Imperial College London

Henry Rzepa

The electrophilic substitution of indoles is a staple of any course on
organic chemistry. Indoles also hold a soft-spot for me, since I
synthesized not a few as part of my Ph.D.
studies.\[cite\]10.1039/P29750001209\[/cite\],\[cite\]10.1039/P29770000281\[/cite\]
The preference for substitution in the 3-position is normally explained
using the arrows shown below (position 3=green,2=blue,1=red). Here I
explore how these arrows might be interpreted in terms of various
quantum mechanical properties.

![indole](http://www.ch.imperial.ac.uk/rzepa/blog/wp-content/uploads/2013/03/indole1.svg){.aligncenter
.size-full .wp-image-9674 decoding="async" width="300"}

I have elsewhere in these posts shown how NBO (natural bond orbitals)
can often be used to probe donor-acceptor interactions in molecules. Can
it be applied to indole (as donor) interacting with an electrophile (as
acceptor) in order to predict where the most nucleophilic centre is? The
law is that the pair of such filled/empty orbitals with the lowest
energy gap will predict the reactivity. Since the electrophile E is
common, we might presume that the NBO donor orbital with the highest
energy is the relevant predictor. Well, this emerges as the NBO
describing the 8,9 bond; it is not any of those shown above! The next
NBO in energy is also located on the benzo group. Only the 3rd-highest
NBO corresponds to the red arrows above. In fact the NBO with the
*least-favourable* energy is the one that maps to positions 2 or 3,
those normally implicated in the reactions of this molecule. What has
gone wrong?

<table class="aligncenter" data-border="1" data-align="center">
<colgroup>
<col style="width: 33%" />
<col style="width: 33%" />
<col style="width: 33%" />
</colgroup>
<tbody>
<tr class="odd">
<td><div id="attachment_9680" class="wp-caption aligncenter"
style="width: 140px">
<img
src="http://www.ch.imperial.ac.uk/rzepa/blog/wp-content/uploads/2013/03/indole-31.jpg"
class="wp-image-9680" decoding="async"
aria-describedby="caption-attachment-9680"
onclick="jmolInitialize(&#39;../Jmol/&#39;,&#39;JmolAppletSigned.jar&#39;);jmolSetAppletColor(&#39;white&#39;);jmolApplet([450,450],&#39;load wp-content/uploads/2013/03/indole_mo31.cub_.xyz;isosurface color pink green wp-content/uploads/2013/03/indole_mo31.cub_.jvxl translucent;&#39;);"
width="130" alt="Click for 3D" />
<p>E=-0.2910au.<br />
Click for 3D</p>
</div></td>
<td colspan="2"><div id="attachment_9680" class="wp-caption aligncenter"
style="width: 180px">
<img
src="http://www.ch.imperial.ac.uk/rzepa/blog/wp-content/uploads/2013/03/indole-30.jpg"
class="wp-image-9680" decoding="async"
aria-describedby="caption-attachment-9680"
onclick="jmolInitialize(&#39;../Jmol/&#39;,&#39;JmolAppletSigned.jar&#39;);jmolSetAppletColor(&#39;white&#39;);jmolApplet([450,450],&#39;load wp-content/uploads/2013/03/indole_mo30.cub_.xyz;isosurface color yellow red wp-content/uploads/2013/03/indole_mo30.cub_.jvxl translucent;&#39;);"
width="170" alt="Click for 3D" />
<p>E=-0.3107au.<br />
Click for 3D</p>
</div></td>
</tr>
<tr class="even">
<td><div id="attachment_9680" class="wp-caption aligncenter"
style="width: 130px">
<img
src="http://www.ch.imperial.ac.uk/rzepa/blog/wp-content/uploads/2013/03/indole-29.jpg"
decoding="async" aria-describedby="caption-attachment-9680"
onclick="jmolInitialize(&#39;../Jmol/&#39;,&#39;JmolAppletSigned.jar&#39;);jmolSetAppletColor(&#39;white&#39;);jmolApplet([450,450],&#39;load wp-content/uploads/2013/03/indole_mo29.cub_.xyz;isosurface color green blue wp-content/uploads/2013/03/indole_mo29.cub_.jvxl translucent;&#39;);"
width="120" alt="Click for 3D" />
<p>E=-0.3113au.<br />
Click for 3D</p>
</div></td>
<td><div id="attachment_9680" class="wp-caption aligncenter"
style="width: 130px">
<img
src="http://www.ch.imperial.ac.uk/rzepa/blog/wp-content/uploads/2013/03/indole-28.jpg"
decoding="async" aria-describedby="caption-attachment-9680"
onclick="jmolInitialize(&#39;../Jmol/&#39;,&#39;JmolAppletSigned.jar&#39;);jmolSetAppletColor(&#39;white&#39;);jmolApplet([450,450],&#39;load wp-content/uploads/2013/03/indole_mo28.cub_.xyz;isosurface color orange green wp-content/uploads/2013/03/indole_mo28.cub_.jvxl translucent;&#39;);"
width="120" alt="Click for 3D" />
<p>E=-0.3142au.<br />
Click for 3D</p>
</div></td>
<td><div id="attachment_9680" class="wp-caption aligncenter"
style="width: 130px">
<img
src="http://www.ch.imperial.ac.uk/rzepa/blog/wp-content/uploads/2013/03/indole-27.jpg"
decoding="async" aria-describedby="caption-attachment-9680"
onclick="jmolInitialize(&#39;../Jmol/&#39;,&#39;JmolAppletSigned.jar&#39;);jmolSetAppletColor(&#39;white&#39;);jmolApplet([450,450],&#39;load wp-content/uploads/2013/03/indole_mo27.cub_.xyz;isosurface color yellow blue wp-content/uploads/2013/03/indole_mo27.cub_.jvxl translucent;&#39;);"
width="120" alt="Click for 3D" />
<p>E=-0.3335au.<br />
Click for 3D</p>
</div></td>
</tr>
</tbody>
</table>

To start understanding, we must review the assumptions made in the above
analysis.

