Imperial College London

Henry Rzepa

The benzidine rearrangement is claimed to be an example of the quite
rare \[5,5\] sigmatropic migration\[cite\]10.1021/ja00335a035\[/cite\],
which is a [ten-electron
homologation](http://www.ch.imperial.ac.uk/rzepa/blog/?p=7756){target="_blank"}
of the very common \[3,3\] sigmatropic reaction (*e.g.* the Cope or
Claisen). Some benzidine rearrangements are indeed thought to go through
the \[3,3\] route\[cite\]10.1021/ja00309a041\[/cite\]. The topic has
been reviewed here\[cite\]10.1002/poc.610020702\[/cite\].

![benzidine](http://www.ch.imperial.ac.uk/rzepa/blog/wp-content/uploads/2013/01/benzidine.svg){.aligncenter
.size-full .wp-image-8962 decoding="async" width="420"}

In this post, I offer a calculated [transition
state](http://hdl.handle.net/10042/22394){target="_blank"} and
[IRC](http://hdl.handle.net/10042/22396){target="_blank"} for this
reaction, to see what insights might accrue. How was this obtained?

1.  At the ωB97XD/6-311G(d,p)/SCRF=water level. This procedure would
    allow for any dispersion-like effects to be allowed for in the
    π-π-stacking. 
2.  The rearrangement is normally promoted by acid, and the active
    species is thought to be
    diprotonated\[cite\]10.1002/ejic.201101115\[/cite\]^‡^ (although
    [monoprotonated
    catalysis](http://www.ch.imperial.ac.uk/rzepa/blog/?p=9018 "Hidden intermediates in the benzidine rearrangement. The monoprotonated mechanism."){target="_blank"}
    is also observed\[cite\]10.1021/ja00335a035\[/cite\]. Here I report
    just the diprotonated route, together with chloride anions to
    balance the charges, and have added a continuum water field to allow
    this double ion-pair to be at least partially stabilised.
3.  The rate determining step is the N-N cleavage/C-C bond formation.
    This is followed by presumed rapid proton transfers, which are not
    modelled here.

<table class="aligncenter" data-border="1" data-align="center">
<colgroup>
<col style="width: 50%" />
<col style="width: 50%" />
</colgroup>
<tbody>
<tr class="odd">
<td><div id="attachment_8964" class="wp-caption aligncenter"
style="width: 220px">
<img
src="http://www.ch.imperial.ac.uk/rzepa/blog/wp-content/uploads/2013/01/benzidine-55.jpg"
class="wp-image-8964" decoding="async"
aria-describedby="caption-attachment-8964"
onclick="jmolInitialize(&#39;../Jmol/&#39;);jmolSetAppletColor(&#39;white&#39;);jmolApplet([450,450],&#39;load wp-content/uploads/2013/01/benzidine-p-1495.381456.log;frame 17;connect (atomno=3) (atomno=1) PARTIAL;connect (atomno=23) (atomno=12) PARTIAL;vectors on;vectors 4;vectors scale 5.0; color vectors magenta; vibration 20;animation mode loop;&#39;);"
width="210"
alt="The [5,5] transition state for the benzidine rearrangement. Click for 3D." />
<p>The [5,5] transition state for the benzidine rearrangement. Click for
3D.</p>
</div></td>
<td><img
src="http://www.ch.imperial.ac.uk/rzepa/blog/wp-content/uploads/2013/01/benzidine-55.gif"
class="aligncenter size-full wp-image-8995" decoding="async" width="210"
alt="benzidine-55" /></td>
</tr>
<tr class="even">
<td><img
src="http://www.ch.imperial.ac.uk/rzepa/blog/wp-content/uploads/2013/01/benzidine-55E.svg"
class="aligncenter size-full wp-image-8997" decoding="async" width="210"
alt="benzidine-55E" /></td>
<td><img
src="http://www.ch.imperial.ac.uk/rzepa/blog/wp-content/uploads/2013/01/benzidine-55G.svg"
class="aligncenter size-full wp-image-8998" decoding="async" width="210"
alt="benzidine-55G" /></td>
</tr>
</tbody>
</table>

This \[5,5\] transition state is 2.9 kcal/mol lower in ΔG^‡^~298~ than
the [transition
state](http://hdl.handle.net/10.6084/m9.figshare.105936){target="_blank"}
for the isomeric \[3,3\] rearrangement. The NCI
(non-covalent-interactions) shows the forming C-C bond to be on the
border of covalent, and non-covalent (blue), but that the π-π-stacking
region is all weakly attractive (green). You can also observe the strong
hydrogen bonds between the chloride anion and an N-H group (blue), and
the weak attractive zones between the two nitrogen centres, between the
chloride and the ortho-C-H hydrogens, and even between the two chloride
anions (blue-green or green). I should point out that the initial
position for these anions was over the aryl ring, but they migrated to
the NH region during optimisation of the transition state.

