Cope rearrangement 1,5-hexadiene, energies

Step through the sequence of stmctures depicting Cope rearrangement of 1,5-hexadiene. Plot energy (vertical axis) vs. the length of either the carbon-carbon bond being formed or that being broken (horizontal axis). Locate the transition state. Measure all CC bond distances at the transition state, and draw a structural formula for it... 

Table 8. Transition structure geometries, activation energies, and reaction energies for transition structures of Cope rearrangement of 1,5-hexadiene...

The Marcus equation provides a nice conceptual tool for understanding trends in reactivity. Consider for example the degenerate Cope rearrangement of 1,5-hexadiene and the ring-opening of Dewar benzene (bicyclo-[2,2,0]hexa-2,5-diene) to benzene. Figure 15.29. The experimentally observed activation energies are 34 kcahmol and 23 kcal/mol, respectively. The Cope reaction is an example of a Woodward-Hoffmann... 

This problem was intensively studied both experimentally and theoretically. The quantum chemical calculations were carried out using various methods at different levels. The earlier calculations for the Cope reanangement based on a CASSCF wave function for six electrons in the bonds rearranged were found to overestimate the diradical character of the wave funclion- --. More recently, MP2 methods for the multireference wave function have been developed whose application to an estimate of the energy of the chair transition state has been described. AMI calculations of altemative transition states for the Cope rearrangement of 1,5-hexadiene derivatives have been discussed by Dewar and colleagues i -217... 

The first is that the chair TS for the Cope rearrangement of 1,5-hexadiene should resemble more closely the lower energy of the two diradical extremes, A and C. The second prediction is that to the extent structures A and C contribute to the Cope TS, radical stabilizing substituents should be capable of lowering the energy of the TS, relative to the reactants, and thus accelerating the Cope rearrangement. Substiments at C2 and C5 of 1,5-hexadiene should stabilize structure A in Fig. 30.1, and substituents placed at Cl, C3, C4, and C6 should stabilize structure C. 

A for the Cope rearrangement of unsubstituted 1,5-hexadiene [30]. AEjist can be easily calculated, since it is just the increase in the energy of the TS for the Cope rearrangement of unsubstimted 1,5-hexadiene on going from Rq = 1.965 A to the value of R in the TS for the Cope rearrangement of a substituted 1,5-hexadiene. 

A and at the equilibrium geometry of the diene, minus the difference between the energies of unsubstituted 1,5-hexadiene at the TS for its Cope rearrangement and at its equilibrium geometry. 

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...

Consideration of the relative entropic contributions to the potential energy surface at the temperatures of the reactions suggest the addition of approximately 9 kcal/mol to the energy of all species described above except 1,5-hexadiene. This then leads to the free energy surface for the reactions including the Cope rearrangement of 1,5-hexadiene described in Scheme 7.97. 

As we shall see later in this section, some extremely interesting Cope rearrangements have been detected in systems in which no gross structural change is apparent. The rearrangement of the parent system, 1,5-hexadiene, has been studied using deuterium-labeled diene and found to occur with an activation energy of 33.5 kcal/mol and an entropy of activation of —13.8 eu. The relatively low... 

From a theoretical point of view, in multi-bond reactions it is essential to use a wavefunction where the possibility of biradical and aromatic transition states can be treated with a balanced level of accuracy. Thus the MC-SCF results of Morokuma et al [21] on the Cope rearrangement of the "model" reaction of 1,5 hexadiene are very convincing and provide reliable evidence that the lowest energy pathway for the "model" reaction is the synchronous one with the biradical intermediate lying 22 Kcal mole higher in energy than the synchronous transition state. 

Analysis of the product ratio from chair and boat TS geometry from a Cope rearrangement of deuterated 1,5-hexadiene indicated that the boat TS is about 6 kcal/mol less stable than the chair TS [35]. It is reflected in the Cope rearrangement of cyclic dienes 59 and 60. Comparison of their reaction rates showed that diene 59 reacted faster by a factor of 18,000. This fact can be rationalized by considering their TS. Compound 59 reacts through a chair-like TS while 60 through a boat-like TS. The chair-like TS has lower activation energy and hence 59 reacts much faster [36]. 

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