Posts Tagged ‘optical rotation’

A golden age for (computational) spectroscopy.

Monday, April 2nd, 2012

I mentioned in my last post an unjustly neglected paper from that golden age of 1951-1953 by Kirkwood and co. They had shown that Fischer’s famous guess for the absolute configurations of organic chiral molecules was correct. The two molecules used to infer this are shown below.


Using the theory Kirkwood had developed, the prediction for the optical rotation at the sodium D line for the (R,R) enantiomer of epoxybutene (Kirkwood did not use this R,R notation, which was still in the future) was +43°. The measured value was [α]D +59°. The (R,R) enantiomer did indeed correspond to Fischer notation.

QED.

A postscript is that a modern equivalent of Kirkwood’s result, using the ωB97XD/6-311+G(d,p) method gives +67° for the gas phase and +57° for solution (in CCl4). The experimental value relates to the pure liquid. In fact, Kirkwood had been very aware that solvation can influence the measured value of an optical rotation, and so even today, a match between experiment and calculation of ± 16 ° is considered a good fit.

But when it comes to the second molecule, (R)-1,2-dichloropropane, we are in a different ball park. In fact, most of Kirkwood’s article is devoted to unravelling this second system. This is because it was realised that it is conformationally flexible. Two conformations (this term was then often used interchangeably with configuration, which might confuse a modern audience) called trans and skew (now called anti and gauche) were considered and it was realised that the relative populations would be influenced by temperature and particularly, the solvent. I quote here the final conclusion: We have assigned the absolute configuration of Fig. 2 to the dextrorotatory isomer of 1,2-dichloropropane. This was done without any experimental data concerning the optically active forms of the molecule, using only the calculated dependence of the rotatory power on conformation (Table II) and the information about the potential of internal conformation obtained from the electron diffraction and dipole moment measurements.

Non trivial then! Perhaps this is why these techniques were not immediately picked up by synthetic chemists to verify the absolute configuration of their own molecules. But my point is that the use of such techniques now seems to be growing exponentially, which is why this post is headed the golden age of computational spectroscopy. So what of such a modern take on  (R)-1,2-dichloropropane (in heptane, which corresponds to the measured value of +20 to +30, and -21° for the (S) enantiomer). Well, there are in fact three viable conformations, not two as Kirkwood supposed. He did not know that the gauche stereoelectronic effect favoured two of them despite the greater steric encumbrance. The calculated rotations are +53 (anti), +96 (gauche) and -182° (second gauche conformer). Such dependence on conformation is sadly not unusual, and it means you have to know the Boltzmann population very accurately indeed to infer an observed value. This might in part explain the rather circuitous argument used by  Kirkwood for dichloropropane!

Fortunately, nowadays optical rotation (more accurately referred to as optical rotatory power, or ORP) is just one of a growing armoury of spectroscopic measurements that can be computed to the accuracy required to draw firm conclusions. These include ORD (optical rotatory dispersion, or variation with the frequency of the polarised light used), ECD (electronic circular dichroism) and VCD (vibrational circular dichroism). It is still not absolutely routine, but these techniques are now found in an increasing number of synthetic chemists’ toolkits.

And my final reflection is to ponder that the golden age of pharmaceutical synthesis (lets say  1950 – 2000, but  I know I may get dissent), in which certainty about the separate physiological effects of both enantiomers of chiral drugs became mandatory, would not have been possible without Kirkwood’s pioneering article, along of course with Bijvoet’s independent result.

A comparison of left and right handed DNA double-helix models.

Saturday, January 1st, 2011

When Watson and Crick (WC) constructed their famous 3D model for DNA, they had to decide whether to make the double helix left or right handed. They chose a right-handed turn, on the grounds that their attempts at left-handed models all “violated permissible van der Waals contacts“. No details of what these might have been were given in their original full article (or the particular base-pairs which led to the observation). This follow-up to my earlier post explores this aspect, using a computer model.

One half of a (CGCG) DNA strand

The DNA model used here is shown above; in shorthand it is d(CGCG)2. A crystal structure reveals it to form a (non-Watson-Crick) left-handed helix. If you open the 3D model below (based on a ωB97XD/6-31G(d)/SCRF=water optimisation), some of the short van der Waals contacts are measured. Most are around 2.25Å and the shortest is 2.1Å. It is worth noting that WC note in their article that a distance of 2.1Å for the B-form is acceptable (p92, bottom) and not a violation. All twelve hydrogen bond lengths H…O or H…N are normal, with lengths around 1.8Å. Given that a H…H distance is at its most attractive at ~2.4Å, and plenty of H…H distances of ~2.1Å are known from the crystal structures of organic molecules, one might conclude that (for the CG base pair), their hypothesis that the Z-form could be eliminated was wrong.

The DNA duplex d(CGCG) showing a left handed helix with short H...H contacts shown. Click for 3D

But might the original WC-right handed form for this system be at least competitive? There is one H…H of 2.05Å and quite a few at ~2.5Å (3D model below). The “violation” of van der Waals contacts is if anything slightly worse than with the left-handed helix. The total difference in the dispersion energy is a rather astonishing ~12 kcal/mol in favour of the Z-form. I will update this post (as a comment) when the relative free energies of the two forms are available (this calculation takes a while), but there is little doubt that the Z-form is indeed the more stable.

The DNA duplex d(CGCG) showing a right handed helix with short H...H contacts shown. Click for 3D

What can also be said about the Watson-Crick right handed form is that the hydrogen bonding is not so optimal. One of the twelve interactions between a (terminal) CG pair has some signs of being “unzipped“, with an N-H…O=C distance of ~1.9Å (there is no sign of similar unzipping in the Z-form). One must wonder whether this difference in the Z- and B-helices for the CG pair has been exploited in nature.

 

One crucial aspect of DNA is the local conformation about the bond connecting the base and the ribose, N9-C8 in the diagram below(green arrow).

Conformation of the base-ribose unit

An analysis of this bond can be expressed in terms of NBO theory. This clearly shows a strong interaction energy (E2) between the lone pair on N9 and the C8-O4 antibonding orbital of 13.3 kcal/mol, a classical anomeric effectin fact. In this case, it promotes the local conformation of this unit, which has a significant effect on the final model.

What else can analysis of the wavefunction tell us? Well, curiously, the optical rotation of this particular small oligomer has never been reported in the literature, and an intriguing question is whether it might have proved useful to distinguish between B- and Z-forms of the duplex? To do this, one needs a reasonably reliable way of computing [α]D for both isomers. This is because optical rotations are not reliably additive, and it is difficult to estimate them accurately based purely on the fragments present in the molecule. In 2011, is is now perfectly possible to calculate this quantity quantum mechanically, even for 250 atoms, using a reasonable basis set and making allowance for solvation (which is known to affect the calculated rotation). The values (CAM-B3LYP/6-31G(d)/SCRF=water) for the Z-isomer are 66° and 32° for the B-isomer. Of course the model is not complete, lacking a counterion for the phosphate and explicit water molecules, but even so, it might appear that the reason optical rotations are not reported is that they truly are not useful!