Imperial College London

Henry Rzepa

Here is another exploration of simple chemical concepts using crystal
structures. Consider a simple diene: how does the central C-C bond
length respond to the torsion angle between the two C=C bonds?

![arm1](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2015/08/dienes.jpg){.aligncenter
.size-full .wp-image-14400 decoding="async" width="440"}

The search of the CSD (Cambridge structure database) is constrained to R
\< 5%, no errors and no disorder and the central  C-C bond is specific
to be acyclic.^‡^

![arm1](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2015/08/conjugation2.jpg){.aligncenter
.size-full .wp-image-14400 decoding="async" width="440"}

1.  Note first that the hotspot occurs for a torsion angle of 180°, a
    trans diene.
2.  There is just a hint that the C-C distance for a cis-diene might be
    a little shorter than the trans diene, but this might not be
    significant.
3.  There is a gentle curve illustrating that the C-C distance is indeed
    a maximum at 90°
4.  The C-C bond extends from \~1.445Å when the two double bonds are
    coplanar (fully conjugated) to \~1.48Å when orthogonal. Not much of
    a change, but statistically highly significant.

Here is another search, this time of the C=C-C=C motif embedded into a
biaryl, of which there are far more examples. This time, the (red)
hotspot is actually at 90°, with local (green) hotspots at 0 and 180°
but also at 45 and 135°. Again, you can easily spot the maximum in C-C
bond length at 90° but notice how much smaller the bond lengthening is
(\~ 0.01Å). This lengthening is inhibited by retention of the
aromaticity of the two aryl rings; again the statistical effect is
highly significant. Perhaps also significant is that the  C-C bond at
torsions of 0 or 180° appear to be no shorter than the values at 45 and
135°.

![arm1](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2015/08/biaryls.jpg){.aligncenter
.size-full .wp-image-14400 decoding="async" width="440"}

![arm1](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2015/08/conjugation1.jpg){.aligncenter
.size-full .wp-image-14400 decoding="async" width="440"}

Both these searches took about  5 minutes each, and serve to illustrate
just how many basic chemical concepts can be teased out of a statistical
analysis of crystal structures.

------------------------------------------------------------------------

^‡^The analogous diagram for O=C-C=C is shown below;

![arm1](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2015/08/oc-cc.jpg){.aligncenter
.size-full .wp-image-14400 decoding="async" width="440"}

That for  O=C-C=O is different however;

![arm1](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2015/08/occo.jpg){.aligncenter
.size-full .wp-image-14400 decoding="async" width="440"}

#### Acknowledgments

This post has been cross-posted in PDF format at
[Authorea](https://doi.org/10.15200/winn.145586.67897){rel="noopener"
target="_blank"}.

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Here is another exploration of simple chemical concepts using crystal structures. Consider a simple diene: how does the central C-C bond length respond to the torsion angle between the two C=C bonds?

Messaggi di Rogue Scholar

A visualisation of the effects of conjugation; dienes and biaryls.