Posts Tagged ‘Hermann Sachse’

Tetrahedral carbon and cyclohexane.

Wednesday, August 22nd, 2018

Following the general recognition of carbon as being tetrahedrally tetravalent in 1869 (Paterno) and 1874 (Van’t Hoff and Le Bell), an early seminal exploitation of this to the conformation of cyclohexane was by Hermann Sachse in 1890.[1] This was verified when the Braggs in 1913[2], followed by an oft-cited article by Mohr in 1918,[3] established the crystal structure of diamond as comprising repeating rings in the chair conformation.† So by 1926, you might imagine that the shape (or conformation as we would now call it) of cyclohexane would be well-known. No quite so for everyone!

When The Journal of the Imperial College Chemical Society (Volume 6) was brought to my attention, I found an article by R. F Hunter;

He proceeds to argue as follows:

  1. The natural angle subtended at a tetrahedral carbon is 109.47°.
  2. “The internal angle between the carbon to carbon valencies of a six-membered ring cyclohexane will, if the ring is uniplanar, be … 120°.
  3. “When the cyclohexane ring is prepared … we must therefore have the pushing apart of two of the valencies”.
  4. The object of the experiments commenced in this College in 1914 was “to find what effect the pushing apart of the valencies …must have on the angle between the remaining pair of valencies“.
  5. You do wonder then why the assumption highlighted in red above was never really questioned during the twelve-year period of investigating angles around tetrahedral carbon.

The article itself is quite long, reporting the synthesis of many compounds in search of the postulated effect. Of course around twenty years later, Derek Barton used the by then generally accepted conformation of cyclohexane to explain reactivity in what become known as the theory of conformational analysis.

These two articles dating from 1926, and probably thought lost to science, show how some ideas can take decades to have any influence, whilst others can take root very much more quickly.

†The chair cyclohexane structure is easily discerned from Figure 7 in the Braggs’ paper![2]

References

  1. H. Sachse, "Ueber die geometrischen Isomerien der Hexamethylenderivate", Berichte der deutschen chemischen Gesellschaft, vol. 23, pp. 1363-1370, 1890. https://doi.org/10.1002/cber.189002301216
  2. W.H. Bragg, and W.L. Bragg, "The structure of the diamond", Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character, vol. 89, pp. 277-291, 1913. https://doi.org/10.1098/rspa.1913.0084
  3. E. Mohr, "Die Baeyersche Spannungstheorie und die Struktur des Diamanten", Journal für Praktische Chemie, vol. 98, pp. 315-353, 1918. https://doi.org/10.1002/prac.19180980123

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A short history of molecular modelling: 1860-1890.

Saturday, February 5th, 2011

In 1953, the model of the DNA molecule led to what has become regarded as the most famous scientific diagram of the 20th century. It had all started 93 years earlier in 1860, at a time when the tetravalency of carbon was only just established (by William Odling) and the concept of atoms as real entities was to remain controversial for another 45 years (for example Faraday, perhaps the most famous scientist alive in 1860 did not believe atoms were real). So the idea of constructing a molecular model from atoms as the basis for understanding chemical behaviour was perhaps bolder than we might think. It is shown below, part of a set built for August Wilhelm von Hofmann as part of the lectures he delivered at the Royal College of Chemistry in London (now Imperial College).

The original August Wilhelm von Hofmann molecular model

This grand-daddy of all molecular models does have some interesting features. The most obvious is that the carbon atom at the centre is square planar (tetrahedral carbon was still 14 years in the future). What HAS survived to the present day is the colour scheme used (black=carbon, white=hydrogen, and not shown here, red=oxygen, blue=nitrogen, green=chlorine).  But another noteworthy aspect is the relative size of the white hydrogen, which is larger than the black carbon. This deficiency was however very soon rectified in 1861 by Josef Loschmidt, who published  a famous pamphlet in which he set out his ideas for the structures of more than  270 molecules (many of which by the way were cyclic, and this some four years before Kekule’s dream!). An example (#239) is shown below, which gets the relative sizes of the atoms more or less correct (OK, chlorine is shown with rather an odd shape). To get an idea of how good Loschmidt’s model actually was, click on the diagram to load a modern model, and compare the two! Even more impressive, these diagrams pre-date van der Waals work on the finite sizes of atoms, first presented in 1873.

Loschmidt’s molecular models. Click for 3D

To conclude, I cannot resist showing one more model. Hermann Sachse believed cyclohexane could not be planar. To try to convince people, in 1890 he included a  “flat-packed” model in the pages of a journal article,  evidently believing that people would cut it out, and assemble it into a 3D shape.

Flat-packed molecular model of cyclohexane

You might have noticed a theme in the present blog of presenting 3D models for many of the molecules I discuss (include the Loschmidt one above). For the historians amongst you, I note our 1995 article in which we updated[1] Sachse’s origami with an article featuring how to incorporate interactive models into journals (still sadly only too rare). Perhaps a history of the molecular model, and how it has been presented over 150 years might be an interesting one to trace!

References

  1. O. Casher, G.K. Chandramohan, M.J. Hargreaves, C. Leach, P. Murray-Rust, H.S. Rzepa, R. Sayle, and B.J. Whitaker, "Hyperactive molecules and the World-Wide-Web information system", Journal of the Chemical Society, Perkin Transactions 2, pp. 7, 1995. https://doi.org/10.1039/p29950000007

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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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