Posts Tagged ‘C’

Hypervalent or not? A fluxional triselenide.

Saturday, February 24th, 2018

Another post inspired by a comment on an earlier one; I had been discussing compounds of the type I.In (n=4,6) as possible candidates for hypervalency. The comment suggests the below as a similar analogue, deriving from observations made in 1989.[1]

This compound was investigated using 77Se NMR, with the following conclusions:

  1. The compound is fluxional, with the lines at room temperature broadened compared to those at -50°C.
  2. At -50°C the peaks are sharp enough to discern 1JSe-Se couplings, with multiplicities and integrations that suggest a central Se is surrounded by four equivalent further Se atoms, with shifts of 655.1 and 251.2 ppm.
  3. The magnitude of this 1JSe-Se coupling (391 Hz) leads to the suggestion of a considerable contribution of a resonance form with Se=Se bonds (structure 2 above).
  4. This was supported by 2J13C-77Se couplings which also imply a symmetrically coordinated central  Se.
  5. Thus the two resonance forms 1 or 2 above were suggested as the predominant form at -50°C, with an increasing incursion of the open chain isomer 3 at higher temperatures giving rise to the observed fluxional dynamic behaviour.
  6. One may surmise from these results that the central Se is certainly hypercoordinated and by the classical interpretations hypervalent.

Here are some calculations (R=H), at the ωB97XD/Def2-TZVPP/SCRF=chloroform level.‡ In red are the calculated Wiberg Se-Se bond orders, which give little indication of any Se=Se double bond character. 

The calculated 77Se shifts are shown in magenta, with the observed values being 655 and 255 ppm. The match is not good, the errors were 120 and 20.5 ppm.†  However calculated shifts for elements adjacent to e.g. Se or Br etc suffer from relativistic effects such as spin orbit coupling.[2] Thus the shift for the central Se, surrounded by four other Se atoms is likely to have a significant error, but the error for the four other Se atoms should be less. The reverse is true.

However, all the calculations of this species (up to Def2-TZVPPD basis set) showed this symmetric form of D2h symmetry to actually be a transition state, as per below.

There is a minimum with the structure below in which one pair of Se-Se lengths are longer than the other pair and for which the free energy is 6.5 kcal/mol lower. The Wiberg bond orders for the two sets of Se-Se bonds are now 0.16 and 0.86, which very much corresponds to structure 3 above.

Assuming that this compound is fluxional even at -50°C, the average of the pairs of Se atoms gives calculated shifts of 667 ppm (655 obs) whilst the central Se is 204.6 ppm (251 obs). The latter, influenced by two especially short Se-Se distances, is likely to have a very large spin-orbit coupling error, whilst for the former the error will be smaller (13C shifts adjacent to one Br typically have induced calculated errors of about 14 ppm[2]).

At this point I searched the Cambridge structure database for Se coordinated by four other Se atoms. A close analogue[3] has the structure shown below, in which pairs of Se-Se interactions have unequal bond lengths, the shorter being ~2.45Å. This matches the calculation above reasonably well.

Reconciling these various observations, we might assume that even at -50°C the fluxional behaviour has not been frozen out. Given that the fluxional barrier is only 6.5 kcal/mol, it is unlikely that the spectrum could be measured at a sufficiently low temperature to reveal not two sets of Se signals in the ratio 4:1 but three in the ratio 2:2:1. The spin-spin couplings reported presumably are a result of averaging a genuine 1JSe-Se coupling with a through space coupling.

So it appears that the analysis of the 77Se NMR reported in this article [1] may not be quite what it seems. A better interpretation is that structure 3 is the most realistic. This means no hypercoordination for the Se, never mind hypervalence!

‡FAIR data at DOI: 10.14469/hpc/3724. †The original reference, Me2Se was incorrectly calculated without solvation by chloroform. The values shown here are now corrected from those shown in the original post.

References

  1. Y. Mazaki, and K. Kobayashi, "Structure and intramolecular dynamics of bis(diisobutylselenocarbamoyl) triselenide as identified in solution by the 77Se-NMR spectroscopy", Tetrahedron Letters, vol. 30, pp. 2813-2816, 1989. http://dx.doi.org/10.1016/S0040-4039(00)99132-9
  2. D.C. Braddock, and H.S. Rzepa, "Structural Reassignment of Obtusallenes V, VI, and VII by GIAO-Based Density Functional Prediction", Journal of Natural Products, vol. 71, pp. 728-730, 2008. https://doi.org/10.1021/np0705918
  3. R.O. Gould, C.L. Jones, W.J. Savage, and T.A. Stephenson, "Crystal and molecular structure of bis(NN-diethyldiselenocarbamato)-selenium(II)", Journal of the Chemical Society, Dalton Transactions, pp. 908, 1976. http://dx.doi.org/10.1039/DT9760000908

