Henry Rzepa's Blog

I have just noticed unexpected links between two old posts, one about benzene, one about diphenyl magnesium and a link to August Kekulé.^†

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The post about benzene dealt with the apparently simple issue of why all the C-C bonds are of equal length. The answer, in brief is purely because of the σ-electrons. If the π-electrons had their way, benzene would have three short and three long C-C bonds. Experimentally, this is detected by the value of a particular stretching vibration known as the Kekulé mode,^† which stretches three C-C bonds in the ring and shortens the other three. In benzene this is depressed from an expected value of ~1600 cm^-1 to ~1318^‡ due to an effect called π-distortivity.[1]

The second post dealt with the unusual structure of Ph₂Mg, which is a bridging dimer of (one of the) species present in solution for the Grignard reagent. In this structure, all the C-C lengths in each phenyl ring are very close to the natural value in benzene itself (~1.405-1.411Å), which suggests that despite the Mg and the bridged coordination for two of the phenyl rings, all four appear to retain aromaticity. Shown above are the displacement vectors at their extreme for one of four Kekulé modes calculated for this system using ωB97XD/6-311G(d,p)[2]. Two have the value 1296 and two 1298 cm^-1. All four are lower than the value for benzene itself.

What does this mean? That the π-electrons in Ph₂Mg are more distortive than in benzene itself. If weakening the π-system (by say promoting two bonding electrons in benzene into π^* MOs to form a quintet state) elevates the Kekulé mode wavenumber to almost its expected normal value, one may ask if the converse is true? Is the π-system and hence aromaticity stronger for a molecule where the Kekulé mode is even more depressed than in benzene itself? I pose the question, but do not answer it here.^†

^†Kekulé will be celebrated on the occasion of the inaugural event on 9 May 2014 in Bonn Germany to keep “Historic Sites of Chemistry”.

^‡ Calculated using ωB97XD/6-311G(d,p) with a mass weighting for the hydrogens of 0.001 to avoid coupling perturbations with CCH wags.

References

1. S. Shaik, A. Shurki, D. Danovich, and P.C. Hiberty, "A Different Story of π-DelocalizationThe Distortivity of π-Electrons and Its Chemical Manifestations", Chemical Reviews, vol. 101, pp. 1501-1540, 2001. http://dx.doi.org/10.1021/cr990363l
2. Henry S. Rzepa., "Gaussian Job Archive for C24H20Mg2", 2014. http://dx.doi.org/10.6084/m9.figshare.1002073