Potential energy diagrams three-dimensional

There is another useiiil way of depicting the ideas embodied in the variable transition state theory of elimination reactions. This is to construct a three-dimensional potential energy diagram. Suppose that we consider the case of an ethyl halide. The two stepwise reaction paths both require the formation of high-energy intermediates. The El mechanism requires formation of a carbocation whereas the Elcb mechanism proceeds via a caibanion intermediate. 

Three-dimensional potential energy diagrams of the type discussed in connection with the variable E2 transition state theory for elimination reactions can be used to consider structural effects on the reactivity of carbonyl compounds and the tetrahedral intermediates involved in carbonyl-group reactions. Many of these reactions involve the formation or breaking of two separate bonds. This is the case in the first stage of acetal hydrolysis, which involves both a proton transfer and breaking of a C—O bond. The overall reaction might take place in several ways. There are two mechanistic extremes ... 

There are examples of each of these mechanisms, and a three-dimensional potential energy diagram can provide a useful general framework within which to consider specific addition reactions. The breakdown of a tetrahedral intermediate involves the same processes but operates in the opposite direction, so the principles that are developed will apply equally well to the reactions of the tetrahedral intermediates. Let us examine the three general mechanistic cases in relation to the energy diagram in Fig. 8.3. 

Fig. 8.3. Three-dimensional potential energy diagram for addition of a proton and nucleophile to a caibonyl group, (a) Proton transfer complete before nucleophilic addition begins (b) nucleophilic addition complete before proton transfer begins (c) concerted proton transfer and nucleophilic addition.

Figure 6 Schematic potential energy diagrams for the interaction between O2 and Ag(l 11). Four panels are shown. In (a), the three states into which O2 can adsorb at the surfaces are depicted as a function of a reaction coordinate. In (b), the two potentials leading to direct inelastic scattering are shown. In (c), a trajectory representing a one dimensional representation of transient trapping-desorption in the O2 state is shown. In (d), two path ways leading to dissociative chemisorption are shown. From Kleyn et al. [45],...

For a triatomic molecule U will be a function of three internuclear distances, and a potential-energy diagram analogous to Fig. X.2 for a diatomic molecule would have to be constructed in four dimensions. For such a case we can construct a three-dimensional model in which we can... 

Fig. 4. Three-dimensional potential-energy diagram for the reaction AH-I-B A -I-The dotted line represents the reaction coordinate and the double arrow the vibration mode of the hydrogen in the transition state (Eqns. 27 and 28).

What information is provided by the fact that the Brdnsted a decreases as the acidity of the alcohol increases Discuss these results in terms of a three-dimensional potential energy diagram with the extent of O—H bond formation and the extent of C—O bond breaking taken as the reaction progress coordinates. 

Three-dimensional potential energy diagram for addition of a proton and nucleophile to a carbonyl group... 

Graphical representation of the saddle point (here marked with an X) for the transfer of atom B as the substance A-B reacts with another species, C. Potential energy is plotted in the vertical direction. Note also that the surface resembles a horse saddle, with the horn of the saddle closest to the observer. As drawn here, the dissociation to form three discrete species (A + B J- C) requires much more energy than that needed to surmount the path that includes the saddle point. A two-dimensional "slice" through a saddle point diagram is typically called a reaction-coordinate diagram or potential-energy profile. 

For further discussion of three-dimensional reaction coordinate diagrams for these processes, see Section 5.4, p. 246, and (a) W. P. Jencks, Chem. Rev., 72, 705 (1972). (b) M. Choi and E. R. Thornton, J. Amer. Chem. Soc., 96, 1428 (1974), have suggested the possibility of more complex reaction paths with two consecutive transition states not separated by any energy minimum and with reaction coordinates perpendicular to each other on the potential energy surface. 

To keep sight of this intramolecular change, the two-dimensional potential curves plotted as functions of the distance B from the adsorbent must be supplemented by a third coordinate giving the interatomic distance in diatomic molecules or between two key atoms in a polyatomic one. The corresponding three-dimensional diagram for a diatomic molecule has been represented by de Boer and Custers 2). It is advisable, however, to keep the usual two-dimensional curves, imagining them to be drawn in space as contour lines on the respective surfaces of potential energy. 

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