Imperial College London

Henry Rzepa

In the previous post, I suggested that inspecting the imaginary modes of
planar cyclohexane might be a fruitful and systematic way in which at
least parts of the conformational surface of this ring might be probed.
Here, the same process is conducted for **cyclo-octane**. The ring
starts with planar D~8h~ symmetry, and at this geometry
(B3LYP/6-311G(d,p), DOI:
[10042/to-3742](http://hdl.handle.net/10042/to-3742)) five negative
force constants (corresponding to imaginary modes) are calculated. The
most negative is non-degenerate, and gives directly the crown
conformation of D~4d~ symmetry (DOI:
[10042/to-3738](http://hdl.handle.net/10042/to-3738)). The remaining
four modes comprise two degenerate pairs. Following either of the E~2u~
eigenvectors downhill leads to another conformation, D~2d~ (DOI:
[10042/to-3741](http://hdl.handle.net/10042/to-3741)), with a geometry
which is noteworthy for exhibiting a pair of unusually close non-bonded
H...H contacts (1.908Å). This value is about  0.3Å shorter than the sum
of the Wan der Waals radii
(DOI: [10.1021/jp8111556](http://dx.doi.org/10.1021/jp8111556){target="_blank"}). We
can debate whether such a close approach or inter-penetration of two
hydrogens is a bond or not (an AIM analysis appears at the bottom of
this post).

<table data-border="1">
<colgroup>
<col style="width: 33%" />
<col style="width: 33%" />
<col style="width: 33%" />
</colgroup>
<tbody>
<tr class="header">
<th colspan="3">D8h, +82.8 kcal/mol</th>
</tr>
<tr class="odd">
<th>Follow B<sub>2u</sub> 467<em>i</em></th>
<th>Follow E<sub>3g</sub> 404<em>i</em></th>
<th>Follow E<sub>2u</sub> 230<em>i</em></th>
</tr>
<tr class="header">
<th>to D<sub>4d</sub> +0.8</th>
<th>to C<sub>i</sub> 131<em>i</em> (A<sub>u</sub>), +7.5</th>
<th>to D<sub>2d</sub> +3.6</th>
</tr>
<tr class="odd">
<th><div id="attachment_1611" class="wp-caption aligncenter"
style="width: 140px">
<img
src="http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2010/01/co-1.jpg"
title="Imaginary modes of planar cyclo-octane"
class="size-full wp-image-1611" loading="lazy" decoding="async"
aria-describedby="caption-attachment-1611"
onclick="jmolInitialize(&#39;../Jmol/&#39;);jmolSetAppletColor(&#39;black&#39;);jmolApplet([450,450],&#39;load wp-content/uploads/2010/01/cyclooctane-d8h.log;frame 13;zoom 5;moveto 4 0 2 0 90 90;vectors on;vectors 4;vectors scale 5.0; color vectors green; vibration 6;animation mode loop;&#39;);"
width="130" height="94" />
<p>B2u</p>
</div></th>
<th><div id="attachment_1612" class="wp-caption aligncenter"
style="width: 130px">
<img
src="http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2010/01/co-2.jpg"
title="Imaginary modes of planar cyclo-octane"
class="size-full wp-image-1612" loading="lazy" decoding="async"
aria-describedby="caption-attachment-1612"
onclick="jmolInitialize(&#39;../Jmol/&#39;);jmolSetAppletColor(&#39;black&#39;);jmolApplet([450,450],&#39;load wp-content/uploads/2010/01/cyclooctane-d8h.log;frame 14;zoom 5;moveto 4 0 2 0 90 90;vectors on;vectors 4;vectors scale 5.0; color vectors green; vibration 6;animation mode loop;&#39;);"
width="120" height="129" />
<p>E3g</p>
</div></th>
<th><div id="attachment_1613" class="wp-caption aligncenter"
style="width: 130px">
<img
src="http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2010/01/co-3.jpg"
title="Imaginary modes of planar cyclo-octane"
class="size-full wp-image-1613" loading="lazy" decoding="async"
aria-describedby="caption-attachment-1613"
onclick="jmolInitialize(&#39;../Jmol/&#39;);jmolSetAppletColor(&#39;black&#39;);jmolApplet([450,450],&#39;load wp-content/uploads/2010/01/cyclooctane-d8h.log;frame 16;zoom 5;moveto 4 0 2 0 90 90;vectors on;vectors 4;vectors scale 5.0; color vectors green; vibration 6;animation mode loop;&#39;);"
width="120" height="129" />
<p>E2u</p>
</div></th>
</tr>
<tr class="header">
<th>C<sub>s</sub> <span
style="vertical-align: baseline;">0.0</span></th>
<th>C<sub>2</sub> +1.6</th>
<th>–</th>
</tr>
&#10;</tbody>
</table>

Following the remaining E~3g~ mode leads to a stationary point of C~i~
symmetry (DOI: [10042/to-3743](http://hdl.handle.net/10042/to-3743)).
This is a valley-ridge potential, since this point turns out to be a
transition state itself, and following the A~u~ imaginary mode at this
point results in another, this time stable conformation, of chiral C~2~
symmetry (DOI: [10042/to-3744](http://hdl.handle.net/10042/to-3744)).
This has a calculated optical rotation \[α\]~D~ of 72° (at 589nm in
chloroform).

