Imperial College London

Henry Rzepa

The hydration of an alkene by an acid is one of those fundamental
reactions, taught early on in most chemistry courses. What can quantum
mechanics teach us about the mechanism of the reaction?

::: {#attachment_4838 .wp-caption .aligncenter style="width: 310px"}
[![](http://www.ch.imperial.ac.uk/rzepa/blog/wp-content/uploads/2011/09/hydration.jpg "hydration"){.size-full
.wp-image-4838 loading="lazy" decoding="async"
aria-describedby="caption-attachment-4838" width="300"
height="52"}](http://www.ch.imperial.ac.uk/rzepa/blog/wp-content/uploads/2011/09/hydration.jpg)

The hydration of ethene by a hydronium cation.
:::

The diagram below shows us the IRC, or intrinsic reaction coordinate for
the process (for definitions, [see
here](http://www.gaussian.com/g_tech/g_ur/k_irc.htm){target="_blank"}),
the reaction proceeding from left to right as shown in the scheme above,
with a (free energy) barrier of 14.4 kcal/mol and exothermic by a
similar amount
([wB97XD/6-311G(d,p)](http://hdl.handle.net/10042/to-9368){target="_blank"}
with a continuum solvation correction for water).

![](http://www.ch.imperial.ac.uk/rzepa/blog/wp-content/uploads/2011/09/hydration.svg){decoding="async"
width="500"}

One first notices that it is not the smooth bell-shaped profile that is
normally drawn in text books. It has bumps/detail. What do these mean?
Before dissecting, lets look at another plot, this time the RMS (root
mean square) gradients of the 3N-6 geometric variables along the
reaction coordinates. These reveal two regions where the RMS gradient is
almost zero (other than reactant and product).

![](http://www.ch.imperial.ac.uk/rzepa/blog/wp-content/uploads/2011/09/hydration_grad.svg){decoding="async"
width="500"}

<table data-border="0">
<colgroup>
<col style="width: 33%" />
<col style="width: 33%" />
<col style="width: 33%" />
</colgroup>
<tbody>
<tr class="header">
<th>1</th>
<th>2</th>
<th>3</th>
</tr>
&#10;<tr class="odd">
<td><div id="attachment_4849" class="wp-caption aligncenter"
style="width: 140px">
<img
src="http://www.ch.imperial.ac.uk/rzepa/blog/wp-content/uploads/2011/09/Hyd_r.jpg.jpg"
title="Hyd_r.jpg" class="size-full wp-image-4849" loading="lazy"
decoding="async" aria-describedby="caption-attachment-4849"
onclick="jmolInitialize(&#39;../Jmol/&#39;);jmolSetAppletColor(&#39;yellow&#39;);jmolApplet([450,450],&#39;load wp-content/uploads/2011/09/hyd_r.mol;&#39;);"
width="130" height="95" />
<p>Hydrogen-bonded reactant</p>
</div></td>
<td><div id="attachment_4851" class="wp-caption aligncenter"
style="width: 140px">
<img
src="http://www.ch.imperial.ac.uk/rzepa/blog/wp-content/uploads/2011/09/Hyd_2.jpg.jpg"
title="Hyd_2.jpg" class="size-full wp-image-4851" loading="lazy"
decoding="async" aria-describedby="caption-attachment-4851"
onclick="jmolInitialize(&#39;../Jmol/&#39;);jmolSetAppletColor(&#39;yellow&#39;);jmolApplet([450,450],&#39;load wp-content/uploads/2011/09/hyd_2.mol;&#39;);"
width="130" height="99" />
<p>Forming bridged protonated ethene</p>
</div></td>
<td><div id="attachment_4852" class="wp-caption aligncenter"
style="width: 140px">
<img
src="http://www.ch.imperial.ac.uk/rzepa/blog/wp-content/uploads/2011/09/Hyd_ts.jpg"
title="Hyd_ts" class="size-full wp-image-4852" loading="lazy"
decoding="async" aria-describedby="caption-attachment-4852"
onclick="jmolInitialize(&#39;../Jmol/&#39;);jmolSetAppletColor(&#39;yellow&#39;);jmolApplet([450,450],&#39;load wp-content/uploads/2011/09/hyd_ts.log; frame 25; zoom 100; connect (atomno=7) (atomno=9) PARTIAL;connect (atomno=9) (atomno=1) PARTIAL;vectors on;vectors 4;vectors scale 5.0; color vectors green; vibration 20;animation mode loop;&#39;);"
width="130" height="86" />
<p>The transition state Click for 3D.</p>
</div></td>
</tr>
</tbody>
</table>

