Path of minimum energy

In a pericyclic reaction, the pathway predicted by the selection rules is the one that allows maximum orbital overlap along the reaction pathway, including the transition state. Maximum orbital overlap corresponds to the path of minimum energy and is achieved if the orbitals involved are similar in energy and if the symmetry of the orbitals is maintained throughout the reaction path. 

Fig. 4 Path of Minimum energy on the E 0 e potential energy surface for values of 2p indicated. For all plots, Aj = —1,000 cm hco = 250cm 8 = 100cm = 50°...

Figure 4 Potential energy profiles along the path of minimum energy shown for reactions proceeding in the exothermic direction. On an attractive surface, as in (a), most of the energy is released as the reactants approach, i.e. before rAB/r.,AB = rBc/r ,Bc In case (b), the surface is more repulsive, the bulk of the energy being released as the products separate...

The path of minimum potential energy that connects reactants and products is known as the reaction coordinate. 

Figure 2.7 shows a representation of this situation. The ordinate is an energy axis and the abscissa is called the reaction coordinate and represents the progress of the elementary step. In moving from P to H, the particle simply moves from one equilibrium position to another. In the absence of any external forces, the energy of both the initial and final locations should be the same as shown by the solid line in Fig. 2.7. Between the two minima corresponding to the initial and final positions is the energy barrier arising from the dislodging of the particles neighboring the reaction path from their positions of minimum energy.

The potential energy surface consists of two valleys separated by a col or saddle. The reacting system will tend to follow a path of minimum potential energy in its progress from the initial state of reactants (A + BC) to the final state of products (AB -F C). This path is indicated by the dashed line from reactants to products in Fig. 5-2. This path is called the reaction coordinate, and a plot of potential energy as a function of the reaction coordinate is called a reaction coordinate diagram. 

We will return to our consideration of RIP diagrams. Figure 5-22 summarizes the possible reaction paths. Recall that an intermediate is a state of minimum energy on the reaction path, so that all four comers may constitute energy minima, but for any given type of reaction it is unlikely that both I and 1 will be of comparable stability. As Table 5-3 indicates, one of these is apt to be the favored intermediate. 

Because the concept of minimum energy path is not well-defined when multiple electronic states are involved, the initial data set is simply taken as the union of points which one considers important on each of the electronic states—for example, local minima on each electronic state. The weights of each data point, Wi in Eq. (2.34), were taken to be the same on all electronic states because they only depend on the location of the data points. Hence, the difference between electronic states (V he[)ard(R)) is manifested only in the parameters of each of the Taylor expansions ... 

It should be pointed out that our description of electrocyclic reactions thus far has been qualitative. Woodward and Hoffmann (1965a) do refer to unpublished HMO calculations which back up the almost intuitive symmetry arguments. Nevertheless, Fukui (1965,1966) and Zimmerman (1966) outlined HMO treatments in which they obtained changes in energy for conrotatory and disrotatory processes. On the basis that paths involving minimum energy between reactants and transition states were favored, their predictions were in essential agreement with those of Woodward and Hoffmann. 

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