1.  Firstly, we need to distinguish between **local** and **global**
    properties of molecules. A local property is one e.g. associated
    perhaps with an atom or bond. A global property might be the
    **aromaticity** of the system as a whole. The NBO analysis, by
    definition, tries to localise the wavefunction to one or two
    centres. This means that it reduces a six-electron aromatic ring to
    three two-centre bonds. But breaking up an aromatic ring may not be
    the best way of looking at the problem. In this case, the 2,3 N=C
    bond emerges as the most stable double bond, largely because the six
    electrons of the benzo group are delocalised and hence not so stable
    locally! So too much localisation can throw the baby away with the
    bath water. So let us try a rather more global property, the
    molecular electrostatic potential (MEP):  

    ::: {#attachment_9691 .wp-caption .aligncenter style="width: 299px"}
    ![Molecular electrostatic potential. Click for
    3D.](http://www.ch.imperial.ac.uk/rzepa/blog/wp-content/uploads/2013/03/indole-mep.jpg){.wp-image-9691
    loading="lazy" decoding="async"
    aria-describedby="caption-attachment-9691"
    onclick="jmolInitialize('../Jmol/','JmolAppletSigned.jar');jmolSetAppletColor('white');jmolApplet([450,450],'load wp-content/uploads/2013/03/indole_esp.cub_.xyz;isosurface color green red wp-content/uploads/2013/03/indole_esp.cub_.jvxl translucent;');"
    width="289" height="241"}
    Molecular electrostatic potential. Click for 3D.
    :::

    This probes the molecule for regions which are the most attractive
    to a proton (=E^+^). Perhaps surprisingly, the benzo group still
    emerges as the most attractive region, but at least there is a small
    attractive finger (green) that reaches out to the 3-position rather
    than the 2-position (the "right" answer). It is not entirely
    convincing though, is it?

2.  Which leads us on to another assumption, which invokes [Hammond's
    postulate](http://www.ch.imperial.ac.uk/rzepa/blog/?p=8508){target="_blank"}
    that the transition state for the reaction will resemble the stable
    species nearest to it in free energy. What if the transition state
    (which is what determines the rate of a reaction) more closely
    resembles the (initial) product of this reaction, the
    [so-called](http://www.ch.imperial.ac.uk/rzepa/blog/?p=5411){target="_blank"}
    [Wheland
    intermediate](http://www.ch.imperial.ac.uk/rzepa/blog/?p=2423){target="_blank"}
    rather than indole itself? I am going to calculate this intermediate
    in a novel manner; as an ion-pair resulting from reaction of indole
    with HCl in methanol (I have blogged elsewhere that I regard it as
    lazy to simple add a proton and put +1 as the overall charge of the
    system). So here are the relative free energies of indole reacted
    with HCl in respectively the 1,2 and 3 positions:
    [4.1](http://hdl.handle.net/10.6084/m9.figshare.643801){target="_blank"},
    [10.0](http://hdl.handle.net/10.6084/m9.figshare.643802){target="_blank"},
    [0.0](http://hdl.handle.net/10.6084/m9.figshare.643800){target="_blank"} kcal/mol.The
    relatively high energy of the 2-substituted intermediate reflects
    its loss of *global* aromaticity compared to the other two, rather
    than necessarily any local property.   

    ::: {#attachment_9696 .wp-caption .aligncenter style="width: 229px"}
    ![3-Wheland intermediate. Click for
    3D.](http://www.ch.imperial.ac.uk/rzepa/blog/wp-content/uploads/2013/03/indole-wheland.jpg){.wp-image-9696
    loading="lazy" decoding="async"
    aria-describedby="caption-attachment-9696"
    onclick="jmolInitialize('../Jmol/','JmolAppletSigned.jar');jmolSetAppletColor('white');jmolApplet([450,450],'load wp-content/uploads/2013/03/indole-3H-824.505997.mol');"
    width="219" height="155"}
    3-Wheland intermediate. Click for 3D.
    :::

    We might therefore conclude that one should not seek evidence in the
    wavefunction of indole itself for the preference for green rather
    than blue or red arrows as shown above, but in a reaction product
    which best reflects the global properties such as aromaticity.

3.  One could go one stage further and actually locate explicit
    transition states for the three isomeric reactions, as was [done
    here](http://www.ch.imperial.ac.uk/rzepa/blog/?p=7344){target="_blank"}.
    I may report back on this in the future.

I set out these approaches aware that a subject is often taught by
reducing it to rules (heuristics) which one then hopes are transferable
between different molecules with common local or global features. One
does not want to reduce it down merely to numbers computed from a wave
equation. But one should also remember that whilst arrow-pushing may be
fine for relatively simple systems, it may not be robust towards
increasing complexity (*i.e.* multiple substituents around the ring). At
some stage, one will have to take the decision to augment the simple
heuristics with computed numbers. Deciding when to do so will be one of
the challenges facing the teaching of chemistry over the next decade.

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


The electrophilic substitution of indoles is a staple of any course on organic chemistry.

Messaggi di Rogue Scholar

Understanding the electrophilic aromatic substitution of indole.