Molecular ascent or descent: NMR and XRD look at Penrose-type molecule

Chemical confuser

The molecular equivalent of M.C. Escher's visual illusion of the perpetually climbing stair has been constructed by Japanese chemists and tracked with NMR spectroscopy.

M.C. Escher's famously paradoxical illustration of 1960 depicting a stairway atop an "impossible" building, and made famous recently in a dreamscape of the Hollywood movie "Inception", that seems to ascend or descend interminably is a good example of how projecting the three-dimensional world into two dimensions in artwork can be exploited to manipulate our perceptions. There are many examples of such visual illusions, Escher's was allegedly inspired by the 1959 work of father and son team Lionel and Roger Penrose and so is known to mathematicians as the "Penrose steps"; the stairs evolved from the Penrose triangle. Now, Hiroyuki Isobe and a research team from Tohoku and Tsukuba University in Japan have recreated the illusion on the molecular scale with the construction of a spiralling [4]helicene molecule that when projected from its space-filling 3D form to the commonly used 2D molecular structure format seems to ascend or descend, depending on the path your eye follows, just like a Penrose stair.

Waka Nakanishi, Taisuke Matsuno, and Hiroyuki Isobe of the Department of Chemistry at Tohoku University in Sendai and Junji Ichikawa of the University of Tsukuba in Ibaraki, were intrigued by the way in which 3D molecules are projected into 2D representations. As with a map representing the globe, there are always distortions, some useful, some amusing. They point out that ever since the invention of the hexagon as iconic symbol for benzene with each vertex representing a carbon atom, flat line drawings of chemical structures have become an indispensable tool for chemists and other scientists. Of course, the precise way in which molecular formulae are represented has evolved over many decades and ornamentation, such as dotted bonds, added as well as ways to give the otherwise entirely flat images some semblance of depth albeit in a quasi-3D manner when compared to the more realistic space-filling type diagrams.

The chemists have now stumbled upon an optical illusion among their molecules. The compound in question is a cyclobis[4]helicene with so-called caracole topology. A caracole is a term usually used to describe a formal half turn movement performed by a horse in dressage, but is also used in architecture to describe a spiral staircase, its etymology is in the Spanish word for snail...caracol.

Spiral synthesis

They synthesised the compound by first preparing a helicene subunit using an intramolecular cyclization reaction of a difluoroalkene they knew to be prone to skeletal rearrangement. They avoided this reaction pathway and instead subjected it to a Friedel-Crafts type cyclization using, appropriately so-called "magic acid" (FSO₃H-SbF₅) at 0 Celsius and then applied a dehydrogenation with trityl tetrafluoroborate to obtain the intermediate they desired. NMR spectroscopy gave them a detailed structure and revealed the yield to be 53% after chromatographic purification. Byproducts included chrysene and various uncyclized compounds. The convergent homocoupling of this intermediate subunit then took them to the desired molecule using nickel-promoted biaryl coupling. NMR gave 60% as the yield for this step and seemingly no amount of improvements could be made. An X-ray crystal structure proved the molecule to contain two helicene subunits with the same helical configuration in each molecule, but the product to comprise a mixture of both left- and right-handed enantiomers. "The X-ray structure indeed showed that each of the stairs descends by sub-angstrom," Isobe told SpectroscopyNOW.

The team explains just how peculiar it was to construct and then draw the molecular structure of this molecule with depth-cue effects and the configuration assignments illustrated. By definition, (P)-helicene is the right-handed helix and you would descend the "aromatic stairs" by circling in a right-handed direction. However, if one follows the overall cycle of a molecule containing two P-form sub-units, in such a diagram one unexpectedly reaches the original position without actually descending, hence the analogy with Penrose steps.

Liquid crystal illusion

Of more purely chemical interest, the team demonstrated that their illusory molecule has odd dynamic behaviour in solution in which a possible combination of both covalent and non-covalent bonding is present that might allow chemists to explore other unique molecular topologies. Indeed, Isobe hopes that this class of molecules will open up new possibilities as a building block for liquid crystals.

"The next step should be the construction of molecular assembly with this congeners, as we noticed that enantiomers of the same handedness pile up in a column and such assembly may find applications in optoelectronics," Isobe added. "Through this molecule, we were pleased to recognize and learn how we perceive two-dimentional molecular line drawings. Mathematical analysis reveals that the original Penrose stairs are 'generically reconstructible and generically uncorrectable'. On the other hand, our molecular version is 'generically reconstructible and generically correct', which shows that the molecular Penrose stairs utilize our perception of molecular world to trick us." Isobe adds that this chemical research with a mathematical twist has also led to intriguing discussions with non-chemists. "It was nice to find that we could discuss molecules with mathematicians and to learn an interesting field of topology," he says, "It is fun to see the work of mathematicians and we hope that we can also amuse them with our own materials."

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