Posts Tagged ‘chiroptical’

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Scalemic molecules: a cheminformatics challenge!

Wednesday, July 6th, 2011

A scalemic molecule is the term used by Eliel to describe any non-racemic chiral compound. Synthetic chemists imply it when they describe a synthetic product with an observable enantiomeric excess or ee (which can range from close to 0% to almost 100%). There are two cheminformatics questions of interest to me:

  1. How many non-trivial scalemic molecules have been reported in the literature (let’s assume their ee is significantly greater than 0%)?
    • The distribution function for the ee of these molecules would be most interesting!
  2. Of those, how many have the absolute configuration of the predominant enantiomer established with high confidence?
    • Or, to put this another way, how many may prove to be mis-assigned?

Note the careful qualification in the above questions. Thus by non-trivial, I mean compounds whose scalemic attributes persist in solution for a chemically useful duration. That could be taken to mean configurationally stable chiral molecules, rather than those that might be conformationally chiral (an example of a trivial scalemic molecule would be e.g. the twist-boat conformation of cyclohexane, which having D2 symmetry is dissymetric, but which would only retain its scalemic property for a trivially short timescale).

What are boundary values? These are some:

  • As I write this, CAS records 61,257,703 chemical substances. Needless to say (unless I missed it), the answer to my first question is not to be found there.
  • Beilstein (Reaxys) records 1,126,995 compounds as having one or more reported chiroptical properties (which is the most direct way of establishing a molecule is scalemic, although strictly, having say an optical rotation of 0° does not necessarily mean the molecule is not scalemic). We have no way of knowing how many molecules are scalemic for which no chiroptical measurement has been made (but one would hope its a small proportion). Perhaps that is a good answer to question 1?
    • of which 1,097,094 relate to optical rotatory power, 17,515 to optical rotatory dispersion and 62,248 to electronic circular dichroism.
    • it is more difficult to answer how many of these 1,126,995 substances have a firmly established absolute configuration. Measuring a chiroptical property per se does NOT in itself establish the absolute configuration. Doing so is a fascinating exercise in sequential logical argument, and how one does it has changed quite a lot over time. And what might I mean with high confidence? An older assignment (made say > 40 years ago) might be less confident than one established in 2011 (fortunately, we can probably trust the absolute configurations of the amino acids!). A bit of a can of worms, nevertheless. But it interests me because it is a good example of what the semantic web is supposed to be all about.
  • The Cambridge crystallographic database reports 560,307 entries, of which 72,340 are in chiral space groups (in which a chiral molecule can crystallise) and exhibit no disorder or other errors. We do not know how many of these are non-trivial, since all manner of small (and low energy) distortions can create a chiral species (in the solid state), but which would not persist  for a chemically useful duration in solution (i.e. it might for example immediately racemize and become non-scalemic).
  • The Flack parameter has been used since 1983 for enantiomorph estimation (a value of ~≤ 0.10(10) would be considered meaningful). This could in principle provide an answer of known confidence to my question 2 above (but would not address the issue of non-triviality).
    • The challenge now is to quantify how many compounds have a meaningful reported Flack parameter (presumably a sub-set of 72,340?)

Let me declare one personal interest. Over the last four years or so, we have been asked to confirm the absolute configuration of around eight scalemic molecules. After a detailed study, we concluded three were mis-assigned. Now this in no way implies anything about what the answer to question 2 above might be! But it does make one think!

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Metallic carbon nanotori

Thursday, June 2nd, 2011

The interface between physics, chemistry (and materials science) can be a fascinating one. Here I show a carbon nanotorus, devised by physicists[1] a few years ago. It is a theoretical species, and was predicted to have a colossal paramagnetic moment.

Carbon nanotorus. Click for 3D.

At 1364 carbon atoms, it is a little too big to calculate any of its expected chiroptical properties (the torus twists in a helical manner, and so is chiral). So we can only speculate whether e.g. its optical rotation would also be colossal! Or, what applications such a nanodevice might have. This post, by the way, was induced by seeing Steve Bachrach’s fascinating exploration of chiral nanohoops.

