Much like climbing Mt. Everest because its there, some hypothetical molecules are just too tantalizing for chemists to resist attempting a synthesis. Thus in 1964, Edgar Heilbronner speculated on whether a conjugated annulene ring might be twistable into a Möbius strip. It was essentially a fun thing to try to do, rather than the effort being based on some anticipated (and useful) property it might have. If you read the original article (rumour has it the idea arose during a lunchtime conversation, and the manuscript was completed by the next day), you will notice one aspect of these molecules that is curious by its absence. There is no mention (10.1016/S0040-4039(01)89474-0) that such Möbius systems will be chiral. By their nature, they have only axes of symmetry, and no planes of symmetry, and such molecules therefore cannot be superimposed upon their mirror image; as is required of a chiral system (for a discussion of the origins and etymology of the term, see 10.1002/chir.20699).
Heilbronner’s little vignette had little overt effect on the synthetic community until around 2003, when Rainer Herges announced that a crystalline annulene following this recipe had been rationally synthesized (10.1038/nature02224). This time, the chemical community really sat up and took notice. The synthesis was hailed as a major achievement, ranking (chemically) as similar to climbing Everest. But if you read Herges’ article carefully, yet again you will note the absence of any discussion of the chirality of their molecule. Their synthesis was of course racemic, in other words an equal proportion of both enantiomers was made. Indeed, it is not obvious how a non-racemic synthesis could be carried out, although resolution of the product might be an easier task. So in the absence of any pure enantiomer of this molecule, can one speculate on its chiral properties? One obvious such property is the optical rotation, and in particular the [α]D value in chloroform. Most optically pure molecules with molecular weights of < 500 Daltons tend to have rotations also < 500°. Few molecules have values > 1000°. Now it should be said at the outset that a molecule with a large optical rotation is not more chiral than a molecule with a smaller value; indeed it seems generally agreed that the question “how chiral is this molecule” is either fairly, or even completely meaningless. But it seems a useful task of having a value to hand which is at least approximately accurate, so that some idea of whether any attempted resolution of the enantiomers has produced optically pure product or not. Fortunately, in the last decade or so, computing a value for [α]D has been entirely viable using the standard programs (see 10.1002/chir.20466 and 10.1021/jo070806i for a discussion). This is also useful for two reasons:
- If the magnitude of the rotation is > 100°, then the sign of this rotation can be very reliably matched to either enantiomer. This allows the absolute configuration to be assigned with a lot of confidence, and probably much more easily than trying to do it by other methods.
- The magnitude itself can be reliably predicted to within 10% of the true value if the molecule is conformationally rigid. However, if it has any rotatable groups (and that even includes e.g. OH groups), then the result can be enormously sensitive to that conformation (or Boltzmann mixture of conformations). Put the other way, calculating the optical rotation could be regarded as a very sensitive way of determining conformations!
So what of the 16-annulene synthesized by Herges and co-workers. Well at the B3LYP/6-311G(2df,2pd) and SCRF(CPCM,solvent=chloroform) level of theory (which is reasonably accurate, although one can do better of course), the enantiomer shown by clicking on the graphic above is predicted to have a rotation of -1355° (for the digital repository entry for the calculation, see 10042/to-2176). That is indeed a large value for such a relatively small molecule, and is probably more reliable because of the lack of conformational ambiguity. Well, you saw the prediction here! Anyone up for testing it experimentally?