Rates Reaction path curvature

In practice, we approximate the exact transmission coefficient by a mean-field-type of approximation that is we replace the ratio of averages by the ratio for an average or effective potential. For gas-phase reactions with small reaction-path curvature, this effective potential would just be the vibrationally adiabatic ground-state potential. In the liquid phase and enzymes we generalize this with the canonical mean-shape approximation. In any event, though, the transmission coefficient should not be thought of as a perturbation. The method used here may be thought of as an approximate full-dimensional quantum treatment of the reaction rate. 

D. K. Bondi, J. N. L. Connor, B. C. Garrett, and D. G. Truhlar, Test of variational transition state theory with a large-curvature tunneling approximation against accurate quantal reaction probabilities and rate coefficients for three collinear reactions with large reaction-path curvature Cl + HC1, Cl + DC1, and Cl + MuCl, 7. Chem. Phys. 78 5981 (1983). 

In Figure 19a, the reaction path curvature k(s) is shown as a function of the reaction coordinate s. There are two distinct peaks of k(s) in the transition state (TS the location of the TS is defined by s = 0) region at s = -0.1 and 0.7 amu /2 Bohr (peaks k2 and k3), which are associated with the normal modes 11/8 (i.e. 11 before and 8 after the avoided crossing at s = -0.3) and to some smaller extend with modes 5 and 8/11 as the decomposition of k(s) in terms of normal mode contributions reveals. If energy is stored in mode 11/8, it will be channelled into the reaction path mode and lead to rate acceleration. Dissipation of energy into mode 8/11 is small since the avoided crossing between modes 11 and 8 at s =... 

Test of Variational Transition State Theory with a Large-Curvature Tunneling Approximation Against Accurate Quantal Reaction ProbabiUties and Rate Coefficients for Three Collinear Reactions with Large Reaction-Path Curvature Atomic Chlorine -I- Hydrogen Chloride, Atomic Chlorine + Deuterium Chloride, and Atomic Chlorine + MuCl. 

It has been shown that there is a two-dimensional cut of the PES such that the MEP lies completely within it. The coordinates in this cut are 4, and a linear combination of qs-q-j. This cut is presented in fig. 64, along with the MEP. Motion along the reaction path is adiabatic with respect to the fast coordinates q -q and nonadiabatic in the space of the slow coordinates q -qi-Nevertheless, since the MEP has a small curvature, the deviation of the extremal trajectory from it is small. This small curvature approximation has been intensively used earlier [Skodje et al. 1981 Truhlar et al. 1982], in particular for calculating tunneling splittings in (HF)2- The rate constant of reaction (6.45a) found in this way is characterized by the values T<. = 20-25 K, = 10 -10 s , = 1-4 kcal/mol above T, which compare well with the experiment. 

In studies of the reactions of S-(4-nitrophenyl) 4-methylthiobenzoate with a series of six secondary alicyclic amines and a series of eight pyridines in 44 wt% ethanol-water at 25 °C, the Brpnsted-type plots were non-linear with the curvature centre defined as pK(j located at pK.d 9.7 and 9.4 for the reactions of secondary alicyclic amines and pyridines, respectively. The plots are consistent with a zwitterionic tetrahedral intermediate on the reaction path and, as the basicity of the amine increases, a change in rate-determining step from its breakdown to its formation.47... 

The first applications (230-234) concerned a study of the dependence of the tunneling effect on the curvature of the reaction path, of an energy transfer among different vibrational modes in the course of a reaction, and of the evaluation of microcanonical rate constants for study-case reactions, HCN - CNH, H2CO -> H2 + CO, H2CC -> HC=CH, and proton transfer in malonaldehyde. 

Working with a similar model Fischer and Ratner (1972) developed a theory applicable to polyatomics, but simplified in practice by introduction of reaction path variables, s, along the path and p for the other degrees of freedom (neglecting rotations). Rather than focusing on cross sections, they developed expressions for rate coefficients to predict the effect on vibrational excitation of products of relative energy, curvature of the reaction path, changes in normal-mode frequencies and position of the saddle point of the surface. 

In general, proton transfer occurs via a combination of over-barrier and through-barrier pathways. The rate constant of over-barrier transfer is usually calculated by standard transition state theory (TST) [22] by separating the reaction coordinate from the remaining degrees of freedom. If tunneling effects and the curvature of the reaction path are neglected, this leads to the expression... 

A qualitatively appealing feature of the RPH is that the kinematic coupling between motion along the reaction coordinate and the vibrational modes is made explicit in the matrix elements. From the early work of Polanyi and co-workers on collinear triatomic reactions, we know that from the position of the saddle point relative to the corner in the reaction path, qualitative conclusions can be drawn about the effect of the energy distribution in the reactants on the rate and about the distribution of energy in the products [20, 22]. The Bj appear to contain quite analogous and quite detailed information about curvature effects for polyatomic systems, identifying which modes should couple to (and... 

The results discussed in the previous section reveal that the reaction rate corresponding to the formation of major by-products of the oxidation reaction is important to determine the lifetime of dimethylphenol in the atmosphere. The rate constants are calculated using canonical variational transition state theory (CVT) with small curvature tunneling (SCT) corrections over the temperature range of 278-350 K. As described in Figure 19.2, the formation of product channels consists of four reaction channels. The rate constants for the formation of alkyl radical (11), peroxy radical (12), m-cresol and the product channels are designated as k, ki2, and kp, respectively, and are summarized in Tables 19.2 and 19.3. The reaction path properties and rate constant obtained for the most favorable product channels, P5 and P6, are discussed in detail. 

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