Ask a chemist (I'll do) about optical rotation, and you'll get a confident answer about how right- and left-handed isomers of chiral compounds will rotate polarized light that shines through a solution of one of them. Ask one of us exactly how it does that, and in 99 cases out of a hundred, you'll witness a hurried change of the subject or a nervous admission that they have no actual idea. The phenomenon is well-known to us chemists, but the deeper explanation is even worse than NMR; you step off into a deep physics hole (by chemist standards) rather quickly. I can get you up to the point that circularly polarized light is actually chiral itself, because of the way their electric and magnetic fields are rotating, and that this means that chiral molecules will actually change the phase velocity of the two different circular polarizations - they don't come out of the solution the way that they came in.
Beyond that, don't ask me. But the consequences of this effect are obvious: a solution of a chiral ("handed") molecule will rotate polarized light, and the amount of that rotation depends on the wavelength of the light, the concentration of the solution (and its path length), and the intrinsic properties of the chiral molecule itself (which is where even more physics kicks in). If you control for those other variables, you can use the optical rotation value of a pure substance as a distinctive identifiable property.
Well, sometimes. As this paper shows, the situation can be pretty messy. Sometimes you have natural products whose optical rotations are reported as varying quite a bit, and when that happens, you know that there's almost certainly a chiral impurity in there with an intrinsically greater ability to rotate light. And since there's no way to figure structural information from the actual rotation data itself (sign or magnitude), there can be some open questions. The paper's from a group at Merck, who have previously shown that you can use calculated VCD (vibrational circular dichroism) spectra to assign absolute chirality. That's another one of those ideas that formerly was too computationally expensive to do routinely, but has come within reach, and it's been rewriting some structural assignments the last few years.
And now it's the turn of frondosin B, and about time. That compound has been synthesized several times, but the absolute chirality has been very much open for debate. The R and S forms have been variously described as having positive and negative optical rotations over the years, with different syntheses flatly disagreeing on which is which (note - this new work apparently invalidates some of the reasoning in that reference!) And these are folks who know what they're doing (Danishefsky, Trauner, Ovaska, Macmillan, Wright). So what's going on?
The Merck (NYSE:MRK) group calculated the most likely conformers of the molecule and then predicted the IR spectrum that one should obtain. Once that checked out, they moved on to the VCD spectrum. I have never done any VCD work, but it appears to be something of a pain, especially for natural products work. You really need five or ten milligrams of the material, because the signal is very faint, and that's often just too much material demand for such rare compounds. In addition, the solution has to be quite concentrated, which can be a problem even if you do have enough material on hand. This paper also resorted to ECD, electronic circular dichroism, for which the signal/noise is apparently better (although you have fewer bands to work with). Their calculations showed that the R compound should have a positive sign of rotation.
When Danishefsky and his group synthesized frondosin B, they targeted the R enantiomer and indeed got a small positive optical rotation. That was a pretty close match to the reported value for the natural product itself, so they assigned it as (+)R. But then the Trauner group also synthesized the R compound and got a negative rotation of almost exactly the same magnitude, and they concluded that the natural product was thus (+)S. Trauner thought that Danishefsky's synthesis had inadvertently flipped a chiral center, while later work (which lined up more with Danishefsky) made people think that it was Trauner's synthesis that had mistakenly inverted it.
In order to get material to work with, the Merck group painstakingly recreated the syntheses, and found that the problem is not a stereochemical inversion, but an impurity that's formed afterwards, in a second methylation step. This has the same mass and almost the identical retention time under most chromatographic conditions (which is the real nightmare possibility for anyone doing purification work). The O-demethylation step that is the final step in some of the reported syntheses is very hard on the enantiopurity, as it turns out, but it's the impurity that causes the main mischief: it has the opposite sign of the natural product, and rotates polarized light ten times more strongly (+13 degrees compared to -155 degrees). The impurity ends up with its second methyl group on a completely different carbon, because of an allyl cation that forms during the reaction (see the paper, which is open-access, for more details). So you end up with the same mass, and extremely similar chromatographic behavior, but with a different structure that gives a completely different optical rotation. As I said, a real nightmare.
So there was no unexpected stereochemical inversion in any of the published syntheses. And it turns out that Danishefsky was correct - the natural product is indeed (+)R. The Trauner synthesis actually did prepare the R compound, as it was designed to, but it was contaminated with enough of the highly-rotating impurity to give a very plausible opposite conclusion. A small but nagging mystery has been solved - and another analytical technique has proven its merit by doing so.