Tunneling reaction path curvature

As a first approximation we will assume that the reaction-path curvature can be neglected, but we will eliminate this approximation after Eq. (27.22) because the curvature of the reaction path is very important for tunneling. 

Reaction path curvature is actually a vector with 3N — 7 components [80]. Each component is associated with a particular generalized normal mode, and it measures the extent to which the system curves into a particular direction as it progresses along the MEP. Corner-cutting tunneling involves a coupled motion involving the reaction coordinate and all the generalized normal modes that are associated with nonzero curvature components [81]. 

When reaction-path curvature is small, the tunneling is dominated by paths on... 

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). 

The conditions (133.HI) mean that the tunneling through the adiabatic potential barriers (99.HI) is neglected however, the non-adiabatic transitions from a lower to a higher electronic state are not excluded. The reflexion effects due to the reaction path curvature may be simply included in the dynamical definition (121.11) of the reaction coordinate. An adiabatic separation of that coordinate may be also used as an approximation at these conditions. Then, the "transmission coefficient — 1 takes into account only sudden changes... 

For intermediate reaction-path curvature, one may use either the SCSA or LC3 approximation, but even more accurate results are obtained by a least-action (LA) method.In the LA method, the tunneling paths are linear interpolations between the MEP and the LC3 paths. Thus this method does not require knowing the potential over a wider swath than is necessary for the LC3 method. 

If accurate tunneling corrections are required, the situation rapidly becomes more complicated. Issues related to separability of motion along the reaction coordinate, curvature of the reaction coordinate, and multidimensional tunneling arise and must be dealt with. Marcus and Coltrin [51] found that reaction path curvature forces the reaction to cut... 

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