Imperial College London

Henry Rzepa

I am on a mission to persuade my colleagues that the statistical
analysis of crystal structures is a useful teaching tool.  One colleague
asked for a demonstration and suggested exploring the classical
[Jahn-Teller
effect](http://en.wikipedia.org/wiki/Jahn–Teller_effect){target="_blank"} (thanks
Milo!). This is a geometrical distortion associated with certain
molecular electronic configurations, of which the best example is
illustrated by octahedral copper complexes which have a d^9^ electronic
configuration. The e~g~ level shown below is occupied by three electrons
and which can therefore distort in [one of two
ways](http://www.ch.imperial.ac.uk/rzepa/blog/?p=2973){target="_blank"}
to eliminate the e~g~ degeneracy by placing the odd electron into either
a x^2^-y^2^ or a z^2^ orbital. Here I explore how this effect can be
teased out of crystal structures.

[![JT](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2015/05/JT.svg){.aligncenter
.size-full .wp-image-14044 decoding="async"
width="300"}](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2015/05/JT.svg)

The search is set up with Cu specified as precisely 6-coordinate, and
X=oxygen. The six X-Cu distances are defined as DIST1-DIST6. The
R-factor is specified as \< 0.05 (no disorder, no errors). The problem
now is how to plot what is in effect a six-dimensional set of data, from
which we are exploring whether four of the distances are different from
the other two, and whether those four are the longer or the shorter.
This requires analysis beyond the capability (as far as I know) of the
Conquest program, and so here I will show sets of plots showing just the
relationship between any two distances at a time. Of the 15 possible
combinations of two distances, only four are shown below.

Some obvious patterns can already be spotted in the 400 or so compounds
which satisfy the search criteria.

- The largest clustering occurs at \~1.95Å, with two clusters each of
  fewer hits at \~2.5Å. The [Wikipedia
  page](http://en.wikipedia.org/wiki/Jahn–Teller_effect){target="_blank"}
  notes that for Cu(OH~2~)~6~ the Jahn-Teller distortion favours four
  short bonds at \~1.95Å and two long ones at \~2.38Å, which agrees
  approximately with the positions and sizes of the centroids of these
  clusters.^†^
- Plots 1 and 2 show very little along the diagonals, where the two
  plotted distances have the same value. This probably means that one of
  the distances relates to an equatorial ligand and the other to
  an axial ligand.
- Plots 3 and 4 show a strong diagonal trend, and so these distances
  both relate to either axial or equatorial, but not one of each.
- All four plots show a hot spot at \~1.95Å, which hints that the
  Jahn-Teller distortion is four short bonds/two long.
- Plot 4 also shows a green spot at \~2.5Å which is a tantalising
  suggestion of examples of four long bonds/two short.^‡^

1.  [![CuO-12](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2015/05/CuO-12.jpg){.aligncenter
    .size-full .wp-image-14050 decoding="async" width="440"
    srcset="https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2015/05/CuO-12.jpg 890w, https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2015/05/CuO-12-300x238.jpg 300w"
    sizes="(max-width: 890px) 100vw, 890px"}](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2015/05/CuO-12.jpg)
2.  [![CuO-34](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2015/05/CuO-34.jpg){.aligncenter
    .size-full .wp-image-14049 decoding="async" width="440"
    srcset="https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2015/05/CuO-34.jpg 1016w, https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2015/05/CuO-34-300x231.jpg 300w, https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2015/05/CuO-34-900x692.jpg 900w"
    sizes="(max-width: 1016px) 100vw, 1016px"}](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2015/05/CuO-34.jpg)
3.  [![CuO-56](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2015/05/CuO-56.jpg){.aligncenter
    .size-full .wp-image-14048 decoding="async" width="440"
    srcset="https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2015/05/CuO-56.jpg 1018w, https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2015/05/CuO-56-300x238.jpg 300w, https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2015/05/CuO-56-900x713.jpg 900w"
    sizes="(max-width: 1018px) 100vw, 1018px"}](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2015/05/CuO-56.jpg)
4.  [![CuO-13](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2015/05/CuO-13.jpg){.aligncenter
    .size-full .wp-image-14047 decoding="async" width="440"
    srcset="https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2015/05/CuO-13.jpg 925w, https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2015/05/CuO-13-300x242.jpg 300w, https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2015/05/CuO-13-900x725.jpg 900w"
    sizes="(max-width: 925px) 100vw, 925px"}](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2015/05/CuO-13.jpg)