::: {#attachment_8967 .wp-caption .aligncenter style="width: 344px"}
![NCI surface. Click for
3D.](http://www.ch.imperial.ac.uk/rzepa/blog/wp-content/uploads/2013/01/benzidinenci.jpg){.wp-image-8967
loading="lazy" decoding="async"
aria-describedby="caption-attachment-8967"
onclick="jmolInitialize('../Jmol/');jmolSetAppletColor('white');jmolApplet([450,450],'load wp-content/uploads/2013/01/benzidine-55_den.cub.xyz;isosurface wp-content/uploads/2013/01/benzidine-55_den.cub.jvxl;');"
width="334" height="238"}

NCI surface. Click for 3D.
:::

The molecular electrostatic potential (isosurface = 0.11 au) shows both
aryl rings as a single unit attracted by a positive potential (blue)

::: {#attachment_8970 .wp-caption .aligncenter style="width: 309px"}
![Calculated electrostatic potential. Click for
3D.](http://www.ch.imperial.ac.uk/rzepa/blog/wp-content/uploads/2013/01/benzidineesp.jpg){.wp-image-8970
loading="lazy" decoding="async"
aria-describedby="caption-attachment-8970"
onclick="jmolInitialize('../Jmol/');jmolSetAppletColor('white');jmolApplet([450,450],'load wp-content/uploads/2013/01/benzidine-55_esp.cub.xyz;isosurface wp-content/uploads/2013/01/benzidine-55_esp.cub.jvxl translucent;');"
width="299" height="203"}

Calculated electrostatic potential. Click for 3D.
:::

The highest-occupied molecular orbital shows the two bonds involved in
the \[5,5\] shift (N-N and C-C) are both bonding, but more
significantly, the central region of the two stacked aryl rings is also
bonding. This is a clear manifestation of a π-complex, which the
benzidine rearrangement has often (and it has to be said
controversially) described as, and which elevates this particular
reaction from that of a simple bond forming/bond cleaving sigmatropic.
Another way of looking at it is that secondary orbital interactions
(such as often invoked in Diels-Alder cycloadditions) are exceptionally
important here.

::: {#attachment_8986 .wp-caption .aligncenter style="width: 270px"}
![HOMO for 5,5 benzidine rearrangement. Click for
3D.](http://www.ch.imperial.ac.uk/rzepa/blog/wp-content/uploads/2013/01/benzidine-HOMO.jpg){.wp-image-8986
loading="lazy" decoding="async"
aria-describedby="caption-attachment-8986"
onclick="jmolInitialize('../Jmol/');jmolSetAppletColor('white');jmolApplet([450,450],'load wp-content/uploads/2013/01/benzidine_mo67.cub.xyz;isosurface wp-content/uploads/2013/01/benzidine_mo67.cub.jvxl translucent;');"
width="260" height="202"}

HOMO for 5,5 benzidine rearrangement. Click for 3D.
:::

The LUMO is strongly antibonding in that region; indeed adding two
electrons to form a 12-electron process would be strongly destabilising.
In this regard, this unusual sigmatropic reaction follows the same 4n+2
electron rule as more conventional ones.

::: {#attachment_8989 .wp-caption .aligncenter style="width: 256px"}
![LUMO. Click for
3D.](http://www.ch.imperial.ac.uk/rzepa/blog/wp-content/uploads/2013/01/benzidine-LUMO.jpg){.wp-image-8989
loading="lazy" decoding="async"
aria-describedby="caption-attachment-8989" width="246" height="193"}

LUMO. Click for 3D.
:::

The next two diagrams illustrate the competing (higher energy) \[3,3\]
shift, which also has some π-complex character.

