Imperial College London

Henry Rzepa

The [Grignard
reaction](http://en.wikipedia.org/wiki/Grignard_reaction){target="_blank"}
is encountered early on in most chemistry courses, and most labs include
the preparation of this reagent, typically by the following reaction:

2PhBr + 2Mg → 2PhMgBr ↔ MgBr~2~ + Ph~2~Mg

The reagent itself exists as part of an equilibrium, named after
[Schlenk](http://en.wikipedia.org/wiki/Schlenk_equilibrium){target="_blank"},
in which a significant concentration of a dialkyl or diarylmagnesium
species is formed. The topic of this blog entry is to analyse the
structure and bonding in this latter species.

First, the structure is shown below (for 2,6-diethylphenyl magnesium).
This reveals a dimeric structure with a four membered ring core,
comprising two  Mg atoms  connected by two bridging  aryl groups.

::: {#attachment_1186 .wp-caption .aligncenter style="width: 293px"}
![The crystal structure of a di-aryl magnesium. Click to view
3D](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2009/12/udaqiz.jpg "udaqiz"){.size-full
.wp-image-1186 loading="lazy" decoding="async"
aria-describedby="caption-attachment-1186"
onclick="jmolInitialize('../Jmol/');jmolSetAppletColor('yellow');jmolApplet([450,450],'load wp-content/uploads/2009/12/UDAQIZ.cif;zoom 120;');"
width="283" height="262"}

The crystal structure of a di-aryl magnesium. Click to view 3D
:::

The question to be addressed here is the nature of the aryl groups. Put
simply, it seems as if their bridging role means that one of the six
carbons involved in the benzene ring has become sp^3^ hybridized. This
would in turn mean that the cyclic conjugation of the benzene ring is
interrupted, and a species akin to the Wheland intermediate is formed in
which the aromaticity of two of the benzene rings is no longer
sustained. This situation could be depicted thus;

::: {#attachment_1191 .wp-caption .aligncenter style="width: 178px"}
![A Simple bonding representation in Ph2Mg
dimer](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2009/12/Ph2Mg.jpg "Ph2Mg"){.size-full
.wp-image-1191 loading="lazy" decoding="async"
aria-describedby="caption-attachment-1191" width="168" height="228"}

A Simple bonding representation in Ph2Mg dimer
:::

Is this really the best way of depicting the bonding in this species? A
more subtle analysis of the bonding can be achieved using a technique
known as ELF (involving analysis of the electron localization function).
This reveals bonds as so-called synaptic basins, which come in two
varieties; disynaptic basins corresponding to two-centre bonds, and
trisynaptic basins which reveal three-centre bonds (there is also a
monosynaptic basin which corresponds to electron lone pairs). Such an
ELF analysis (based on a B3LYP/6-311G(d,p) computed wavefunction for
Ph~2~Mg dimer) is shown below;

::: {#attachment_1194 .wp-caption .aligncenter style="width: 448px"}
![ELF analysis of the bonding in Ph2Mg
dimer](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2009/12/ph2mg-elf.jpg "ph2mg-elf"){.size-full
.wp-image-1194 loading="lazy" decoding="async"
aria-describedby="caption-attachment-1194"
onclick="jmolInitialize('../Jmol/');jmolSetAppletColor('yellow');jmolApplet([450,450],'load wp-content/uploads/2009/12/Ph2Mg-elf.mol;zoom 120;spin 3;set fontscaling TRUE; font label 14;select atomno=47;color orange;label %A 2.48;select atomno=48;color red;label %A 2.7;');"
width="438" height="289"}

ELF analysis of the bonding in Ph2Mg dimer. Click for 3D model
:::

The small purple dots represent synaptic basins. Several of these are
circled. The  ones circled in orange are conventional disynaptic forms,
and the basins can be integrated to to 2.48 electrons each. The red
basin however is clearly revealed as a trisynaptic form (covering both
metal centres and the carbon) and integrating to  2.7 electrons. The
 three basins surrounding each Mg atom integrate to 7.91 electrons,
which reveal the metal to have a conventional octet of electrons in its
valence shell. The bonding in the central region could therefore be
described as comprising two ***three-centre-three-electron*** bonds. The
key aspect of this is that the two bridging phenyl groups do not break
their aromaticity, ie all **four** phenyl/aryl groups largely retain
their aromaticity! Thus the disynaptic basins for  the *normal*
non-bridging phenyl group and  circled in green integrates to 2.6
electrons and the blue to 2.8 (an ideal aromatic bond would of course
integrate to 3.0 electrons), whereas the equivalent basins for the
bridging phenyl (brown and purple, 2.5 and  2.8) are virtually the same.

It is interesting how a veritable mainstay of most taught chemistry
courses, the Grignard reagent,  can have such subtle aspects of the
bonding surrounding both the metal atom and the aromatic groups, and how
rarely this bonding is actually dissected in most text books.

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


The Grignard reaction is encountered early on in most chemistry courses, and most labs include the preparation of this reagent, typically by the following reaction:    2PhBr + 2Mg → 2PhMgBr ↔ MgBr
<sub>
 2
</sub>
+ Ph
<sub>
 2
</sub>
Mg  The reagent itself exists as part of an equilibrium, named after Schlenk, in which a significant concentration of a dialkyl or diarylmagnesium species is formed.

Messages de Rogue Scholar

Multi-centre bonding in the Grignard Reagent