Tunnelling Truhlar small curvature

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]. 

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. 

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