Multi-centre bonding in the Grignard Reagent

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 ↔ MgBr₂ + Ph₂Mg

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. 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.

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 sp³ 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;

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 Ph₂Mg dimer) is shown below;

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.