Osculating model

The HOCO lifetime, estimated from the asymmetry in T( d) within the "osculating model" for chemical reactions [43], is about 0.6 ps at Ec = 59 kJ/mol and 1 ps at Ec = 36 kJ/mol, and compares well with the lifetime values measured by Zewail and co-workers [17a] and by Wittig and co-workers [17b] and with theoretical values [13,26]. 

To solve Eqs. 12 and 13 with oscUlating velocity boundary conditions, simple models such as the Couette flow model and ID Stokes model have been used. These models ignore the finite size and edge effects, as both of them model the device as two infinitely large parallel plates with one (the proof mass) oscillating on the top of the other (substrate). The Couette model further assumes a steady flow, resulting in a linear velocity profile between the plates. As shown later, the quality factor obtained by these two models is overpredicted by a factor of two, indicating the importance of 3D effects. 

Figure 11 Rigid dumbbell and multibead rod models. The unit vector u gives the direction from — v to +v, and = [Lv/2(N — l)]i = (va/2)ii gives the position of bead v with respect to the center of mass. The ratio dja is called (with 0< < 1) if ( = 1 the model is the osculating multibead rod ...

Fig. 17. Solid-angle differential cross section for the reaction 0( D) + H OH + H proceeding via the insertion-decomposition pathway. The best fit from the osculating complex model (OCM) is the solid curve which is shown superimposed on the histogrammic representation of the trajectory data. The collision energy is 2 kcal/mol. Arrows indicate the range of scattering angles obtained in the trajectory calculations.

The aS3rrametric forward-backward peaking may be modelled by assuming that the angular distribution, 1(0), can be factored into a term with forward-backward symmetry and an "osculation" term ... 

Summary of the application of the osculating complex model (OCM) to reactions of 0( D) with isotopic hydrogen molecules proceeding via the insertion-decomposition pathway. 

The direction in which the light atom leaves is uncorrelated with the initial direction of the carbon atom. Neither reaction channel, therefore, may be appropriately treated by the osculating complex model. 

One system is 0( D) with the (v=0,j=l) state of H2, HD, or D2 at a collision energy of 2 kcal/mol. Most reactions proceed via an intermediate complex. An analysis of the differential cross sections by the osculating complex model indicates that the average lifetime of the complex is less than or on the order of a rotational period. 

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