Collinearly dominant reaction

Another obvious defect of both the RLM and BCRLM models is that they assume a collinearly dominated reaction intermediate. While the potential energy surfaces for many collision systems do favor collinear geometries, there are of course many reactions which do not. Extensions of the BCRLM model are therefore needed to treat noncollinear systems, perhaps along the lines defined by the Carrington and Miller reaction surface Hamiltonian theory. 

The BCRLM is by its very nature constrained to treating collinearly dominated reaction processes. One could extend the method to non-colllnear systems by Including effective potential terms and more complicated kinetic energy operators to represent the motion of the reacting system along its (bent) minimum energy path from reactants to products. This is indeed an example of the Carrington and Miller reaction surface Hamiltonian theory, which at present is probably the most fruitful approach for noncollinear systems. 

The reaction probability for the Hi + OH shows a strong steric effect as reflected in its sensitive dependence on the initial rotational states of the reagents, especially the reactive diatomic Hi. As shown in Fig. 3, the reaction probability initially increases quite significantly as the reagent rotation increases. In particular the maximum of the reaction probability always shows up for the j = 1 state of H(D)i, which is believed to be a general phenomenon for collinearly dominated reactions at zero... 

In going from Eq. 4 to Eq. 5, we have assumed a collinearly dominant reaction with Erp > Eq(9=0) (otherwise we would have C3(Et) s 0). The angle 9max( ) in Eq. 5 is the maximum angle of attack at which reaction can occur, and is obtained from... 

This neglect of coupling between the two channels should be reasonable for reactions with potentials that are collinearly dominated, and have significant repulsive bending potentionals away from collinearity. 

These reactions are subject to stereoelectronic control. The transition state for S 2 displacement requires collinear (180°) disposition of the nucleophile (C ) and the leaving group L. In some cases, for steric reasons, 0-alkylation dominates over C-alkylation. See Section 6.3 below for additional details. 

Figure 9.11 illustrates time evolution of the nonequilibrium rate constant ki2(t) and the electronic population in the donor state Pi(f) in the course of the back-transfer reaction in a model ET complex (rigid collinear triatomic molecule with equivalent donor and acceptor sites separated by a neutral spacer) in a polar solvent. The long-time value of k 2(t) is seen to be much smaller than the maximum values it achieves during the relaxation process. Hence, it is the evolution of ki2(t) that dominates the electronic state population evolution at short times. After this rapid nonequilibrium stage of nuclear relaxation is over, with its eharaeteristie sequence of plateaus and dips, ET proceeds further very slowly in its usual way with a small (activated) equilibrium rate eonstant. 

Figure 10.12 Rotational alignment coefficient of the XeX product vs. the collision energy for the reaction of a fast Xe ( P2> beam with HX, X = Cl, Br, I. The dashed horizontal lines represent the maximum theoretical limit on the alignment [adapted from Simons (1987)]. The deviations of the experimental results from the spectator limit can be accounted for if there is a repulsive release of the exoergicity. Such an impulse can contribute significantly when the ejected atom is light and if the transition state is not collinear. With the available understanding of kinematic effects, experimental conditions can be chosen such that dynamical features arising from forces operating during the collision process can dominate.

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