Centrifugal barrier models

Another approach is to abandon the full description of solid state effects, and to study more closely the atomic description, in the hope of identifying mechanisms which might then be adapted and included in a model of the solid. 

A well-known example of critical phenomena encountered in solid state physics is the pressure-sensitive isomorphic phase transition in the amorphous solid SmS [621]. A similar effect is the a-y transition on solid Ce. In both cases, the structure of the solid does not change, but there is 

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The 7-shifting method depends on our ability to identify a unique bottleneck geometry and is particularly well suited to reactions that have a barrier in the entrance channel. For cases where there is no barrier to reaction in the potential energy surface, a capture model [149,150,152] approach has been developed. In this approach the energy of the centrifugal barrier in an effective onedimensional potential is used to define the energy shift needed in Eq. (4.41). For the case of Ai = 0, we define the one-dimensional effective potential as (see Ref. 150 for the case of AT > 0)... 

Moments of inertia at fixed geometries are calculated by changing only the bond distance in the reaction coordinate. The potential energy surface along the reaction coordinate is modeled by a Morse function including the centrifugal barrier [48]... 

It is evident that the major effects on the values for and e related to the value of n and to the reduced mass. Thus, the H loss reactions have centrifugal barriers that are as high as the rotational energy in the molecule. On the other hand, loss of a massive particle results in barriers that are much smaller than the molecular rotational energy. While this model drastically simplifies the reaction by ignoring the rotations of the products, the uniqueness of the H loss reaction demonstrated by these results is accurate. 

Chesnavich and Bowers (1977a,b 1979) modified the phase space theory model by assuming (a) an orbiting transition state located at the centrifugal barrier, and (b) that orbital rotational energy at this transition state is converted into relative translational energy of the products. The Hamiltonian used for this orbiting transition state/phase... 

Another system which has been treated in a rather complete manner is the dissociation of HOOH (Brouwer et al., 1987). The rates as well as the product energy distributions were calculated. As with the NO2 reaction, the interaction potential was assumed to have no barriers so that Ef for each HOOH reaction channel is assumed to be associated with the centrifugal barrier. In order to calculate this barrier, the reaction is treated as a triatomic dissociation, ABC AB + C. The effective rotational constant, at the centrifugal barrier is calculated according to formulas derived by Troe (1983). In addition, the model was simplified by replacing two adjustable parameters, a (from the interpolation function) and B (from the Morse potential), by their ratio, a/p. A value of 0.44 was found to adequately account for the data. Figure 7.25 shows the comparison of the SACM k E) curves with those obtained from experiments or trajectory calculations. 

A VRRKM/ECC model for product vibrational and rotational distributions was introduced by Wardlaw and Marcus (1988). Subsequently, Marcus (1988) constructed a refined version which successfully describes rotational quantum number distributions of products arising from the decomposition of NCNO (Klippenstein et al., 1988) and CH2CO (Klippenstein and Marcus, 1989). In the latter model, the conserved modes are assumed vibrationally adiabatic (as in SACM) after passage through the transition state and, consequently, the distribution of vibrational quantum numbers for the products is the same as it is at the transition state. The transitional modes are assumed nonadiabatic between the variationally determined TS and a loose TS located at the centrifugal barrier. [These are the same two transition states associated with the TS switching... 

A full analysis, similar to that for two-body radiative combination (Section 3), is difficult because of this steep variation of 1V R). However, because fV R)lh is much larger than radiative transition probabilities, a completely different approach is possible, of which the simplest example is an orbiting model, in which aU collisions surmounting the centrifugal barrier lead to ionization, with the transition restricted solely to the inner turning-point, Rc. By assuming a form for fV(R), the possibility... 

At the simplest level, it is assumed that a necessary and sufficient condition for reaction is that the colliding reactants must surmount the centrifugal barrier in the effective radial potential. A model for the ion-molecule potential must then be assumed when that chosen is the ion-induced-dipole potential, this approach yields, of course, the familiar Langevin model. ... 

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