You don't hear much about bullvalene, outside of physical organic chemistry textbooks. It's a funny-looking symmetric tricyclic compound, which just seems to be another weirdo hydrocarbon until you consider what it can do with all those alkenes. Everything is lined up just right to rearrange - and then the product you get is lined up just right to rearrange, which gives you a product that rearranges, and so on and so on. The molecule has no permanent structure at reasonable temperatures; this process never stops.
We owe William von E. Doering and Wolfgang Roth for this one (the background story is here). I hadn't realized that the "bull" in the name was put in there by Doering's grad students - it was his nickname! (Believe me, there are a lot of research groups out there where that trick wouldn't provide anything printable). The molecule was synthesized by Gerhard Schröder of Karlsruhe, who continued to work in the bullvalene field (and on related cycloalkene oddities) for many years
There are 10!/3 distinct bullvalene structures, or 1,209,600 of the things. And while you can see the fluxional character in the NMR (one peak at high temperature in the carbon NMR, four sharp singlets at -60 C, and a mess at room temp), no one's really worked out what happens with substituted derivatives. They're going to wander around, too, but how much of that space do they explore? Schröder's group prepared a number of derivatives over the years and showed that they have dynamic structures, but figuring out just how dynamic is a complicated problem. Here's a picture of what happens with a tetrasubstituted compound, for example.
Now Jeffrey Bode (and coworker Maggie He) at the ETH in Zürich may have started to answer this question. They prepared a chiral trisubstituted bullvalone, no picnic in itself. That structure doesn't rearrange, but then they prepared an enolate and trapped it as an enol carbamate. That completes the three alkenes, and off things go. Of course, the alkenes are rather different from each other now, so not every pathway is going to be energetically similar, but there are still enough of them to make for quite a scatter.
When they analyzed the product(s) of that enolate trapping reaction, they found that there was still some chirality present. That must have been an exciting moment, but checking the HPLC carefully showed that there was a chiral impurity present that was left over from the starting material. Once that was cleaned out, it was clear that the situation was still pretty complex: they pulled out four fractions from the HPLC, all of which were mixtures of rearranging substituted bullvalenes. Two of the fractions had no optical activity at all, and showed (and kept) the same HPLC trace as each other over time. One of the other original HPLC cuts, though, had some residual optical activity, which disappeared over another 24 hours. During that time, too, its HPLC trace gradually evened out to be the same as the other two racemic cuts. The fourth cut of the original HPLC trace had even more optical activity in it, and normalized out even more slowly.
Their best explanation for all this is that the molecule starts off on its crazy course of interconverting rearrangements, but occasionally gets to a structure that, energetically speaking, is somewhat painted into a corner. Its pathways to get back out into the rapidly-rearranging manifold are higher-energy, so that part of the population retains chirality longer than the ones that took a different path. Eventually, though, everything does even out: the metastable structures back out of their respective dead ends and start flipping back around through the lower-energy rearrangement pathways.
As they get more of a handle on these molecules, they hope to start to control some of the rearrangement population, messing with the various rate constants so that the isomers sort themselves out (possibly) into discrete populations. There could be some very unusual applications for such shape-shifting molecules, although I have to say that training them away from their bucket-of-marbles-on-the-floor tendencies will not be easy. Still, this is the kind of physical organic chemistry I've always been happy to read about (and glad that I'm not having to do myself!)