Symmetry Analysis of the Cope Rearrangement

The following analysis is abstracted from a recent publication [25], in which its assumptions and conclusions were then checked computationally. As noted above, the highest symmetry that can be retained along the pathway via the chair TS is C2 and that via the boat is C. The former is conrotatory and the latter disrotatory but there are two variants of each, depending on the relative sense of rotation of the four methylene groups. The four reaction paths are il- 

The reader is assured that the qualitative symmetry analysis preceded its computational confirmation. 

Both of the pathways that allow out-of-plane relaxation of the a frame are [3s -f 3s], and are therefore allowed by the Rules. So are the other two, which are [3a + 3a], but these can be rejected as sterically unfavorable. Instead of setting up two separate orbital correlation diagrams, between the reactant and the chair and boat transition structures respectively, we make do with a single correspondence diagram in D2/1. For this purpose, the syn and anti conformers of the reactant are anasymmetrized to D2/1, in analogy to the superposition 

The two stable conformations of hexadiene, syn and anti are nearly isoen-ergetic and are separated by a sufficiently low barrier ( 20 kcal/mol) that they can be assumed to be in rapid equilibrium at the temperatures required for the rearrangement. It was confirmed computationally that their electron configurations correlate smoothly with that of the planar molecule, so both conformers are represented on the left side of Fig. 8.4 by their superposition in The four out-of-plane CH orbitals span all four irreps of whereas two of the four in-plane combinations are aj and the other two are 62. 

The CH orbitals correlate along either a conrotatory (02) or a disrotatory (61) pathway. The totally symmetric (Jqc correlates with one a orbital and the symmetric tt combination with the HOMO (61), but the antisymmetric 02 combination has to be induced to correlate with the second ai a orbital by displacement along a conrotatory (02) pathway via the chair transition state, in agreement with experiment. It follows that the HOMO and LUMO in the chair TS remain those that were specified in Fig. 8.4 for the STS.  

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