::: {#attachment_8973 .wp-caption .aligncenter style="width: 233px"}
![A \[3,3\] alternative to the benzidine rearrangement. Click for
3D.](http://www.ch.imperial.ac.uk/rzepa/blog/wp-content/uploads/2013/01/benzidine-33.jpg){.wp-image-8973
loading="lazy" decoding="async"
aria-describedby="caption-attachment-8973"
onclick="jmolInitialize('../Jmol/');jmolSetAppletColor('white');jmolApplet([450,450],'load wp-content/uploads/2013/01/benzidine-o-1495.376855.log;frame 93;connect (atomno=3) (atomno=1) PARTIAL;connect (atomno=7) (atomno=17) PARTIAL;vectors on;vectors 4;vectors scale 5.0; color vectors magenta; vibration 20;animation mode loop;');"
width="223" height="238"}

A \[3,3\] alternative to the benzidine rearrangement. Click for 3D.
:::

 

::: {#attachment_8980 .wp-caption .aligncenter style="width: 341px"}
![NCI surface for 3,3 rearrangement. Click for
3D.](http://www.ch.imperial.ac.uk/rzepa/blog/wp-content/uploads/2013/01/benzidinenci33.jpg){.wp-image-8980
loading="lazy" decoding="async"
aria-describedby="caption-attachment-8980"
onclick="jmolInitialize('../Jmol/');jmolSetAppletColor('white');jmolApplet([450,450],'load wp-content/uploads/2013/01/benzidine-33_den.cub.xyz;isosurface wp-content/uploads/2013/01/benzidine-33_den.cub.jvxl;');"
width="331" height="212"}

NCI surface for 3,3 rearrangement. Click for 3D.
:::

I will end with three autobiographical notes.

1.  The benzidine rearrangement was one of the earliest reactions I did
    in my home laboratory, at the age of about  13. As I recollect, I
    prepared about 1.5 grams (blissfully ignorant of how carcinogenic it
    is), and used it *via* diazotization to couple to phenol. My
    fascination with chemistry most certainly started with colour (and
    how to express the bonding in nitric oxide).
2.  About eight years later, I was about to commence my Ph.D. studies.
    The objective was to use kinetic isotope effects to infer the
    structure of transition states. In my case (proton transfers to
    indoles) I never did achieve this objective. But it is noteworthy
    that the mechanism of the benzidine rearrangement was largely
    unravelled using such isotopic studies.
3.  By 1974 as a post-doctoral researcher, I had moved on to studying
    mechanisms using  quantum theory and had decided that it was easier
    to invert the use of isotope effects by predicting a transition
    structure using this method, and then seeing if the computed isotope
    effects matched the experiment. We did this for the Diels-Alder
    reaction\[cite\]10.1021/ja00486a013\[/cite\] and more
    generally\[cite\]10.1021/ja00493a008\[/cite\], and then for some
    gas-phase eliminations\[cite\]10.1039/C39810000939\[/cite\], this
    latter being my first entirely independent publication.
4.  So, putting all this together, one might infer that armed with a
    computed transition state structure for the benzidine rearrangement,
    it is trivial to compute the kinetic isotope effects and hence to
    see if they correspond to those measured. [You might expect a report
    on this in a future post
    here](http://www.ch.imperial.ac.uk/rzepa/blog/?p=9105 "The  Benzidine rearrangement. Computed kinetic isotope effects."){target="_blank"}.

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

^‡^ Crystal structures of diprotonated dimethyl
hydrazines\[cite\]10.1002/ejic.201101115\[/cite\] show a N-N bond length
of \~1.45Å (typical counter-anions being nitrate, perchlorate or
sulfate). That calculated for the diprotonated diphenyl hydrazine is
\~2.5Å, which suggests that with the phenyl group, electrons from the
N-N region may be borrowed to contribute to the π-π-complex.

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


The benzidine rearrangement is claimed to be an example of the quite rare [5,5] sigmatropic migration[cite]10.1021/ja00335a035[/cite], which is a ten-electron homologation of the very common [3,3] sigmatropic reaction (
<em>
 e.g.
</em>
the Cope or Claisen). Some benzidine rearrangements are indeed thought to go through the [3,3] route[cite]10.1021/ja00309a041[/cite]. The topic has been reviewed here[cite]10.1002/poc.610020702[/cite].      In

Messages de Rogue Scholar

The mechanism of the Benzidine rearrangement.