Imperial College London

Henry Rzepa

Is there a preferred pack size for electrons on the move? Or put less
flamboyantly, is there an optimum, and a maximum number of arrows
(electron pairs) that one might push in revealing the mechanism of a
concerted reaction? A sort of village-instinct for electrons. Consider
the following (known, DOI:
[10.1016/S0040-4039(00)98289-3](http://dx.doi.org/10.1016/S0040-4039(00)98289-3){target="_blank"})
reaction

::: {#attachment_3188 .wp-caption .aligncenter style="width: 248px"}
[![](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2010/12/333.jpg "333"){.size-full
.wp-image-3188 loading="lazy" decoding="async"
aria-describedby="caption-attachment-3188" width="238"
height="107"}](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2010/12/333.jpg)

A double 3,3 sigmatropic reaction
:::

It is a double \[3,3\] sigmatropic rearrangement, each component
involving two packs of three arrows (six electrons) each. Do these packs
move together, or do they prefer to move one at a time? If the former,
then we come up against another interesting question. How many of say
the six bonding electrons in a triple bond can simultaneously
participate in a reaction? Many a tutor of the arrow pushing exercise
might say the limit is always two (I have even seen this written into a
set of rules for arrow pushing). But could it be four, as shown in the
above example? Or perchance even six as discussed in [this
post](http://www.ch.ic.ac.uk/rzepa/blog/?p=1158){target="_blank"}? OK,
the question is rather loaded for this example, since being a pericyclic
reaction it has a built in (thermal) preference for packs of 4n+2
electrons, which enable the transition state for the process to be
considered as aromatic. So in a sense it boils down to whether two
aromatic packs would have any advantage in both marauding concurrently.

A connection can also be made to recent work by Rainer Herges
(DOI: [10.1021/jo801390x](http://dx.doi.org/10.1021/jo801390x){target="_blank"})
in which he suggests that pericyclic reactions involving four electrons
at an alkyne can indeed be concerted, giving them the specific name of
coarctate reactions (ones which exhibit one or more coarctate atoms at
each of which two bonds are made and two bonds are broken). And one
further connection is to [Clar
islands](http://www.ch.ic.ac.uk/rzepa/blog/?p=1292){target="_blank"}, in
which the tendency of electrons in polycyclic aromatic hydrocarbons
(PAH) to form packs of six is discussed (these of course are not
marauding).

So onwards to a computational exploration (B3LYP/6-311G(d,p),
[10042/to-6354](http://hdl.handle.net/10042/to-6354){target="_blank"}).
Two geometries can be located, with respectively C~2~ and C~i~
symmetries. They differ in the orientation of the two chair-like rings,
and the former (shown below) is the more (*cis*) stable. Two negative
force constants are calculated (shown below) which indicate that the two
\[3,3\] sigmatropic rearrangements like to go consecutively and not
concurrently.

<table data-border="0">
<colgroup>
<col style="width: 50%" />
<col style="width: 50%" />
</colgroup>
<tbody>
<tr class="odd">
<td><div id="attachment_3202" class="wp-caption aligncenter"
style="width: 203px">
<img
src="http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2010/12/333-cis.jpg"
title="333-cis" class="size-full wp-image-3202" loading="lazy"
decoding="async" aria-describedby="caption-attachment-3202"
onclick="jmolInitialize(&#39;../Jmol/&#39;,true);jmolSetAppletColor(&#39;green&#39;);jmolApplet([600,600],&#39;load wp-content/uploads/2010/12/333-C2.log;frame 40;set measurementUnits Angstroms;delay 5;vectors on;vectors 4;vectors scale 5.0; color vectors purple; vibration 15;animation mode loop;connect (atomno=19) (atomno=2) PARTIAL;connect (atomno=9) (atomno=3) PARTIAL;connect (atomno=12) (atomno=6) PARTIAL;connect (atomno=1) (atomno=22) PARTIAL;&#39;);"
srcset="https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2010/12/333-cis.jpg 579w, https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2010/12/333-cis-300x231.jpg 300w"
sizes="(max-width: 193px) 100vw, 193px" width="193" height="149" />
<p>Geometry of the asynchronous pathway. Click for 3D</p>
</div></td>
<td><div id="attachment_3203" class="wp-caption aligncenter"
style="width: 203px">
<img
src="http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2010/12/333-cis-sym.jpg"
title="333-cis-sym" class="size-full wp-image-3203" loading="lazy"
decoding="async" aria-describedby="caption-attachment-3203"
onclick="jmolInitialize(&#39;../Jmol/&#39;,true);jmolSetAppletColor(&#39;red&#39;);jmolApplet([600,600],&#39;load wp-content/uploads/2010/12/333-C2.log;frame 39;set measurementUnits Angstroms;delay 5;vectors on;vectors 4;vectors scale 5.0; color vectors purple; vibration 15;animation mode loop;connect (atomno=19) (atomno=2) PARTIAL;connect (atomno=9) (atomno=3) PARTIAL;connect (atomno=12) (atomno=6) PARTIAL;connect (atomno=1) (atomno=22) PARTIAL;&#39;);"
srcset="https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2010/12/333-cis-sym.jpg 579w, https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2010/12/333-cis-sym-300x231.jpg 300w"
sizes="(max-width: 193px) 100vw, 193px" width="193" height="149" />
<p>Geometry of the synchronous pathway. Click for 3D</p>
</div></td>
</tr>
</tbody>
</table>

The ΔG† is calculated as high as 58.3 kcal/mol, which given that the
reaction does proceed experimentally at \~410°C suggests this cannot be
the true mechanism (discussion of which I leave to a future post). The
electrons therefore move in [smaller
packs](http://hdl.handle.net/10042/to-6355){target="_blank"}, but
certainly not 12!

::: {#attachment_3225 .wp-caption .aligncenter style="width: 260px"}
[![](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2010/12/333async1.jpg "333async"){.size-full
.wp-image-3225 loading="lazy" decoding="async"
aria-describedby="caption-attachment-3225" width="250" height="109"
srcset="https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2010/12/333async1.jpg 1000w, https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2010/12/333async1-300x130.jpg 300w"
sizes="(max-width: 250px) 100vw, 250px"}](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2010/12/333async1.jpg)

Hunting in packs of six, not twelve.
:::

In conclusion, one might make the analogy of electrons as medieval
travellers, preferring to travel in small groups, and probably
invariably stopping off a in a coaching inn for a rest whenever they see
one close to their route (or perhaps even sometimes well off the route).
I suspect (but cannot prove) that there are few types of bond forming or
bond breaking reactions which involve more than five arrows (ten
electrons) participating in a single concerted step. More, and I think
the travelling electrons are likely to find a resting place  on the
journey (which, if not a closed shell species, may well be a biradical,
or in suitable solvent, zwitterion).

So that is the challenge posed here; to find an example of a reaction
involving six or more arrows which theory appears to show is concerted
and where new bonds are formed, or old ones broken (this last clause
excludes artificial reactions such as bond shifting in higher
annulenes).

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


Is there a preferred pack size for electrons on the move? Or put less flamboyantly, is there an optimum, and a maximum number of arrows (electron pairs) that one might push in revealing the mechanism of a concerted reaction? A sort of village-instinct for electrons.

Postagens de Rogue Scholar

Do marauding electrons go in packs?