Clearly this analysis can be followed up by a visual inspection of
individual molecules in each cluster (as well as the outliers which
appear to follow no pattern!), together with a more bespoke analysis of
the six distances. Unfortunately, the spin state of the complexes cannot
be quickly checked (are they all doublets?) since the database does not
record these.  But the basic search described above takes only a few
minutes to do, and it is surprising at how quickly the Jahn-Teller
effect can be statistically tested with real experimental data obtained
for \~400 molecules. Of course, here I have only explored X=O but this
can easily be extended to X=N or X=Cl, to other metals or to alternative
coordination numbers such as *e.g.* 4 where the Jahn-Teller effect can
also in principle operate.

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

^‡^ One genuine example of this type, also called compressed octahedral
coordination, was reported for the species CuFAsF~6~ and
CsCuAlF~6~\[cite\]10.1002/chem.200400397\[/cite\]

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

^†^ The measured geometry of Cu(H~2~O)~6~ may in fact manifest with six
equal Cu-O bond lengths due to the *dynamic Jahn-Teller effect*, because
the kinetic barrier separating one Jahn-Teller distorted form and
another (equivalent) isomer is small and hence averaged atom positions
are measured which mask the effect. Thus the Jahn-Teller effects shown
in the plots above may be under-estimated because of this dynamic
masking. Reducing the temperature of the sample at which data was
collected would reduce this dynamic effect. Indeed, Cu(D~2~O)~6~
collected at 93K shows a very clear Jahn-Teller
distortion\[cite\]10.1021/ja905399x\[/cite\] with four short bonds
ranging from 1.97-1.99Å and two long bonds
2.37-2.39Å.\[cite\]10.5517/CCTBSPL\[/cite\] Another example measured at
89K with dimethyl formamide replacing water and coordinated *via*
oxygen\[cite\]10.5517/CC14CL36\[/cite\] shows four short (1.97-1.98Å)
and two long (2.315Å) bonds. This latter example is also noteworthy
because this analysis is as yet unpublished in a journal, but the data
itself has a DOI *via* which it can be acquired. A nice example of
modern [research data
management](http://www.ch.imperial.ac.uk/rzepa/blog/?p=10972){target="_blank"}!

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

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


I am on a mission to persuade my colleagues that the statistical analysis of crystal structures is a useful teaching tool.

Discovering chemical concepts from crystal structure statistics: The Jahn-Teller effect

I previously blogged about [anomeric effects involving π electrons as
donors](http://www.ch.imperial.ac.uk/rzepa/blog/?p=5368){target="_blank"
rel="noopener"}, and my post on the [conformation of
1,2-difluorethane](http://www.ch.imperial.ac.uk/rzepa/blog/?p=1887){target="_blank"
rel="noopener"} turned out one of the most popular. Here I thought I
would present the results of searching the Cambridge crystal database
for examples of the ***gauche effect***. The basic search is defined
below![CCDC-search](http://www.ch.imperial.ac.uk/rzepa/blog/wp-content/uploads/2013/01/CCDC-search.jpg){.aligncenter
.size-full .wp-image-8899 loading="lazy" decoding="async" height="107"
width="411"}

Here, we define a four-atom torsion (TOR1), the two central carbon atoms
having two groups R which can be only H or C. These two carbons are also
defined as ***acyclic***. The restrictions of the search as defined
above also include R-factor \< 0.05, not disordered and no errors. These
combine to reduce the number of hits significantly (although not
dissimilar distributions are obtained for less restricted searches).
Each search takes only a few seconds, and one can rattle through many
permutations very quickly.

