Henry Rzepa's blog

Text books often show the following diagram, famously consolidated over many years by Emil Fischer from 1891 onwards. At the top sits D-(+)-glyceraldehyde, to which all the monosaccharides below are connected by painstaking chemical transformations.

In this notation, D (for all these structures) indicates the absolute configuration of the series, deriving from placing the last highest priority group before an achiral carbon at the bottom of the representation (the hydroxyl group) to the right of the diagram (= dextro = D). The mirror images of all these species would be designated L (since the hydroxide group would now be on the left). The challenge emerges in connecting this absolute configuration to some measurable property, and during the late 19th century, the only feasible measurement would be the sign of the optical rotation. It was decided that since no method existed at the time to connect absolute configuration to the sign of optical rotation, D-glyceraldehyde (nowadays more commonly referred to by its CIP notatation (R)-glyceraldehyde), would be by convention connected to the enantiomer giving a positive rotation, hence D-(+)-glyceraldehyde. This species has indeed mostly been reported as having a small positive rotation of e.g. +9.2[1] in water. If a future procedure were to confirm that the D-enantiomer had a positive rotation, Fischer’s guess would be proven correct. Possibly.

I quickly mention that this experiment was of course carried out in 1951, as noted in the previous post[2], but on a rubidium tartrate salt and not on glyceraldehyde itself (which is a liquid). Since the two could be connected by chemical synthesis, Fischer’s guess was indeed confirmed as correct. This proof rapidly made D-(+)-glyceraldehyde less relevant as the tentpole of absolute configuration (in sugars) and people stopped worrying about it. But the assertion that the D/(R) enantiomer has a positive rotation by indicating (+) continues in all the diagrams related to the above that I have come across. So is it correct?

Well, an earlier attempt in 1937 to assign optical rotation to absolute configuration had been attempted by Kirkwood[3] using quantum mechanical theory to make that connection. I thought I might apply the modern version of that approach to (R)-glyceraldehyde, using the same procedure I had tried earlier. A conformational analysis of the molecule, followed by dispersion-corrected calculation of free energies and then of the optical rotations gives the following table. Data is at 10.14469/hpc/6436These calculations show that the rotation is strongly negative! Can they be in serious error? Perhaps however there are two different species in solution. Indeed, the equilibrium below is shown to favour the rhs for aldehydes, as shown by the following concentration profile as a function of temperature.[4] This shows that at 30°, only 4% of this molecule is in the aldehyde form.

The article also reports optical rotations, at three wavelengths. I should note here that the notation (+) means only the rotation at 589nm (yes, you can get sign inversions on moving from one wavelength to another![5]). At 30° the observed rotation for D-glyceraldehyde is indeed strongly negative, whilst it is the hydrated form that is moderately (+).

There is a discrepancy of ~47° between these measured values and the calculated one at 589nm. I hope to explore the origins of this error in a separate post.

So we see by both experiment and theory that D-(+)-glyceraldehyde, if the meaning of that (+) is to be upheld, should really be D-(-)-glyceraldehyde. Note that many of the sugars shown in the top diagram have (-) as well as (+), and so there is no reason that glyceraldehyde should be any different.

References

1. H.J. Lamble, M.J. Danson, D.W. Hough, and S.D. Bull, "Engineering stereocontrol into an aldolase-catalysed reaction", Chemical Communications, pp. 124, 2005. https://doi.org/10.1039/b413255f
2. J.M. BIJVOET, A.F. PEERDEMAN, and A.J. van BOMMEL, "Determination of the Absolute Configuration of Optically Active Compounds by Means of X-Rays", Nature, vol. 168, pp. 271-272, 1951. https://doi.org/10.1038/168271a0
3. J.G. Kirkwood, "On the Theory of Optical Rotatory Power", The Journal of Chemical Physics, vol. 5, pp. 479-491, 1937. https://doi.org/10.1063/1.1750060
4. M. Fedoroňko, "Optical activity of D-glyceraldehyde in aqueous solutions", Collection of Czechoslovak Chemical Communications, vol. 49, pp. 1167-1172, 1984. https://doi.org/10.1135/cccc19841167
5. M.S. Andrade, V.S. Silva, A.M. Lourenço, A.M. Lobo, and H.S. Rzepa, "Chiroptical Properties of Streptorubin B: The Synergy Between Theory and Experiment", Chirality, vol. 27, pp. 745-751, 2015. https://doi.org/10.1002/chir.22486

Some areas of science progressed via very famous predictions that were subsequently verified by experiments. Think of Einstein and gravitational waves or of Dirac and the positron. There are fewer well-known examples in chemistry; perhaps Watson and Crick’s prediction of the structure of DNA, albeit based on the interpretation of an existing experimental result. Here I take a look at a what if, that of John Kirkwood’s prediction of the absolute configuration of a small molecule based entirely on matching up the sign of a measured optical rotation with that predicted by (his) theory.

