In the previous post, it was noted that Möbius annulenes are intrinsically chiral, and should therefore in principle be capable of resolution into enantiomers. The synthesis of such an annulene by Herges and co-workers was a racemic one; no attempt was reported at any resolution into such enantiomers. Here theory can help, since calculating the optical rotation [α]D is nowadays a relatively reliable process for rigid molecules. The rotation (in °) calculated for that Möbius annulene was relatively large compared to that normally measured for most small molecules.
Recently, quite a number of cyclopolypyrroles, more commonly called phyrins, have been reported. The conventional number of pyrrole rings in many biological systems is of course four (chlorophyll, haemoglobin, etc), but these extended porphyrins can have anywhere between five and sixteen such rings comprising a larger macrocycle. For those with six-eight such rings, a commonly adopted geometric motif is found to be a figure-eight, or more properly a lemniscular one. Such shapes have recently (10.1021/ol703129z) been recognized as also being Möbius systems, albeit this time with two half twists in the π-electron cycle rather than just the single twist synthesized by Herges. As such, they also follow a simple electronic selection rule, being aromatic if 4n+2 π-electrons circulate around the ring.
One such molecule is shown below (10.1039/b502327k), albeit with four of the pyrroles replaced by a thiophene ring.Just as with the Herges syntheses, most of these phyrins are also made as racemates. There appears to be only one report of such octaphyrin actually being separated into enantiomers (10.1002/(SICI)1521-3773(19991216)38:24<3650::AID-ANIE3650>3.0.CO;2-F) but no optical rotation could be measured due to its intense colour (in other words, so much light is absorbed by the system that too little remains to measure its rotation). So no-one knows what the magnitudes of the optical rotation values for these figure-eight or lemniscular molecules actually are.
Here again, theory can come to the rescue. The octaphyrin shown above for example (simplified such that Ar=H), [α]D has the stupendous value of -25517° (See 10042/to-2185). Values above 10,000 are common for this type of molecule! So these relatively small and simple class of molecules are currently easily the record holders for the size of their optical rotations. OK, the latter are merely predictions, but it certainly should serve as an encouragement for experimental measurements of this property.
Oh, by the way, if you click on the graphic above, you will get to see a molecular orbital calculated for the molecule. It is the most stable of the π-type of MOs, and shows the characteristic features of the lemniscate, namely the π-electrons take the form of a torus link (10.1039/b810301a).