{"id":21499,"date":"2019-11-30T09:01:43","date_gmt":"2019-11-30T09:01:43","guid":{"rendered":"https:\/\/www.ch.imperial.ac.uk\/rzepa\/blog\/?p=21499"},"modified":"2019-12-24T12:06:12","modified_gmt":"2019-12-24T12:06:12","slug":"prediction-preceding-experiment-in-chemistry-how-unlucky-was-john-kirkwood","status":"publish","type":"post","link":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=21499","title":{"rendered":"Prediction preceding experiment in chemistry – how unlucky was John Kirkwood?"},"content":{"rendered":"
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Some areas of science progressed via<\/em> 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<\/em>, that of John Kirkwood’s prediction of the absolute configuration<\/a> of a small molecule based entirely on matching up the sign of a measured optical rotation with that predicted by (his) theory.<\/p>\n

The confirmation that Emil Fischer’s 1891 proposed convention<\/a> for the absolute configuration of sugars was in fact correct was famously made by Bijvoet in 1951 using crystallography.[1]<\/a><\/span> I first told this story<\/a> in 2012, noting that Kirkwood apparently made his seminal contribution a year later in 1952[2]<\/a><\/span> 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><\/span> a full 14 years before Bijvoet’s famous result (for which incidentally the Nobel prize was not<\/strong> awarded).\u00a0<\/p>\n

I have been asked to talk about this story at a Historical meeting of the Royal Society of Chemistry<\/a> 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;<\/p>\n

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I have redrawn it below in more modern form (and name). The difference between the two is in the notations\u00a0d\u00a0<\/b><\/em>and\u00a0(R<\/i>)<\/strong>. The former relates to the sign of the measured optical rotatio<\/strong>n [\u03b1]D<\/sub> where d<\/em> stands for d<\/em>extrorotation, or clockwise and is also often represented by (+).\u2665<\/sup> (R<\/i>) is the modern notation for the absolute configuration<\/strong> shown by Kirkwood in his diagram (Fig. 1).<\/p>\n

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He is asserting below that the enantiomer of butan-2-ol with a measured rotation of 13.9\u00b0 has (in modern notation) the absolute configuration (R<\/i>)\u00a0because his calculations predict somewhere between 9.5\u00b0 and 21.9\u00b0 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<\/em>)-butan-2-ol has a negative rotation of -13.9\u00b0![4]<\/a><\/span><\/p>\n

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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.
\n<\/a>\"\"<\/a><\/p>\n

and<\/p>\n

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Now, in 1937 the area of such conformational analysis was hardly known; only in 1948[5]<\/a><\/span> would Barton first put it firmly on the map (and win the Nobel prize for this work). So, in attempting his connection between d\u00a0<\/b><\/em>and\u00a0(R<\/i>)<\/strong>, 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]<\/a><\/span> although he WAS<\/strong> correct in 1952[2]<\/a><\/span>).<\/p>\n

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  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]<\/a><\/span>) 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 1.1 kcal\/mol! All are likely to have a significant Boltzmann population.\"\"<\/a><\/li>\n
  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<\/a>) and at the minimum energy geometry for each conformation, an optical rotation is calculated (at the\u00a0\u03c9B97XD\/Def2-TZVPP\/SCRF=diethyl ether) level. Whilst not the highest practical level possible nowadays,\u2020<\/sup> it far exceeds in accuracy what Kirkwood had at his disposal in 1937. The results are at\u00a010.14469\/hpc\/6367<\/a>\u00a0and available as a spreadsheet if you want to adapt this for your own needs.<\/li>\n<\/ol>\n

    \"\"<\/a><\/p>\n

    What can we conclude?<\/p>\n

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    1. All seven conformations have a significant population (at 298K).\u2021<\/sup>\u00a0The ordering, with one small exception, is the same for both Molecular and Quantum mechanics. The relative free energies span a similar range to the steric energies obtained from molecular mechanics (1.0 kcal\/mol) and all have a population of >4%.<\/li>\n
    2. Three conformations have a negative or (-) predicted rotation, and four are positive (+).<\/li>\n
    3. When weighted by population, the overall predicted rotation is -4.3\u00b0, which compares with that observed (-13\u00b0).<\/li>\n
    4. 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!).<\/li>\n<\/ol>\n

      So the “what if<\/strong>“.<\/p>\n