Cope rearrangements interallylic distances

Not only do the relative contributions of structures A and C to the C2/, wave function for the Cope rearrangement change with the interallylic distance, R, their relative contributions also change with the number and placement of radical stabilizing substituents, such as cyano and phenyl. Since the relative contributions of structures A and C and the optimal value of R in the Cope TS are functionally related, the value of R in the TS is also highly substiment dependent. 

Table 30.1 Calculated and experimental activation enthalpies (kcal/mol) for the Cope rearrangements of phenyl substituted 1,5-hexadienes and the calculated interallylic distance, R (A), in each TS and intermediate...

Consider, for example, the effect of the pair of phenyl substituents in the TS for Cope rearrangement of 1,3-diphenyl-1,5-hexadiene. The calculated interallylic distance in this... 

On addition of a second pair of phenyl substituents at C4 and C6, the interallylic distance further lengthens so that the contribution of structure C to the TS wave function is further enhanced. The ability of the second pair of phenyl substituents to increase the optimal value of R from 7 = 2.218 A to 7 = 2.649 A allows each of the phenyl substituents in l,3,4,6-tetraphenyl-l,5-hexadiene to provide more stabilization for the Cope TS than the pair of phenyl substituents in 1,3-diphenyl-1,5-hexadiene. This cooperative effect of the four phenyl groups in 1,3,4,6-tetraphenyl-1,5-hexadiene lowers AT/ for Cope rearrangement by, not twice, but by four times as much as the pair of phenyl substituents in 1,3-diphenyl-1,5-hexadiene. 

Table 30.2 Dissection of the effects of phenyl substituents on lowering the energy of the TS for the chair Cope rearrangement of 1,5-hexadiene. Energies (kcal/mol) were obtained from B3LYP/6-31G calculations at different interallylic distances (R) in the maimer described in the text...

Calculations perfoimed at the same interallylic bond distance, i , as in the TS for Cope rearrangement of l,3,5-diphenyl-l,5-pentadiene. 

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