Imperial College London

Henry Rzepa

Here I offer another spin-off from writing a lecture course on
conformational analysis. This is the famous example of why
**1,2-difluoroethane** adopts a *gauche* rather than *antiperiplanar*
conformation.  

::: {#attachment_1888 .wp-caption .aligncenter style="width: 410px"}
[![](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2010/04/difluoroethane.jpg "difluoroethane"){.size-full
.wp-image-1888 loading="lazy" decoding="async"
aria-describedby="caption-attachment-1888" width="400" height="158"
srcset="https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2010/04/difluoroethane.jpg 952w, https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2010/04/difluoroethane-300x118.jpg 300w"
sizes="(max-width: 400px) 100vw, 400px"}](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2010/04/difluoroethane.jpg)

The gauche and antiperiplanar conformations of 1,2-difluoroethane
:::

One major contribution to the greater stability of the gauche is the
stereoelectronic interactions, and this is best probed using the NBO
(Natural Bond Orbital) approach of Weinhold (DOI:
[10.1021/ja00501a009](http://dx.doi.org/10.1021/ja00501a009)). The
process is approximately described as first reducing the wavefunction
down to a set of orbitals which have been localized (using appropriate
algorithms) down to two or one centres (corresponding to two-centre
covalent bonds, or one-centre electron lone pairs). Perturbation theory
is then used to evaluate the interaction energy between any filled and
any empty combination. For the molecule above, **six** such combinations
are inspected, involving any one of the six filled C-H or C-F
σ-orbitals, and the best-overlapping σ\* orbital which turns out to be
located on the C-H or C-F bond anti-periplanar to the filled orbital.

<table data-border="0">
<colgroup>
<col style="width: 50%" />
<col style="width: 50%" />
</colgroup>
<tbody>
<tr class="odd">
<td><div id="attachment_1891" class="wp-caption aligncenter"
style="width: 210px">
<img
src="http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2010/04/fluoroethane1.jpg"
title="fluoroethane1" class="size-full wp-image-1891" loading="lazy"
decoding="async" aria-describedby="caption-attachment-1891"
onclick="jmolInitialize(&#39;../Jmol/&#39;);jmolSetAppletColor(&#39;white&#39;);jmolApplet([450,450],&#39;load wp-content/uploads/2010/04/11.jvxl;isosurface  &quot;&quot; color yellow green translucent;isosurface append wp-content/uploads/2010/04/18.jvxl translucent;set fontscaling TRUE; font label 18;select atomno=3;color black;label %A C-H σ orbital;&#39;);"
width="200" height="207" />
<p>Filled C-H NBO orbital. Click for 3D to superimpose empty C-F anti
bonding orbital.</p>
</div></td>
<td><div id="attachment_1892" class="wp-caption aligncenter"
style="width: 210px">
<img
src="http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2010/04/fluoroethane2.jpg"
title="fluoroethane2" class="size-full wp-image-1892" loading="lazy"
decoding="async" aria-describedby="caption-attachment-1892"
onclick="jmolInitialize(&#39;../Jmol/&#39;);jmolSetAppletColor(&#39;white&#39;);jmolApplet([450,450],&#39;load wp-content/uploads/2010/04/18.jvxl;isosurface &quot;&quot; translucent;set fontscaling TRUE; font label 18;select atomno=7;color black;label %A C-F σ* orbital;&#39;);"
width="200" height="245" />
<p>Empty C-F antibonding NBO orbital. Click for 3D</p>
</div></td>
</tr>
</tbody>
</table>

A filled C-H orbital is shown above on the left, accompanied by an empty
C-F σ\* orbital on the right which is anti-periplanar to the first. This
alignment allows the phases of the two orbitals to overlap maximally
(blue-blue on the top, red-red beneath).

The interaction energy between this pair is determined not only by the
efficacy of the overlap, but by the energy gap between the two. The
smaller the gap, the better the interaction energy (referred to as
**E2**, in kcal/mol). For the gauche conformation, the six pairs of
orbitals have the following interaction energies; two σ~C-H~/σ\*~C-F~
interactions (illustrated above), 4.9; two σ~C-H~/σ\*~C-H~ 2.6 and two
σ~C-F~/σ\*~C-H~ 0.8 kcal/mol. For the anti-periplanar conformation, the
terms are four σ~C-H~/σ\*~C-H~ 2.5 and two σ~C-F~/σ\*~C-F~ 1.8 kcal/mol.
The two totals (16.6 vs 13.6) indicate that gauche is stabilized more by
such interactions.

There is of course a bit more to this story, but I have documented the
above here, since I can include an explicit (and rotatable) illustration
of the orbitals involved (which  I have not seen elsewhere). If you want
a recipe for generating these orbitals, [go
here](http://www.ch.ic.ac.uk/local/organic/conf/c1_nbo.html){target="_blank"
rel="noopener"}.

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

#### Acknowledgments

This post has been cross-posted in PDF format at
[Authorea](https://doi.org/10.15200/winn.143125.51716){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"}
:::


Here I offer another spin-off from writing a lecture course on conformational analysis. This is the famous example of why
<strong>
 1,2-difluoroethane
</strong>
adopts a
<em>
 gauche
</em>
rather than
<em>
 antiperiplanar
</em>
conformation.

Messaggi di Rogue Scholar

The conformation of 1,2-difluoroethane