So here come the results. First, QA=4M=F. All but one of the examples
has a torsion in the region of 60°, the classic gauche effect!

::: {#attachment_8910 .wp-caption .aligncenter style="width: 420px"}
![F-C-C-F](http://www.ch.imperial.ac.uk/rzepa/blog/wp-content/uploads/2013/01/FCCF.jpg){.size-full
.wp-image-8910 decoding="async"
aria-describedby="caption-attachment-8910" width="410"}

F-C-C-F
:::

Next, QA=O, 4M=F. Rather more hits, and the effect is almost as
clear-cut. I should point out that the apparent \"exceptions\" to the
gauche conformation may arise from structural restrictions, and each
really would have to be inspected individually for the reasons (which I
do not attempt here). 

::: {#attachment_8909 .wp-caption .aligncenter style="width: 420px"}
![OCCF](http://www.ch.imperial.ac.uk/rzepa/blog/wp-content/uploads/2013/01/OCCF.jpg){.size-full
.wp-image-8909 decoding="async"
aria-describedby="caption-attachment-8909" width="410"}

OCCF
:::

With QA=4M=O,  one has many more instances. The effect is pretty
convincing (it may be that hydrogen bonding may also control the
conformation).

::: {#attachment_8913 .wp-caption .aligncenter style="width: 420px"}
![O-C-C-O](http://www.ch.imperial.ac.uk/rzepa/blog/wp-content/uploads/2013/01/OCCO.jpg){.size-full
.wp-image-8913 decoding="async"
aria-describedby="caption-attachment-8913" width="410"}

O-C-C-O
:::

Now for QA=4M=Cl. The distribution is slanted more to the anti
conformation, but there are still quite a few gauche.

::: {#attachment_8908 .wp-caption .aligncenter style="width: 420px"}
![Cl-CC-Cl](http://www.ch.imperial.ac.uk/rzepa/blog/wp-content/uploads/2013/01/Cl-C-C-Cl.jpg){.size-full
.wp-image-8908 decoding="async"
aria-describedby="caption-attachment-8908" width="410"}

Cl-CC-Cl
:::

With QA=4M=S, the conformations are now almost all anti; the gauche
effect is no more! 

::: {#attachment_8906 .wp-caption .aligncenter style="width: 420px"}
![S-C-C-S](http://www.ch.imperial.ac.uk/rzepa/blog/wp-content/uploads/2013/01/S-C-C-S.jpg){.size-full
.wp-image-8906 decoding="async"
aria-describedby="caption-attachment-8906" width="410"}

S-C-C-S
:::

And for QA=4M=Br, it has also almost vanished (there is only one
instance for I, and that too is antiperiplanar).

::: {#attachment_8907 .wp-caption .aligncenter style="width: 420px"}
![Br-C-C-Br](http://www.ch.imperial.ac.uk/rzepa/blog/wp-content/uploads/2013/01/Br-C-C-Br.jpg){.size-full
.wp-image-8907 decoding="async"
aria-describedby="caption-attachment-8907" width="410"}

Br-C-C-Br
:::

I now return to an earlier post in which I speculated that a cyano group
might participate in the anomeric effect. Well here it is in the gauche
effect; QA=CN, 4M = any of N,O,F,Cl,S. Quite a few gauche orientations
for this pseudo-halogen!

::: {#attachment_8911 .wp-caption .aligncenter style="width: 420px"}
![Neg-C-C-CN](http://www.ch.imperial.ac.uk/rzepa/blog/wp-content/uploads/2013/01/Neg-C-C-CN.jpg){.size-full
.wp-image-8911 decoding="async"
aria-describedby="caption-attachment-8911" width="410"}

Neg-C-C-CN
:::

Another group that can act as a powerful acceptor of electrons from a
donor is QA=N(Me)~3~^+.^. With 4M= N, O, F, Cl, here  the population of
gauche conformers is large. QA=CF~3~ is a similar group.

