Small curvature tunnelling approximation

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. 

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. 

Most recently, Truhlar, Garrett, and co-workers employ a combination of various small-curvature SAG and large-curvature (straight-line tunneling) approximations [106,110,124,154,155]. 

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