Are these three conformations all there are? Well, a thorough analysis
of the conformational space has in fact identified six minima (DOI:
[10.1002/(SICI)1096-987X(19980415)19:5\<524::AID-JCC5\>3.0.CO;2-O](http://dx.doi.org/10.1002/(SICI)1096-987X(19980415)19:5%3C524::AID-JCC5%3E3.0.CO;2-O){target="new"}),
of which the most stable has C~s~ symmetry (the so-called **chair-boat**
conformation, and the one most frequently found in crystal structures of
cyclo-octanes). Where is that one in the above analysis? It arrives by a
distortion of the D~4d~ form (DOI:
[10042/to-3747](http://hdl.handle.net/10042/to-3747)) *via* a transition
state of no symmetry (DOI:
[10042/to-3752](http://hdl.handle.net/10042/to-3752))

Whilst the full potential surface clearly has many more features,
following the modes of the planar conformation of cyclo-octane is a
simple and rapid way of establishing four of the six limiting stable
conformations (the two remaining forms have  D~2~ and S~4~ symmetry, see
DOI
[10.1016/0166-1280(88)80008-3](http://dx.doi.org/10.1016/0166-1280(88)80008-3){onclick="var doiWin; doiWin=window.open('http://dx.doi.org/10.1016/0166-1280(88)80008-3','doilink','scrollbars=yes,resizable=yes,directories=yes,toolbar=yes,menubar=yes,status=yes'); doiWin.focus()"
target="doilink"}).

::: {#attachment_1619 .wp-caption .aligncenter style="width: 173px"}
[![](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2010/01/co-4.jpg "co-4"){.size-full
.wp-image-1619 loading="lazy" decoding="async"
aria-describedby="caption-attachment-1619" width="163"
height="233"}](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2010/01/co-4.jpg)

AIM analysis of D2d cyclo-octane.
:::

Finally as promised, the AIM analysis of the D~2d~ conformer (above).
The ρ(r) value at the interesting H...H critical point is 0.015, which
is pretty high in comparison to most normal hydrogen bonds, and would be
conventionally taken to indicate **attraction**. The Laplacian ∇^2^ρ(r)
is +0.05. The "bond" ellipticity ε has a value of 0.29. Single bonds are
close to zero, and C=C double bonds are \~0.4, so this is pretty high
(see also
DOI: [10.1002/anie.200805751](http://dx.doi.org/10.1002/anie.200805751){target="new"}).

The two highest C-H stretching vibrations for this conformation are well
separated from all the others (ν 3095, 3103 cm^-1^ for the symmetric
A~1~ and antisymmetric B~2~ combinations, below for animations). These
vibrations serve to both decrease and increase the H...H distances as
part of the atomic (harmonic) displacements, and clearly doing so takes
more energy than vibrating any of the other C-H bonds. It seems unlikely
that the C-H bonds are themselves stronger, so does that mean that the
H...H interaction is attractive or is it repulsive? In this context, it
is worth noting that the symmetric vibration (both H...H distances
decrease/increase at the same time) is lower in wavenumber than the mode
which decreases one and increases the other.

<table data-border="1">
<colgroup>
<col style="width: 50%" />
<col style="width: 50%" />
</colgroup>
<tbody>
<tr class="odd">
<td><div id="attachment_1611" class="wp-caption aligncenter"
style="width: 196px">
<img
src="http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2010/01/co-6.jpg"
title="Imaginary modes of planar cyclo-octane"
class="size-full wp-image-1611" loading="lazy" decoding="async"
aria-describedby="caption-attachment-1611"
onclick="jmolInitialize(&#39;../Jmol/&#39;);jmolSetAppletColor(&#39;black&#39;);jmolApplet([450,450],&#39;load wp-content/uploads/2010/01/cyclooctane-d2d.log;frame 95;zoom 5;moveto 4 0 2 0 90 90;vectors on;vectors 4;vectors scale 5.0; color vectors green; vibration 6;animation mode loop;&#39;);"
width="186" height="206" />
<p>A1</p>
</div></td>
<td><div id="attachment_1611" class="wp-caption aligncenter"
style="width: 191px">
<img
src="http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2010/01/co-5.jpg"
title="Imaginary modes of planar cyclo-octane"
class="size-full wp-image-1611" loading="lazy" decoding="async"
aria-describedby="caption-attachment-1611"
onclick="jmolInitialize(&#39;../Jmol/&#39;);jmolSetAppletColor(&#39;black&#39;);jmolApplet([450,450],&#39;load wp-content/uploads/2010/01/cyclooctane-d2d.log;frame 96;zoom 5;moveto 4 0 2 0 90 90;vectors on;vectors 4;vectors scale 5.0; color vectors green; vibration 6;animation mode loop;&#39;);"
width="181" height="167" />
<p>B2</p>
</div></td>
</tr>
</tbody>
</table>

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


In the previous post, I suggested that inspecting the imaginary modes of planar cyclohexane might be a fruitful and systematic way in which at least parts of the conformational surface of this ring might be probed.

Messaggi di Rogue Scholar

The conformational analysis of cyclo-octane