Eckart barriers mechanisms

Based on this physical view of the reaction dynamics, a very broad class of models can be constructed that yield qualitatively similar oscillations of the reaction probabilities. As shown in Fig. 40(b), a model based on Eckart barriers and constant non-adiabatic coupling to mimic H + D2, yields out-of-phase oscillations in Pr(0,0 — 0,j E) analogous to those observed in the full quantum scattering calculation. Note, however, that if the recoupling in the exit-channel is omitted (as shown in Fig. 40(b) with dashed lines) then oscillations disappear and Pr exhibits simple steps at the QBS energies. As the occurrence of the oscillation is quite insensitive to the details of the model, the interference of pathways through the network of QBS seems to provide a robust mechanism for the oscillating reaction probabilities. 

Fig. 6.2 (a) Bell (parabolic) and Eckart barriers, both widely used in approximate TST calculations of quantum mechanical tunneling, (b) Transmission probability (Bell tunneling) as a function of energy for two values of the reduced barrier width, a... 

Fig. 6.4.2 Tunneling probabilities for an Eckart barrier. The barrier height is 40 kJ/mol and the magnitudes of the imaginary frequency associated with the reaction coordinate are 1511 cm-1 (solid line), corresponding to the reaction H + H2, and 1511/ /2 cm-1 (dashed line), corresponding to the reaction D +D2. The step function is the transmission probability according to classical mechanics.

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