The confirmation that Emil Fischer’s 1891 proposed convention for the absolute configuration of sugars was in fact correct was famously made by Bijvoet in 1951 using crystallography.[1] I first told this story in 2012, noting that Kirkwood apparently made his seminal contribution a year later in 1952[2] using his quantum mechanical theory of optical rotation to independently come up with the same result. Nowadays he rarely gets the credit for solving the problem of absolute configuration. But wait, Kirkwood’s first stab at solving this problem in fact came in 1937,[3] a full 14 years before Bijvoet’s famous result (for which incidentally the Nobel prize was not awarded). 

I have been asked to talk about this story at a Historical meeting of the Royal Society of Chemistry in March 2020, and for this purpose thought I should take a closer look at Kirkwood’s 1937 article. In it, he sets out his quantum mechanical theory of optical rotation. Remember that in that era, there was no recourse to computers and solving the required (heavily approximated) equations had to be done entirely using mechanical calculators. Kirkwood chooses to analyse the following molecule;

I have redrawn it below in more modern form (and name). The difference between the two is in the notations d and (R). The former relates to the sign of the optical rotation [α]_D where d stands for dextrorotation, or clockwise and is also often represented by (+) and being the sign of the measured rotation.^♥ (R) is the modern notation for the absolute configuration shown by Kirkwood in his diagram (Fig. 1).

He is asserting below that the enantiomer of butan-2-ol with a measured rotation of 13.9° has (in modern notation) the absolute configuration (R) because his calculations predict somewhere between 9.5° and 21.9° for this specific three-dimensional geometry. So why is Kirkwood not lauded for solving this problem in 1937? Well, because we now know that (R)-butan-2-ol has a negative rotation of -13.9°![4]

Kirkwood is however very aware of the potential problems with his approach. In a nutshell, conformation! In particular, the conformers resulting from rotation about the central C-C bond and especially the C-O bond, where for the purposes of his theory he assumed axial symmetry about that bond.

and

Now, in 1937 the area of such conformational analysis was hardly known; only in 1948[5] would Barton first put it firmly on the map (and win the Nobel prize for this work). So, in attempting his connection between d and (R), Kirkwood was in a sense far too ahead of his time. It worth asking what modern quantum mechanical theory makes of this problem and does it cast any light on why Kirkwood actually got his assignment wrong (in 1937,[3] although he WAS correct in 1952[2]).

1. Firstly, I carried out a comprehensive search of the rotamers about the C-C and C-O bond using molecular mechanics (a method first introduced by Barton in 1948[5]) and using the MMFF94 forcefield. This identifies seven distinct conformations arising from rotations about these two bonds. Some warning signs area aready present; these seven are bounded by an energy of only 1.2 kcal/mol! All are likely to have a significant Boltzmann population.
2. Next, to ramp up the level of theory to density functional quantum mechanics, at the B3LYP+GD3+BJ/Def2-TZVPP/SCRF=diethyl ether level (FAIR Data: 10.14469/hpc/6367) and at the minimum energy geometry for each conformation, an optical rotation is calculated (at the ωB97XD/Def2-TZVPP/SCRF=diethyl ether) level. Whilst not the highest practical level possible nowadays,^† it far exceeds in accuracy what Kirkwood had at his disposal in 1937. The results are at 10.14469/hpc/6367 and available as a spreadsheet if you want to adapt this for your own needs.

What can we conclude?

