DIPR model

The modified spectator stripping model (polarization model) thus appears to be a satisfactory one which explains the experimental velocity distribution from very low to moderately high energies. The model emphasizes that the long-range polarization force has the dominant effect on the dynamics of some ion—molecule reactions. However, a quite different direct mechanism based on short-range chemical forces has been shown to explain the experimental results equally satisfactorily [107, 108]. This model is named direct interaction with product repulsion model (DIPR model) and was originally introduced by Kuntz et al. [109] in the classical mechanical trajectory study of the neutral reaction of the type 

While the polarization model does not predict angular distribution, the DIPR model does the product ion will be scattered forward with respect to the direction of the primary ion beam for all values of such that 1 p 1 1. From eqn. (83), this will occur for Fr 3.6 kcal mole when w = 0.265 and for Fr 14.2 kcal mole when u =—0.578. This forward scattering down to quite low energies is also consistent with the experimental findings [110]. 

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A widely-used model in this class is the direct-interaction with product repulsion (DIPR) model [173—175], which assumes that a generalised force produces a known total impulse between B and C. The final translational energy of the products is determined by the initial orientation of BC, the repulsive energy released into BC and the form of the repulsive force as the products separate. This latter can be obtained from experiment or may be assumed to take some simple form such as an exponential decay with distance. Another method is to calculate this distribution from the quasi-diatomic reflection approximation often used for photodissociation [176]. This is called the DIPR—DIP model ( distributed as in photodissociation ) and has given good agreement for the product translational and rotational energy distributions from the reactions of alkali atoms with methyl iodide. 

The mechanism of the electron transfer and the subsequent dynamics of the system have both been oversimplified at the moment. A more refined model of the dynamics is discussed in the next section the direct interaction with product repulsion (DIPR) model and its variant called DIPR-DIP(DIP-distributed as in photodissociation). The purpose of sections 2.4 and 2.5 is to explicit the multi-dimensional and multi-PES character of the electron jump step. 

More precisely, the DIPR model is founded on the following set of assumptions, as shown in the pictorial representation in Figure 4. 

The DIPR model is often used to help in understanding the stereodynamics of direct reactions [82-85]. The important parameter of the model is thus the electron-transfer probability as a function of the molecular orientation. The same parameter, which actually defines the best geometry of the system in the electron transfer step, also plays a role in determining the product alignment in chemiluminescent reactions [86, 87]. A new model has been introduced recently, the anisotropic impulsive model [88]. It is conceptually close to the DIPR model, and also helps to determine the preferred angle of approach between the reactants. 

Equation (84) contains a single parameter w which can be chosen to give the best fit to the experimental data, just as the polarization theory by Herman et al. [103] includes an adjustable parameter tr. In order to obtain the values of w, Kuntz et al. fitted eqn. (84) to the nineteen representative experimental points for reaction (71), taken from the work by Hierl et al. [110], by the method of least squares. Figure 13 shows two best fits corresponding to u = —0.578 and w = 0.265, together with the best fit of the polarization theory, eqn. (78). It is seen from the figure that both the polarization and DIPR models agree equally well with... 

As mentioned previously, the modified spectator stripping model (polarization model) of Herman et al. [103] explains the velocity distribution of products very well but does not predict the angular distribution, whereas the DIPR model explains both. Thus there had been no full comparison between the two models until Chang and Light [113] refined and extended the polarization model to yield the angular distribution of products as well. 

A special case of our consideration is the spectator limit. Here the old bond has no energy and so Q2 = 0. Because Ej = Q2/2 (and similarly for E ) E = cos Et. In the DIPR model, one modifies the basic approximation by assuming that bond switching is accompanied by adding a sudden repulsion. This repulsion imparts a large extra velocity, say q, along the old bond Q2, so that... 

F. The DIPR model. The model improves on the simple kinematic limit for direct reactions by adding repulsion between the products. See P. Kuntz, Trans. Faraday Soc. 66, 2980 (1970) for a detailed analytical treatment and Truhlar and Muckerman (1979) for a review. Here we just consider the instantaneous product repulsion, (a) Show that you can add an impulse along both the products separation coordinates by modifying the equation in Problem A to... 

A detailed account of the DIPR model P. Kuntz, Trans. Faraday Soc. 66,2980 (1970). 

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