Cut the corner

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

What seemed to be a similar "energy anomaly had been reported by Blais and Bunker [303]. They also found that there was a reduction in the vibrational energy yield when A was light but their potential possessed considerable long-range attraction. However, this effect did not survive a modification of their potential and the extension of the calculations to three dimensions [305]. Nevertheless, the exact conditions under which the light-atom anomaly appears are not yet entirely clear. Calculations by Bunker and Parr [319] on a wide-corner potential, that is, one on which the reaction path on the collinear surface cuts the corner [210], showed no indication of the light-atom anomaly, and it seems that still more study will be required before the interrelations between the way different surfaces display this phenomenon can be completely understood [319],... 

When I was a flight engineer, you re not expected to know anything so you can ask dumb questions like, Oh, are we meant to be in Nav Mode now Yeah Oh, the Flight Director s not working Oh no, I m just cutting the corner. What No,... 

The wave function decays most slowly if the system tunnels where the effective barrier is lowest however, the distance over which the decay is operative depends on the tunneling path. Therefore, the optimum tunneling paths involve a compromise between path length and effective potential along the path. As a consequence, the optimum tunneling paths occur on the concave side of the minimum energy path i.e., they cut the corner... 

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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