More OFerrall Jencks Diagrams

The BEP/Hammond/Marcus treatment only considers changes due to energy differences between the reactant and product, i.e. changes in the TS position along the reaction coordinate. It is often useful also to include changes that may occur in a direction perpendicular to the reaction coordinate. Such two-dimensional diagrams are associated with the names of More O'Ferrall and Jencks (MOJ diagrams).34

Consider for example the Cope rearrangement of 1,5-hexadiene. Since the reaction is degenerate the TS will have D2h symmetry (the lowest energy TS has a conformation resembling a chair-like cyclohexane). It is, however, not clear how strong the forming and breaking C—C bonds are at the TS. If they both are essentially full C— C bonds, the reaction may be described as bond formation followed by bond breaking. The TS therefore has the character of being a 1,4-biradical, as illustrated by path B in Figure 15.30. Alternatively, the C—C bonds may be very weak at the TS, corresponding to a situation where bond breaking occurs before bond formation, and the TS can be described as two weakly interacting allyl radicals (path C). The intermediate situation, where both bonds are roughly half formed/broken can be described as having a delocalized structure similar to benzene, i.e. an "aromatic" type TS (path A).

Figure 15.30 MOJ diagram for the Cope rearrangement of 1,5-hexadiene

In such MOJ diagrams the x- and ^-coordinates are normally taken to be bond orders (Section 9.1) or (1 - bond order) for the breaking and forming bonds, such that the coordinates run from 0 to 1. A third axis corresponding to the energy is implied, but rarely drawn.

At the TS, the energy along the reaction path is a maximum, while it is a minimum in the perpendicular direction(s). A one-dimensional cut through the (0,0) and (1,1)

corners for path A in Figure 15.30 thus corresponds to Figure 15.28. A similar cut through the (0,1) and (1,0) corners will display a normal (as opposed to inverted) parabolic behaviour, with the TS being at the minimum on the curve. The whole energy surface corresponding to Figure 15.29 will have the qualitative appearance as shown in Figure 15.31.

Figure 15.31 MOJ diagram corresponding to Figure 15.30 with the energy as the vertical axis

There is good evidence that the Cope reaction in the parent 1,5-hexadiene has an "aromatic" type TS, corresponding to path A in Figure 15.30, i.e. a "central" or "diagonal" reaction path. The importance of MOJ diagrams is that they allow a qualitative prediction of changes in the TS structure for a series of similar reactions. The addition of substituents that stabilize the product relative to the reactant corresponds to a lowering of the (1,1) corner, thereby moving the TS closer to the (0,0) corner, i.e. towards the reactant. The one-dimensional BEP/Hammond/Marcus treatment thus corresponds to changes along the (0,0)-(1,1) diagonal.

Substituents that do not change the overall reaction energy may still have an influence on the TS geometry. Consider for example 2,5-diphenyl-1,5-hexadiene.The reaction is still thermoneutral but the phenyl groups will preferentially stabilize the 1,4-biradical structure, i.e. lower the energy of the (1,0) corner. From Figure 15.31 it is clear that this will lead to a TS that is shifted towards this corner, i.e. moving the reaction from path A towards B in Figure 15.30. Similarly, substituents that preferentially stabilize the bis-allyl radical structure (such as 1,4-diphenyl-1,5-hexadiene) will perturb the reaction towards path C, since the (0,1) corner is lowered in energy relative to the other corners.

From such MOJ diagrams it can be inferred that changes in the system that alter the relative energy along the reaction diagonal (lower-left to upper-right) imply changes in the TS in the opposite direction. Changes that alter the relative energy perpendicular to the reaction diagonal (upper-left to lower-right) imply changes in the TS in the same direction as the perturbation.

Energy

Energy

Figure 15.31 MOJ diagram corresponding to Figure 15.30 with the energy as the vertical axis

Bond order

Bond order

The structures in the (1,0) and (0,1) corners are not necessarily stable species; they may correspond to hypothetical structures. In the Cope rearrangement, it appears that the reaction only involves a single TS, independent of the number and nature of sub-stituents. The reaction path may change from B ^ A ^ C depending on the system, but there are no intermediates along the reaction coordinate.

In other cases, one or both of the perpendicular corners may correspond to a minimum on the potential energy surface, and the reaction mechanism can change from being a one-step reaction to two-step. An example of this would be elimination reactions. The x-axis in this case corresponds to the breaking bond between carbon and hydrogen, while the y-axis is the breaking bond between the other carbon and the leaving group.

Figure 15.32 MOJ diagram for elimination reactions

An E2 type reaction has simultaneous breaking of the C—H and C—L bonds while forming the B—H bond, and corresponds to the diagonal path A in Figure 15.32. Path C involves initial loss of the leaving group to form a carbocation (upper-left corner), followed by loss of H+ (which is picked up by the base), i.e. this corresponds to an E1 type mechanism involving two TS's and an intermediate. Path B, on the other hand, involves formation of a carbanion, followed by elimination of the leaving group in a second step, i.e. an E1cb mechanism. Substituents that stabilize the carbocation thus shift the reaction from an E2 to an E1 type mechanism, while anionic stabilizing sub-stituents will shift the reaction towards an E1cb path.

In principle MOJ diagrams can be extended to more dimensions, for example by also including the B—H bond order in the above elimination reaction, but this is rarely done, not least because of the problems of illustrating more than two dimensions.

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