<table data-border="0">
<colgroup>
<col style="width: 50%" />
<col style="width: 50%" />
</colgroup>
<tbody>
<tr class="header">
<th>4</th>
<th>5</th>
</tr>
&#10;<tr class="odd">
<td><div id="attachment_4855" class="wp-caption aligncenter"
style="width: 140px">
<img
src="http://www.ch.imperial.ac.uk/rzepa/blog/wp-content/uploads/2011/09/Hyd_3.jpg"
title="Hyd_3" class="size-full wp-image-4855" loading="lazy"
decoding="async" aria-describedby="caption-attachment-4855"
onclick="jmolInitialize(&#39;../Jmol/&#39;);jmolSetAppletColor(&#39;yellow&#39;);jmolApplet([450,450],&#39;load wp-content/uploads/2011/09/Hyd_3.mol;&#39;);"
width="130" height="99" />
<p>Second phase, C-O bond formation</p>
</div></td>
<td><div id="attachment_4856" class="wp-caption aligncenter"
style="width: 140px">
<img
src="http://www.ch.imperial.ac.uk/rzepa/blog/wp-content/uploads/2011/09/Hyd_4.jpg"
title="Hyd_4" class="size-full wp-image-4856" loading="lazy"
decoding="async" aria-describedby="caption-attachment-4856"
onclick="jmolInitialize(&#39;../Jmol/&#39;);jmolSetAppletColor(&#39;yellow&#39;);jmolApplet([450,450],&#39;load wp-content/uploads/2011/09/Hyd_4.mol;&#39;);"
width="130" height="153" />
<p>Rotating from eclipsed to staggered</p>
</div></td>
</tr>
</tbody>
</table>

Five distinct stages can be seen.

1.  The hydronium ion approaches the ethene, and forms quite a strong
    π-facial hydrogen bond.
2.  Water now starts separating from the hydrogen bonded complex, thus
    relocating the H-bond from the alkene to the water.
3.  The formal transition state (the only one) is reached, with the
    proton moving from the symmetric bridged ethyl cation to one end,
    and the water is starting to move to the other end. Not perhaps the
    most obvious of transition states!
4.  The formation of the C-O bond is now completing, and the C-C bond is
    now almost purely converted from double to single.
5.  Only at this stage does the eclipsed conformation of the newly
    formed ethanol start to rotate into a staggered and final
    conformation.
6.  Overall, the reaction is concerted (if not synchronous), and its
    reverse would be classified as an E2 elimination.

You can see quite a lot of simple basic principles in chemistry are
illustrated along this reaction coordinate. We have space for one more:
what happens if you make the alkene very much more reactive? How about
cyclobutadiene, which in avoiding anti-aromaticity, has become highly
reactive.

::: {#attachment_4871 .wp-caption .aligncenter style="width: 310px"}
[![](http://www.ch.imperial.ac.uk/rzepa/blog/wp-content/uploads/2011/09/hydration1.jpg "hydration1"){.size-full
.wp-image-4871 loading="lazy" decoding="async"
aria-describedby="caption-attachment-4871" width="300"
height="86"}](http://www.ch.imperial.ac.uk/rzepa/blog/wp-content/uploads/2011/09/hydration1.jpg)

Hydration of cyclobutadiene.
:::

The IRC for this variation is shown below. Notice now the much smaller
barrier to reaction (\~0.4 kcal/mol in ΔG), and the much greater
exothermicity overall.

![](http://www.ch.imperial.ac.uk/rzepa/blog/wp-content/uploads/2011/09/cbd_1.svg){decoding="async"
width="500"}

![](http://www.ch.imperial.ac.uk/rzepa/blog/wp-content/uploads/2011/09/cbd_2.svg){decoding="async"
width="500"}

The transition state is also different. It corresponds to proton
transfer from the hydronium cation to one carbon of the cyclobutadiene,
to form a stabilised allyl cation. In terms of the reverse elimination,
this now corresponds to an E1 type, involving an intermediate species,
and the reaction is no longer concerted.

::: {#attachment_4873 .wp-caption .aligncenter style="width: 210px"}
![](http://www.ch.imperial.ac.uk/rzepa/blog/wp-content/uploads/2011/09/cbd_5.jpg "cbd_5"){.size-full
.wp-image-4873 loading="lazy" decoding="async"
aria-describedby="caption-attachment-4873"
onclick="jmolInitialize('../Jmol/');jmolSetAppletColor('yellow');jmolApplet([450,450],'load wp-content/uploads/2011/09/cbd+h2o_ts.log; frame 55; zoom 100; connect (atomno=7) (atomno=1) PARTIAL;connect (atomno=5) (atomno=7) PARTIAL;vectors on;vectors 4;vectors scale 5.0; color vectors green; vibration 20;animation mode loop;');"
width="200" height="168"}

The transition state for protonation of cyclobutadiene
:::

I will stop here, reminding that these two simple reactions have taught
us a lot about basic organic chemistry.

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


The hydration of an alkene by an acid is one of those fundamental reactions, taught early on in most chemistry courses. What can quantum mechanics teach us about the mechanism of the reaction? The hydration of ethene by a hydronium cation.

Messaggi di Rogue Scholar

Anatomy of a simple reaction: the hydration of an alkene.