Caustics in Chemical Reaction Dynamics

The second example is a three-dimensional triatomic chemical reaction mimicking the reaction C + H2 CH - - H for total angular momentum J = 0. The motivation here is naturally to make it possible to take into account the effects of tunneling in chemical reaction dynamics in both classical and semiclassical treatments. In order to run tunneling trajectories in the classically forbidden region, it is inevitable to find caustics along each trajectory in the classically allowed region. We have used the DIM (diatomics-in-molecule) potential matrix of CH2 [209-211]. The DIM matrix 

FIGURE 9.6 Family of reactive trajectories in the ground adiabatic potential energy surface determined by Equation (9.11). The crosses indicate caustics. (Taken from Reference [47] with permission.) 

Without loss of generality, a triatomic system can be described by the Jacobi coordinates. Then using the assumption that the center of mass is stationary and 

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