3. All seven conformations have a significant population (at 298K).^‡ The ordering, with one small exception, is the same for both Molecular and Quantum mechanics. The relative free energies span a slightly larger range than the steric energies obtained from molecular mechanics (1.7 kcal/mol) but all have a population of >6%.
4. Three conformations have a negative or (-) predicted rotation, and four are positive (+).
5. When weighted by population, the overall predicted rotation is -18°, which compares well with that observed (~-13°).
6. Kirkwood, who was not able to include all seven conformations in his analysis, was deeply unlucky that his particular choices/assumptions of conformations happened to have (+) rotations. But he was very much aware that this result could happen (although he does underestimate this in concluding that his tentative result is “probably accurate”. To be fair, if he had been more realistic, the referees might well have rejected his article!).

So the “what if“.

• If Kirkwood had chosen a conformationally simpler molecule which did not have as many as seven populated conformations, he may well have got his prediction correct (and for mostly the right reasons!). 
• But he has to be given lots of credit for recognising that optical rotations can be sensitive to conformational analysis. In this regard he could be regarded as one of the early fathers of that entire (Nobel prizing winning) field.
• He was 14 years ahead of the eventual unambiguous experiment that verified the Fischer convention. Of course he would have needed to correlate the absolute configuration of butan-2-ol with those of both sugars and amino acids using chemical transformations. In 1937, this may well have been quite synthetically challenging (but of course perhaps this correlation may have been actually known at the time. Does anybody reading this know?)
• But given that two other discoveries, both of which won the Nobel prize (the structure of peptides and the structure of DNA), depended on knowing with certainty the absolute configurations of amino acids and sugars respectively, Kirkwood’s method could be argued directly impacted upon no less than three Nobel prizes within two decades of his initial work.
• Remember that Watson and Crick “predicted” that the DNA helix is right-handed, as it happens on the basis of a single “short” H…H contact in their model which apparently disfavoured a left-handed helix. Boy was that a lucky guess (since that conclusion cannot be sustained nowadays on the basis of short H…H contacts). And that Pauling, in his own initial structures suggesting an α-helix in some proteins, predicted (wrongly) that the helix was left handed.  

So I think that yes, Kirkwood was pretty unlucky in his 1937 effort. And by 1952 (when he was correct), the opportunity for widespread recognition for this work and perhaps even a Nobel prize, had passed.

^♥Stereochemical notation has suffered from some measure of confusion over the years. Much of that confusion was cleared up with the introduction of the CIP rules, but historical vestiges remain. Thus d was originally used by Fischer himself to indicate configuration using the sense of direction on his diagram, but by others (including Kirkwood in 1937) to indicate the sense of direction of polarised light, an entirely different property. Eventually, the configurational sense became distinguished from the rotational light sense by capitalising the former (which of itself can still lead to confusions). Nowadays, the configuration of an entire molecule tends to be described by specifying the absolute configuration of all the asymmetric units using the CIP formalism, whilst Fischer’s formalism (now rationalised D/L), is only applied to sugars and cannot be used generally for other molecules. ^‡If you want to explore the temperature dependence of the Boltzmann populations and hence the predicted change in rotation with temperature, do please download the spreadsheet and try it out for yourself! ^†The elapsed time for these 14 calculations took about 2 hours. The exhaustive molecular mechanics calculations took <20 seconds.

References

1. J.M. BIJVOET, A.F. PEERDEMAN, and A.J. van BOMMEL, "Determination of the Absolute Configuration of Optically Active Compounds by Means of X-Rays", Nature, vol. 168, pp. 271-272, 1951. https://doi.org/10.1038/168271a0
2. W.W. Wood, W. Fickett, and J.G. Kirkwood, "The Absolute Configuration of Optically Active Molecules", The Journal of Chemical Physics, vol. 20, pp. 561-568, 1952. https://doi.org/10.1063/1.1700491
3. J.G. Kirkwood, "On the Theory of Optical Rotatory Power", The Journal of Chemical Physics, vol. 5, pp. 479-491, 1937. https://doi.org/10.1063/1.1750060
4. A.Z. Gonzalez, J.G. Román, E. Gonzalez, J. Martinez, J.R. Medina, K. Matos, and J.A. Soderquist, "9-Borabicyclo[3.3.2]decanes and the Asymmetric Hydroboration of 1,1-Disubstituted Alkenes", Journal of the American Chemical Society, vol. 130, pp. 9218-9219, 2008. https://doi.org/10.1021/ja803119p
5. D.H.R. Barton, "83. Interactions between non-bonded atoms, and the structure of cis-decalin", Journal of the Chemical Society (Resumed), pp. 340, 1948. https://doi.org/10.1039/jr9480000340