Posts Tagged ‘metal-metal bonding’

The subtle effect of dispersion forces on the shapes of molecules: benzyl magnesium bromide.

Sunday, November 10th, 2013

In the previous post I mentioned in passing the Grignard reagent benzyl magnesium bromide as having tetrahedral coordination at Mg. But I have now noticed, largely through spotting Steve Bachrach’s post on “Acene dimers – open or closed?” another geometric effect perhaps worthy of note, certainly one not always noted in the past; that of dispersion forces.

crystal structure Calc structure
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On the left is the crystal structure.[1] and on the right a ωB97Xd/6-311G(d,p) calculation, with built-in dispersion correction. If you compare the two you will find that the ethyl groups from the ether are about 0.3Å closer to the face of the phenyl group in the calculated structure. Why? Well, in the crystal structure, each dimeric Grignard unit is surrounded by adjacent units in the periodic lattice. You would think that this would have the effect of compressing the structure. Instead it is more open, and it is the isolated calculated structure that is compressed. The dispersion forces are responsible for this. In the crystal structure, the phenyl group is attracted not only to the ethyl groups but also by adjacent units in the lattice by dispersion forces. This balancing effect is absent in the calculated structure and so manifests as just an attraction between the phenyl face and the methyl groups, which pulls them together by ~0.3Å. One can see this more clearly when an NCI (non-covalent-interactions) isosurface is shown at both geometries:

X-ray geometry[2] Calc. geometry [3]
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The surface on the right is ringed (red) in the relevant region to show how the green NCI surface is so much larger compared to the one computed for the  crystal structure. Notice by the way the strong stabilizing (blue) zone between the two Mg atoms. Whether it should be called metal-metal bonding is another issue, but it is a clear effect.

One can compare this result with NCI surfaces computed for the examples described in Steve’s blog (deriving from this article[4]). There two geometric isomers of the same molecule were described, differing only in the dispersion attractions. The top one is an open form and the NCI surface shows no features along the acene chain away from the central pivot. The second isomer shows stabilizing green regions (indicating a zone of dispersion forces in action) between the extended acene groups.

Open Closed
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Click for 3D. Open acene
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Click for 3D. Closed acene with more green regions.

Whilst the acene system is an extreme example of this sort of effect, it may well be that even quite small molecules such as benzyl magnesium bromide etherate might manifest effects due to dispersion. After all, 0.3Å is not a particularly small change in geometry! I conclude by noting that isopropyl groups are rather better in their attraction to a phenyl ring than ethyl groups, and so one might speculate whether e.g. the di-isopropyl etherate of benzyl magnesium bromide might be worth someone making?

References

  1. M.A. Nesbit, D.L. Gray, and G.S. Girolami, "Di-μ-bromido-bis[benzyl(diethyl ether)magnesium]", Acta Crystallographica Section E Structure Reports Online, vol. 68, pp. m942-m942, 2012. https://doi.org/10.1107/s1600536812025445
  2. "C 22 H 34 Br 2 Mg 2 O 2", 2013. http://doi.org/10042/26062
  3. "C 22 H 34 Br 2 Mg 2 O 2", 2013. http://doi.org/10042/26061
  4. S. Ehrlich, H.F. Bettinger, and S. Grimme, "Dispersion‐Driven Conformational Isomerism in σ‐Bonded Dimers of Larger Acenes", Angewandte Chemie International Edition, vol. 52, pp. 10892-10895, 2013. https://doi.org/10.1002/anie.201304674

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Is CLi6 hypervalent?

Friday, July 5th, 2013

A comment made on the previous post on the topic of hexa-coordinate carbon cited an article entitled “Observation of hypervalent CLi6 by Knudsen-effusion mass spectrometry“[1] by Kudo as a amongst the earliest of evidence that such species can exist (in the gas phase). It was a spectacular vindication of the earlier theoretical prediction[2],[3] that such 6-coordinate species are stable with respect to dissociation to CLi4 and Li2.

