKM theory calculations. The two dissociations channels are closely competitive and it is not clear that ab initio methods are sufficiently reliable to distinguish between two reactions that have such similar energy requirements. Also, the Zhao et al. results [33] are not in accord with the theoretical predictions. 

The dynamics of the H-I-C2H4 association step deposits the 40 kcal/mol reaction exothermicity and the 30 kcal/mol relative translational energy non-randomly in the energized C2H5 radical, with the C-H bond, that is formed, preferentially excited as compared to the other C-H bonds. The expectation is that this non-random excitation may lead to an initial dissociation rate that is larger than that of RRKM theory. However, C2H5 is... 

Most of us are preconditioned by the conventional wisdom developed over the last 30 years or so to think of unlmolecular decay rates as being dominated by statistical factors rather than by microscopic features of the dynamics. This Is the basis of the RRK and RRKM theories which have been generally successful In Interpreting thermal rate data for unlmolecular reactions (24). 

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