Corner-cutting trajectory

The cross indicates the saddle point. One possible corner-cutting trajectory is shown (schematic). The unbound initial state corresponds to a gas-phase reaction. (From Ovchinnikova [1979].)... 

Physically the cutting-corner trajectory implies that the particle crosses the barrier suddenly on the time scale of the slow -vibration period. In the literature this approximation is usually called sudden , frozen bath and fast flip approximation, or large curvature case. In the opposite case of small curvature (also called adiabatic and slow flip approximation), coj/coo < sin tp, which is relevant for transfer of fairly heavy masses, the MEP may be taken to a good accuracy to be the reaction path. 

Figure 5.9 A potential energy contour diagram for a reaction with a late barrier, following a cutting the corner trajectory...

Since 1971, persistent efforts have been made to relate the experimental results from the F + H2, D2 and HD reactions to potential surfaces via trajectory calculations.All surfaces have been of the repulsive type and favor collinear approach of F to H2. The calculated results lead to rather large , even on the repulsive surfaces, because of the mixed energy release that is characteristic of the F-H-H mass combination, i.e., the H H repulsive energy is released while the Rhf distance is still extended, which for collinear collisions corresponds to trajectories that cut the corner of the potential energy surface. However, the surfaces do differ in specific ways and the calculations illustrate various consequences emanating from these small differences. It is beyond the scope of this discussion to consider the individual potential surfaces and attention will be focused on the calculations that permit comparisons with energy disposal data (see Table 2.20). The collinear ab initio surface was fitted to a semiempirical expression that subsequently was used in a one-dimensional trajectory calculation to obtain... 

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