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The conformation of cyclohexane

Thursday, January 28th, 2010

Like benzene, its fully saturated version cyclohexane represents an icon of organic chemistry. By 1890, the structure of planar benzene was pretty much understood, but organic chemistry was still struggling somewhat to fully embrace three rather than two dimensions. A grand-old-man of organic chemistry at the time, Adolf von Baeyer, believed that cyclohexane too was flat, and what he said went. So when a young upstart named Hermann Sachse suggested it was not flat, and furthermore could exist in two forms, which we now call chair and boat, no-one believed him. His was a trigonometric proof, deriving from the tetrahedral angle of 109.47 at carbon, and producing what he termed strainless rings.

Whilst the chair form of cyclohexane now delights all generations of chemistry students, the boat is rather more mysterious. Perhaps due to Sachse, it is still often referred to as a higher energy form of the chair (Barton, in the 1956 review that effectively won him the Nobel prize, clearly states that the boat is one of only two conformations free of angle strain, DOI: 10.1039/QR9561000044). Over the last 30 years or so, and especially with the advent of molecular modelling programs, the complexity of the conformations of cyclohexane has become realised. A nice recent illustration of that complexity is by Jonathan Goodman using commercial software. Here a slightly different take on that is presented.

The starting point is the flat Baeyer model for cyclohexane. Like benzene, it has D6h symmetry. When subjected to a full force constant analysis using a modern program (in this instance Gaussian 09), this geometry is revealed (DOI: 10042/to-3708) to have three negative force constants, which in simple terms means it has three distortions which will reduce its energy. The eigenvectors of these force constants are shown below, and each set of vectors acts to reduce the symmetry of the species. Such symmetry-reduction is a well known aspect of group theory, and its analysis in the Lie symmetry groups is used in many areas of physics and mathematics, but it is a less used in chemistry.

348i cm-1 (B2g) 244i (E2u) 244i (E2u)
D6h to C2h for cyclohexane

D6h to C2h for cyclohexane. Click for animation.
D6h to D2

D6h to D2. Click for animation.
D6h to C2v

D6h to C2v. Click for animation.

The first of these symmetry-reducing vibrations (the B2g mode) converts the geometry immediately to the chair conformation of cyclohexane. So in some ways, this use of symmetry is a modern equivalent of the trigonometry used by Sachse to prove his point.

The next two modes are degenerate in energy, and the first of these reduces the symmetry to D2. The result is what we now call the twist-boat. It is interesting, because the D2 group is one of the (relatively few) chiral groups, and the twist-boat exhibits disymmetric symmetry. In other words, following the vibrational eigenvectors in one direction leads to one enantiomer of the twist boat, and in the other direction to the other enantiomer. So (in theory only), one might actually be able to produce chiral cyclohexane (the experiment and resolution would have to be done at very low temperatures!). It is also interesting that theory nowadays could quite reliably calculate the optical rotation of this species (and its circular dichroism spectrum), so we certainly would know what to look out for.

The second component of the degenerate E imaginary mode leads directly to a species of C2v symmetry, which we recognize as Sachse’s second possible form of cyclohexane. The symmetry-reductions of D6h to C2h, D2 and C2v all have paths on the grand diagram of the 32 crystallographic point groups and their sub groups, and is an interesting application of group theory to a mainstream topic in organic chemistry.

But the story is not quite complete yet. The C2v boat is not the final outcome of the last distortion! It too is a transition state, connecting again the two D2 forms. So the path from D6h to C2v is NOT a minimum energy reaction path, but a rather different type of path known as a valley-ridge inflection path. An example of such a surface can be seen for the dimerisation of cyclopentadiene (DOI: 10.1021/ja016622h) and effectively it connects one transition state to a second transition state, without involving any intermediates on the pathway. At some stage, the dynamics of the system takes over, and the symmetry breaks without the system ever actually reaching the second transition structure. This final aspect of the potential energy surface of cyclohexane was not discussed by Jonathan Goodman in his own article on the topic.

So symmetry-breaking is the topic of this blog, and its connection to physics and mathematics. And, I might add that the same approach can be taken for looking at the conformations of cyclobutane, pentane, heptane and octane. But that will be left for another post.

Postscript.  See this more recent post.

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Posted in General, Interesting chemistry | 17 Comments »