Imperial College London

Henry Rzepa

It is not often that an article on the topic of illusion and deception
makes it into a chemical journal. Such is addressed
(DOI: [10.1002/anie.201102210](http://dx.doi.org/10.1002/anie.201102210){target="_blank"})
in no less an eminent journal than *Angew Chemie*. The illusion (or
deception if you will) actually goes to the heart of how we represent
three-dimensional molecules in two dimensions, and the meanings that may
be subverted by doing so. A it happens, it is also a recurring theme of
this particular blog, which is the need to present chemistry with data
for all three dimensions fully intact (hence the *Click for 3D* captions
which often appear profusely here).

::: {#attachment_4440 .wp-caption .aligncenter style="width: 229px"}
![](http://www.ch.imperial.ac.uk/rzepa/blog/wp-content/uploads/2011/06/penrose.jpg "penrose"){.size-full
.wp-image-4440 loading="lazy" decoding="async"
aria-describedby="caption-attachment-4440"
onclick="jmolInitialize('../Jmol/');jmolSetAppletColor('yellow');jmolApplet([450,450],'load wp-content/uploads/2011/06/806565.cif;');"
width="219" height="332"
srcset="https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2011/06/penrose.jpg 656w, https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2011/06/penrose-197x300.jpg 197w"
sizes="(max-width: 219px) 100vw, 219px"}

Molecular Penrose stair. Click for 3D.
:::

The molecule above has been synthesized and a crystal structure obtained
(if you click above, you will get the 3D coordinates; the above is
pruned of some sidechains which are irrelevant here). The authors assert
it as an example of a **Penrose stair**, or perhaps the better known
lithograph by M. C. Escher known as **[Ascending and
Descending](http://en.wikipedia.org/wiki/File:Ascending_and_Descending.jpg){target="_blank"}**.
This is a visual paradox, the point of which is to show how the eye can
be easily deceived if the brain is asked to fill in a third dimension
given only two. The molecule above has been drawn with the illusion of
depth, using (or mis-using) the embolded bonds akin to those proposed by
[Maehr](http://pubs.acs.org/doi/abs/10.1021/ed062p114){target="_blank"}
(who meant something quite different as it happens). It should be
worrying to any chemist who cares about stereochemistry to think that
use of these time honoured conventions could actually result in a
paradox! So perhaps this accounts for why an article on this very topic
has made it onto the pages of such an eminent journal.

What might be of (chemical) interest about this molecule, other than its
illusory aspects? Well, could you for example work out, given ONLY the
representation above, that the molecule has D~2~ symmetry, and is
therefore chiral? I wondered if it might also be Möbius (with perhaps
two half twists), although in fact the π-system in this case has a
linking number Lk of zero (not 2). It also has some interesting rather
close H...H contacts in the middle, and the inner periphery appears to
be a 14-annulene and the outer 26, both conforming to the Huckel 4n+2
rule. Despite this the central C-C bond is actually quite long, and the
conjugation is hence significantly interrupted. There is more chemistry
in the original article.

But I want to close here on the point that to overcome the deception and
illusion, you need to get the three dimensional data in chemistry. You
can do this by clicking above. Or, by going to the original article and
striving to do so there. I think you will find the latter route the
greater challenge! Then, ask yourself why an eminent journal, in
publishing an article on the topic of deception and illusion, makes it
so relatively difficult to overcome that illusion. Certainly more
difficult than I hope it proves to be on this blog!

::: {.wp_orcid_field}
[https://orcid.org/0000-0002-8635-8390](https://orcid.org/0000-0002-8635-8390){target="_blank"
rel="author"}
:::


It is not often that an article on the topic of illusion and deception makes it into a chemical journal.

Messaggi di Rogue Scholar

Molecular illusions and deceptions. Ascending and Descending Penrose stairs.