Tunneling swath

The region of coordinate space between the LC3 path at the lowest total energy for which tunneling must be considered and the region where a quadratic expansion about the MEP is valid is included in the reaction swath clearly the swath becomes wider when lower-energy tunneling processes must be considered. 

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. 

Babamov and Marcus have proposed tunneling models in which the tunneling paths correspond to a fixed hyper-radius, where the hyper-radius is the distance from the origin in mass-scaled hyperspherical coordinates. These require a knowledge of the potential over about the same swath as required for LC3 calculations. 

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. 

This chapter provides an account of our recent efforts to interface dynamics calculations based on reaction-path potentials and tunneling, including tunneling through the large-curvature reaction swath, with electronic structure theory. 

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