::: {#attachment_8905 .wp-caption .aligncenter style="width: 420px"}
![Neg-C-C-NMe3](http://www.ch.imperial.ac.uk/rzepa/blog/wp-content/uploads/2013/01/Neg-C-C-NMe3.jpg){.size-full
.wp-image-8905 decoding="async"
aria-describedby="caption-attachment-8905" width="410"}

Neg-C-C-NMe3
:::

::: {#attachment_8919 .wp-caption .aligncenter style="width: 420px"}
![Neg-C-C-CF3](http://www.ch.imperial.ac.uk/rzepa/blog/wp-content/uploads/2013/01/Neg-C-C-CF31.jpg){.size-full
.wp-image-8919 decoding="async"
aria-describedby="caption-attachment-8919" width="410"}

Neg-C-C-CF3
:::

One can envisage other combinations. Thus QA= C=C, 4M = any of  N, O, F,
Cl. An alkene seems one of the more powerful gauche effect participants!

::: {#attachment_8903 .wp-caption .aligncenter style="width: 420px"}
![alkene-C-C-Neg](http://www.ch.imperial.ac.uk/rzepa/blog/wp-content/uploads/2013/01/alkene-C-C-Neg.jpg){.size-full
.wp-image-8903 decoding="async"
aria-describedby="caption-attachment-8903" width="410"}

alkene-C-C-Neg
:::

And alkynes, perhaps slightly less so.

::: {#attachment_8903 .wp-caption .aligncenter style="width: 420px"}
![Alkyne-C-C-Neg](http://www.ch.imperial.ac.uk/rzepa/blog/wp-content/uploads/2013/01/alkyne-C-C-Neg.jpg){.size-full
.wp-image-8902 decoding="async"
aria-describedby="caption-attachment-8903" width="410"}

Alkyne-C-C-Neg
:::

What about metals (QA = any metal, 4M = any of N, O, F, Cl, S). Well,
not particularly biased either way, but clearly one in which the
identity of the metal may matter.

::: {#attachment_8901 .wp-caption .aligncenter style="width: 420px"}
![Metal-C-C-electronegative](http://www.ch.imperial.ac.uk/rzepa/blog/wp-content/uploads/2013/01/metal-C-C-Neg.jpg){.size-full
.wp-image-8901 decoding="async"
aria-describedby="caption-attachment-8901" width="410"}

Metal-C-C-electronegative
:::

I should end with inverting the model. If QA is electropositive (any
group to the left of carbon, or below it in the periodic table) and 4M
is electronegative, than they align almost exclusively anti-periplanar
and not gauche. But notice how relatively few examples there are.
 Synthetic chemists, please make more such molecules!

::: {#attachment_8904 .wp-caption .aligncenter style="width: 420px"}
![Electropositive-C-C-Electronegative](http://www.ch.imperial.ac.uk/rzepa/blog/wp-content/uploads/2013/01/Pos-C-C-Neg.jpg){.size-full
.wp-image-8904 decoding="async"
aria-describedby="caption-attachment-8904" width="410"}

Electropositive-C-C-Electronegative
:::

If you thought the gauche effect was restricted to just a few molecules,
think again!

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

#### Acknowledgments

This post has been cross-posted in PDF format at
[Authorea](https://doi.org/10.15200/winn.142795.55871){rel="noopener"
target="_blank"}.

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


I previously blogged about anomeric effects involving π electrons as donors, and my post on the conformation of 1,2-difluorethane turned out one of the most popular.

Messaggi di Rogue Scholar

Discovering chemical concepts from crystal structure statistics: The Jahn-Teller effect

The gauche effect: seeking evidence by a survey of crystal structures.