The terminology describes these lithium carbides as effectively hypervalent; Kudo in the abstract of his 1992 article uses the more explicit phrase “carbon can expand its octet of electrons to form this relatively stable molecule“. We are taught early on in chemistry that the carbon octet is due to double occupation of four molecular orbitals formed using linear combinations derived from the relatively low energy 2s/2p carbon atomic orbital basis. Octet expansion on carbon must therefore involve to some degree the next atomic shell (3s/3p), which is normally regarded as too high in energy to be capable of significant population for carbon. But use of the 3s/3p shell seems at first sight inevitable. If one constructs an octahedral complex CLi6 surely ten electrons must be involved in bonding, four from the carbon and six from the equivalent lithiums? The 3s/3p carbon population must therefore be ~2 electrons, and we can truly describe a molecule where carbon has of necessity expanded its octet of electrons to ten as hypervalent. Or can we?

How does a quantitative (ωB97XD/6-311++G(d) ) calculation[4] reveal this effective hypervalency? 

  1. The octahedral geometry is indeed a stable minimum, with the lowest vibrational wavenumber being 194 cm-1.
  2. It also checks out as clearly a closed shell species, stable to open shell perturbations.
  3. An NBO analysis reveals the Rydberg population (those 3s/3p atomic orbitals) to be only 0.09 electrons.
  4. It partitions the electrons into 13.97 for the 1s cores of the seven atoms, 7.67 “valence-Lewis” (i.e. shared covalent) and a mysterious 2.27 (valence, non-Lewis).

We now have a problem. One of the standard methods for partitioning electrons has isolated two of our ten electrons and placed them, with small partial occupancy, into unshared “lone pairs”, located as it happens on the lithium atoms (shown below for one of these partial lone “pairs”). The carbon is NOT hypervalent, and it has NOT expanded its octet.

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So I tried another procedure, deliberately chosen to be rather different from the orbital-based NBO formalism. This is analysis of the ELF, or electron localisation function, and represents an attempt to derive the result based on a function related to the electron density. The red spheres shown below are the centroids of the twelve ELF basins located:

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Each of these (equivalent) basins has an electron population of ~0.81, making ~9.7 electrons in total. Each lithium sits on a square arrangement of four of these basins, and so has access to ~3.2 valence electrons. How do we interpret the situation for carbon however? Does its valence shell contain an expanded 9.7 electrons? Well, not necessarily. You can see that each of the basins has a three-centre relationship between the one carbon and TWO lithiums. These electrons contribute not just to C-Li bonding, but also to Li…Li bonding. So these 9.7 electrons contribute in part to bonding that does NOT involve the carbon. We can see this in the (Wiberg) bond orders, 0.254 for the C-Li interaction, and 0.116 for adjacent Li…Li interactions (such an explanation was also suggested for why II7 has no expanded octet at the central iodine). In fact, the origins of this effect were first clearly identified in the theoretical analysis of 1983[3]: “the extra electrons beyond the usual octet are involved with metal-metal bonding rather than with interactions of the metals with the central atoms“.

It is nice to see that despite the passage of 30 years, and despite the introduction of many new ways of analysing the wavefunctions and hence the bonding of molecules, the essential original interpretation[3] remains robustly correct! 

References

  1. H. Kudo, "Observation of hypervalent CLi6 by Knudsen-effusion mass spectrometry", Nature, vol. 355, pp. 432-434, 1992. https://doi.org/10.1038/355432a0
  2. E.D. Jemmis, J. Chandrasekhar, E.U. Wuerthwein, P.V.R. Schleyer, J.W. Chinn, F.J. Landro, R.J. Lagow, B. Luke, and J.A. Pople, "Lithiated carbocations. The generation, structure, and stability of CLi5+", Journal of the American Chemical Society, vol. 104, pp. 4275-4276, 1982. https://doi.org/10.1021/ja00379a051
  3. P.V.R. Schleyer, E.U. Wuerthwein, E. Kaufmann, T. Clark, and J.A. Pople, "Effectively hypervalent molecules. 2. Lithium carbide (CLi5), lithium carbide (CLi6), and the related effectively hypervalent first row molecules, CLi5-nHn and CLi6-nHn", Journal of the American Chemical Society, vol. 105, pp. 5930-5932, 1983. https://doi.org/10.1021/ja00356a045
  4. "C 1 Li 6", 2013. http://hdl.handle.net/10042/24790

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