Backward scattering mechanism

Figure 12, Schematic mechanism for impulsive reaction of thermal energy reaction of K with oriented CF3I. The electron is assumed to be transferred at large distance to the molecule irrespective of orientation. The molecular ion is formed in a repulsive state that promptly dissociates, ejecting the T ion in the direction of the molecular axis, and the K is dragged off by the departing T resulting in backward scattering for heads orientation and forward scattering for tails as observed.

Reactions showing backward scattering have small impact parameters and cross sections. The mechanism is called rebound because P hits MN head on, pulls M away from N and, under the influence of the repulsive forces between M and N, PM moves almost totally backwards. N also rebounds backwards from PM under the same repulsive forces, and returns only slightly deflected from its original path (Figure 4.12). 

Repulsive surfaces are associated with the backward scattering of a rebound mechanism, in which A collides with BC in a head-on collision and AB rebounds backwards. 

The rebound mechanism showing backward scattering and small cross sections is typified by... 

The back reaction will have the exact reverse characteristics. The activated complex will lie in the exit valley, and reaction will be enhanced by high vibrational energy. There will be high translational energy in the products, the cross section will be small, and the molecular beam contour diagram will show predominantly backward scattering, typical of a rebound mechanism. 

The models treated by these authors differ not only in the choice of the coupling constants, i. e. whether the backward scattering is included or not, but also in the choice of the physical cut-off parameter. The cut-off has to be introduced in any perturbational calculation to avoid the ultraviolet non-physical divergences. In the field theoretical treatment of the corresponding models (7) the cut-off plays no role since the Thirring model is renormalizable in field theoretical sense, in the statistical mechanical treatment, however, we will keep the cut-off. 

Reactions having small cross sections, in which there is backward scattering of the reaction products. The mechanism is then said to be a rebound mechanism. 

Crossed beam studies of near-thermal F + D2 and F + CD4 reactions yielded direct mechanisms with predominantly backward scattering of DF (l ). 

The reaction exoergic D2 + OH D + DOH is observed to form DOH primarily in the v = 2 state of the D—O stretch with only a small amount of bending excitation and essentially no energy in the OH vibration. This is as expected from the discussion of the reversed reaction in Section 1.2.4. The DOH product is backwards scattered as is DF from the D2 + F reaction, which is consistent with a mechanism where reaction occurs when the two reactants run head-on into one another. 

At the time the experiments were perfomied (1984), this discrepancy between theory and experiment was attributed to quantum mechanical resonances drat led to enhanced reaction probability in the FlF(u = 3) chaimel for high impact parameter collisions. Flowever, since 1984, several new potential energy surfaces using a combination of ab initio calculations and empirical corrections were developed in which the bend potential near the barrier was found to be very flat or even non-collinear [49, M], in contrast to the Muckennan V surface. In 1988, Sato [ ] showed that classical trajectory calculations on a surface with a bent transition-state geometry produced angular distributions in which the FIF(u = 3) product was peaked at 0 = 0°, while the FIF(u = 2) product was predominantly scattered into the backward hemisphere (0 > 90°), thereby qualitatively reproducing the most important features in figure A3.7.5. 

This observation is the first part of the cancellation puzzle [20, 21, 27, 29]. We know from Section lll.B that we should be able to solve it directly by applying Eq. (19), which will separate out the contributions to the DCS made by the 1-TS and 2-TS reaction paths. That this is true is shown by Fig. 9(b). It is apparent that the main backward concentration of the scattering comes entirely from the 1-TS paths. This is not a surprise, since, by definition, the direct abstraction mechanism mentioned only involves one TS. What is perhaps surprising is that the small lumps in the forward direction, which might have been mistaken for numerical noise, are in fact the products of the 2-TS paths. Since the 1-TS and 2-TS paths scatter their products into completely different regions of space, there is no interference between the amplitudes f (0) and hence no GP effects. 

A chemical reaction is then described as a two-fold process. The fundamental one is the quantum mechanical interconverting process among the states, the second process is the interrelated population of the interconverting state and the relaxation process leading forward to products or backwards to reactants for a given step. These latter determine the rate at which one will measure the products. The standard quantum mechanical scattering theory of rate processes melds both aspects in one [21, 159-165], A qualitative fine tuned analysis of the chemical mechanisms enforces a disjointed view (for further analysis see below). 

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