Small-Curvature Tunneling

TST = conventional Transition State Theory, ICVT = Improved Canonical Variational Transition state theory, ICVT/SCT = ICVT/Small Curvature Tunneling, ICVT/p,OMT = ICVT/Microcanonical Optimized Multidimensional Tunneling. 

CCVTST/SCT denotes CVTST plus a small curvature tunnel transmission (SCT) coefficient. dAll vibrations treated by classical mechanics, tunneling and nonclassical reflection are neglected. Alhambra, C. et al. (see Figs. 11.10 and 11.11) employ the term classical . 

Melissas and Truhlar (1993a) studied the kinetic isotope effects (CD4/CH4) of Equation (71) using TST, CVT, and interpolated VTST (IVTST), which uses the small curvature tunneling (SCT) correction (Melissas and Truhlar 1993b). Their calculations show that accuracy of the KIE prediction increased dramatically from TST to IVTST. 

Alternative corrections are Eckart tunneling, multidimensional zero-curvature tunneling, and multidimensional small-curvature tunneling (Truhlar et al. 1982), in increasing order of accuracy. The last two involve points on the PES other than the first order saddle point and have more sophisticated calculations. 

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. 

In the small-curvature tunneling approximation, k(T) requires, in addition to some of the information detailed above, the curvature components Cm(,s) of the curvature of the reaction path, where each curvature component measures the projection of the curvature vector on a particular generalized normal mode direction m. Calculation of Kl-CT(r) or kPOMT(7 requires, in addition, values of the Bom-Oppenheimer potential V in the reaction swath, typically at points where it cannot be computed from the available harmonic expansion around the MEP. 

The IVTST method is presently developed only for small-curvature tunneling. Since large-curvature tunneling often proceeds through regions far from the MEP, it is not clear if this could be interpolated reliably using only the data used for the presently developed interpolation schemes. Further work to extend the IVTST method to large-curvature systems would be desirable. 

Even for small-curvature tunneling, a difficulty with the IVTST method as applied so far is that the nonstationary points on the MEP are very near the saddle point. This is primarily a matter of economics since it is less expensive to follow the MEP only a shoit distance. This could be circumvented in the future by various strategies. For example, one could take a few or several gradient-only points with Ss < As before calculating the additional nonstationary-point hessians, or one could generalize the method to use points off the MEP. 

Another area where technical advances are in progress is the treatment of the vibrations perpendicular to the reaction path. A central assumption of all reaction-path methods, including variational transition state theory and small-curvature tunneling methods, is the separation of the coordinates into three sets external coordinates describing the overall translation and rotation, a reaction coordinate describing the motion of the system along some direct route from reactants to products, and the remaining coordinates, which will be called the bound vibrational coordinates. 

A study of the reaction between Me-OBr and Cl has been carried out at the QClSD(T)/6-311-l-l-G(3df,2p)//MP2/6-311-l-G(d,p) level of theory using canonical variational TST with a small curvature tunneling correction. The calculations predict an anti-E2 elimination accompanied by a small amount of a syn-El elimination reaction that increases in importance as the temperamre is increased and an even smaller amount of S 2 0 reaction giving CH3-OCI. The energy barriers, transition structures, rate constants, and temperature dependences of the rate constants between 200 and 3000 K are given for the three reactions. 

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