Cone of acceptance

Figure 20-18 (a) Optical fiber construction and (b) principle of operation. Any light ray entering within the cone of acceptance will be totally reflected at the wall of the fiber. 

Fig. 9.10 Construction of optical fiber and the coupling geometry defining the cone of acceptance...

The N.A. is the numerical aperture of the fiber and defines the cone of acceptance in terms of refractive indices only. The half-angle o of the cone of acceptance is given by (9.28). 

Here, the phenyl radical once again attacks the unsamrated bond. However, the steric effect and larger cone of acceptance (the methyl group screens the p carbon atom and makes it less accessible to addition) direct the addition process of the radical center of the phenyl radical to the a carbon atoms of methylacetylene and propylene (the carbon atom holding the acetylenic hydrogen atom). Consequently, crossed beam reactions with complex hydrocarbon molecules can be conducted and valuable information on the reaction pathways can be derived if (partially) deuterated reactions are utilized. 

R. Brooks [42-44] the process of electron transfer for K to oriented t-butyl bromide is found strongly dependent on the orientation. Systems involving metal atoms are traditional favorites of molecular beam studies, particularly of stereodynamics. In recent experiments [45], with brute force oriented ICl, experimental determination was made of the cone of acceptance for reactivity (steric effect) in a "harpooning" reaction, Sr + ICl leading to electroiucally excited products detected via their chemiluminescence... 

A natinal extension of the classical LOG model, in which the orientational dependence of the barrier to reaction is taken into account and which leads to the concept of a cone-of-acceptance which depends on collision energy, was proposed by Smith [1,5] and independently by Levine and Bernstein [6], although, as later pointed ont by Levine [7], these models are similar to that suggested as long ago as in 1932 by Pelzer and Wigner... 

A schematic diagram of the surface is shown in Fig. 15. From the centre-of-mass of the HD molecule, a cone of acceptance for the H isotope... 

The slow descent is a consequence of the already large apex angle of the cone of acceptance (2Ayc = 160P). 

In comparison with the results of Section 3.2 (see Table 2), the steric cone of acceptance, Yc 10 decreased quite strongly, from 117 to 78 . This means... 

There is a growing interest in the role of steric effects on the dynamics of elementary chemical reactions [1-11,16-18]. In particular, the steric requirements of a reaction can provide information about the anisotropy and associated cone of acceptance of the potential energy surface. 

The variation of absolnte intensities as a fnnction of 9 depends on the spectrometer design. For many instruments, the space resolution is controlled by acting on the electron collection system, and thus /(0) is not a constant and is not known. Nevertheless, the significance of apparent concentration ratios should be examined in the light of variations of absolute intensities. One should be particularly careful at extreme 9 values as shadowing effects as well as intersection between the sample surface and the cone of acceptance angles for photoelectron collection may be responsible for weak intensities, the ratio of which is neither accurate nor precise. 

An iodine atom is bulky compared to the CH3 group so that the methyl can shield the iodine from the attack only when it is directly in the way. For our earlier example, the Cl + HI reaction, the steric hindrance will be more effective and the cone of acceptance for reaction is expected to be mnch narrower because the Cl atom needs to reach the small H atom, which we expect to be effectively shielded 1 the buUqr I atom. The computational evidence is that in less than a third of aU Cl + HI collisions can the Cl atom come within the cone of acceptance for reaction, a cone spanned by the H atom. 

The cone of acceptance can depend on energy and on the impact parameter... 

The simplest intuitive idea of an atom ora group being in the way ofthe reaction corresponds to a barrier that has a constant height Eq for all approach angles y < Yo, and is infinitely repulsive otherwise. Then yniax = Yo and the cone of acceptance is -independent. This model for o(y) is simpler than Eq. (3.36) but captures well the idea of a steric hindrance and the reactive asymmetry. It leads to a steric factor p given (1 — cos yo)/2. We expect the size of molecules to... 

K. Steric factor for ion-molecule reactions. Purpose to compute the cone of acceptance for reaction. Section 3.2.7.1, for the model discussed in Problem H. When the molecule is not spherical, e.g., H2, the long-range potential depends not only on the ion nolecule distance but also on the orientation angle, y, between the axis of the molecule and the ion-molecule distance R, see Eq. (2.18). (a) For a non-polar molecule we can take this into account by... 

M. The line-of-centers model with a steric requirement, (a) Derive the result (3.35) for the energy dependence of the reaction cross-section when the barrier depends on the approach angle. The point is that you will have to be care fid about the limits of integration and this will make you think in detail about the energy dependence of the cone of acceptance. See Smith (1980). (b) Derive the results... 

Exploring the dynamics using classical trajectories can provide more than a validation of om intnitive view of the cone of acceptance for reaction, Figme 1.5. Nor are they limited to the simple A - - BC problem. A much-studied example is the prototype Sn2 reaction... 

Figure 5.22 Polar representation of the H3 potential energy. Shown is the potential, for a fixed reactant bond distance, as a function of the distance of the approaching H atom from the center of H2 and of the approach angle, cf. Figure 5.3. The two plots are for H2 at its equilibrium separation and for a higher bond distance. Note how a cone of acceptance opens up when the reactant bond is stretched [adapted from I. Schechter, R. Kosloff, and R. D. Levine, Chem. Phys. Lett. 121,297 (1985)].

The cone of acceptance plays a key role in describing steric effects in collisions, and many further extensions and modifications have appeared in the literature, see for example Levine... 

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