Henry Rzepa brought this interesting paper to my attention via his blog post. I have a few comments too.

Isobe and co-workers prepared the interesting polycyclic aromatic compound 1, which they represent with the picture given below.¹ The molecule is non-planar due to the clash of the interior hydrogens. If you stare at this picture long enough you might decide that something looks amiss. If you start at the lower left phenyl ring of the top segment and move counterclockwise you would move upwards, out of the plane of the page. Then you cross into the lower half and continue the counter clockwise motion, again you climb upwards out of the page. And then you cross back over to the top half and your back where you started – but you’ve been climbing uphill all the time! This might remind you of the famous Escher drawing Ascending and Descending.

1

So, what’s the catch? Well, the molecule does exist and its crystal structure shows the key. The molecule is in fact of D₂ symmetry, so the upper and lower halves of the molecule are twisted in and out of the plane. B3LYP/6-31G(d,p) computations on the parent compound 2 indicate the D₂ symmetry of the ground state (see Figure 1). (Don’t forget to click on the structure to be able to manipulate the structure!) This is a chiral species. Racemization occurs through a barrier of 10.1 kcal mol^-1 (3) which connects to the meso structure 4, Passing then through the mirror image of 3 completes the process, joining to the mirror image of 2.

2

3

4

I think the title is a bit misleading here – the molecular expression is misleading as its drawn in 1, but the full 3D structure shows no such illusion; the molecule is in fact not a Penrose Stair. But 1 certainly possesses a structure of interesting shape and topology!

References

(1) Nakanishi, W.; Matsuno, T.; Ichikawa, J.; Isobe, H., "Illusory Molecular Expression of “Penrose Stairs” by an Aromatic Hydrocarbon," Angew. Chem. Int. Ed., 2011, ASAP, DOI: 10.1002/anie.201102210

InChIs

1: InChI=1/C52H52/c1-5-9-13-37-25-41-26-38(14-10-6-2)44-22-19-35-30-48(44)51(41)47-29-33(17-21-43(37)47)34-18-23-45-39(15-11-7-3)27-42-28-40(16-12-8-4)46-24-20-36(35)32-50(46)52(42)49(45)31-34/h17-32H,5-16H2,1-4H3
InChIKey=UNDWIIYPHJODRS-UHFFFAOYAO

2: InChI=1/C36H20/c1-9-25-10-2-22-6-15-29-18-32(22)35(25)31-17-27(13-5-21(1)31)28-14-7-23-3-11-26-12-4-24-8-16-30(29)20-34(24)36(26)33(23)19-28/h1-20H
InChIKey=KBDMNQAUFRTSJI-UHFFFAOYAA