One thing leads to another. Thus in the previous post, I described a thermal pericyclic reaction that appears to exhibit two transition states resulting in two different stereochemical outcomes. I noted that another such reaction appeared to be a [1,6] carousel migration in homotropylium cation, where transition states for both retention and inversion of the configuration of the migrating group (respectively formally allowed and forbidden) were reported (scheme below). Here I explore this system further. Firstly, the pathway leading to inversion. The reaction path (ωB97XD/6-311G(d,p)/SCRF=chloroform) has got a very odd (table-top mountain) shape, whereby the region of the transition state (IRC = 0.0) is very flat, and the region close to reactant and (identical) product is very steep. The gradient norm shows this best, with sharp spikes at IRC ± 4.2. Something clearly is happening here to cause this behaviour. Before moving on to analyze this, I want you first to observe the methyl groups below. Note how one of them rotates at the start of the process, and the other at the end. I have elsewhere called this behaviour the methyl flag, and it is due to stereoelectronic re-alignments of the C-H groups accompanying the changes in the conjugated array. The homotropylium cation is said to be homoaromatic, indicating that cyclic conjugation can be maintained across a ring in which the σ framework is interrupted at one point. A NICS probe placed at the ring critical point of this molecule reveals a chemical shift of -11.3 ppm, very similar to eg that obtained for benzene itself. The three highest doubly occupied NBOs (below) show two normal π-type orbitals and one rather different one that spans the homo-bond (the MOs, before you ask, are a bit of a mess, with lots of mixed contributions from other parts of the σ framework).
A.M. Genaev, G.E. Sal’nikov, and V.G. Shubin, "Energy barriers to carousel rearrangements of carbocations: Quantum-chemical calculations vs. experiment", Russian Journal of Organic Chemistry, vol. 43, pp. 1134-1138, 2007. http://dx.doi.org/10.1134/S1070428007080076
Henry S. Rzepa., "Gaussian Job Archive for C10H13(1+)", 2014. http://dx.doi.org/10.6084/m9.figshare.1134556
Henry S. Rzepa., "Gaussian Job Archive for C10H13(1+)", 2014. http://dx.doi.org/10.6084/m9.figshare.1135694