 

References

  1. L. Liu, G.Y. Guo, C.S. Jayanthi, and S.Y. Wu, "Colossal Paramagnetic Moments in Metallic Carbon Nanotori", Physical Review Letters, vol. 88, 2002. https://doi.org/10.1103/physrevlett.88.217206

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Why are α-helices in proteins mostly right handed?

Saturday, April 9th, 2011

Understanding why and how proteins fold continues to be a grand challenge in science. I have described how Wrinch in 1936 made a bold proposal for the mechanism, which however flew in the face of much of then known chemistry. Linus Pauling took most of the credit (and a Nobel prize) when in a famous paper in 1951 he suggested a mechanism that involved (inter alia) the formation of what he termed α-helices. Jack Dunitz in 2001 wrote a must-read article on the topic of “Pauling’s Left-handed α-helix” (it is now known to be right handed).  I thought I would revisit this famous example with a calculation of my own and here I have used the ωB97XD/6-311G(d,p) DFT procedure to calculate some of the energy components of a small helix comprising (ala)6 in both left and right handed form.

Firstly, it is important to note that Pauling was apparently not aware of the absolute handedness of amino acids (which are (S) in CIP terminology). This had in fact only been established a few months before Pauling’s publication by Bijvoet, and news of this might not have reached Pauling. So Pauling guessed (or perhaps, he had already built his models, and did not have time to reconstruct them) and his famous α-helix diagram turned out to be the enantiomer of the real McCoy. As with DNA itself, the helix bears a diastereomeric relationship to the chirality of the amino acids; both have to be inverted to get the proper enantiomer (which is what Pauling did). The secret that Pauling had discovered was hydrogen bonding, and particular, weak N-H…O=C interactions (Wrinch had thought it was strong covalent N-C-OH bonding instead). Of course, there are other effects at work, which include van der Waals or dispersion interactions, electrostatic effects resulting from the large dipoles in peptides (not least due to the zwitterionic character), the planarity of the peptide bond itself, the potential for other types of hydrogen bond (e.g. C-H…O) and entropic effects. I have split some of these down for left and right handed forms of DNA in another post.

It turns out calculating most of these effects on an even-handed basis is not that easy. Only the recent advent of dispersion-corrected DFT procedures, together with solvation algorithms that allow for accurate geometry optimisation and subsequent evaluation of free energies allows such a calculation to be performed. Hitherto, it has been mostly molecular mechanics that has been used (which itself relies on many parameters from quantum mechanics, such as atom charges, and explicitly identifying interactions for hydrogen bonding). By returning to a quantum-mechanical model, some of these assumptions inherent in the mechanics method need not be made.

We showed in 1991 that an effective solvation treatment required for the zwitterionic form of amino acids in aqueous solutions would ideally comprise not only a self-consistent-reaction-field, but also explicit water molecules as solvent. Here only the former solvation term is included, but expanding the model to include water is certainly possible. Both the zwitterionic and the neutral forms of (ala)6 are included below, so that the effect of a large dipole on the structure and relative helical stability can be estimated. One notes that (even in a dielectric cavity corresponding to water), the extended zwitterions are high energy species.  In a protein, they of course would be stabilized by the immediate environment of the ions. The right-handed helix clearly comes out as more stable (by about 1 kcal/mol per residue, see also DOI: 10.1021/ja960665u),  but this is not really due to either dispersion effects or entropy and must therefore arise largely from the hydrogen-bond like interactions. Ionizing the termini to form a zwitterion increases the propensity for a right handed helix slightly.

Relative thermodynamic energies (kcal mol-1) of (ala)6 α-helices
System Total energy Dispersion ΔΔH298 Δ(T.ΔS298) ΔΔG298
Left, neutral 0.0
 0.0 0.0 0.0 0.0
Right, neutral -4.0
 +0.2 -4.0 0.9 -4.9
Left, zwitterion 0.0 0.0 0.0 0.0 0.0
Right, zwitterion -7.1 0.1 -6.3 1.7 -8.0

Shown below are the calculated structures. The chains have (inter alia) unusual bifurcated hydrogen-bonding interactions, between one carbonyl group and two N-H groups (show as atom with halo). These are not quite the models that Linus Pauling built!

Left handed. Click for 3D

Right handed. Click for 3D

Left handed zwitterion. Click for 3D

Right handed zwitterion. Click for 3D

For a more objective analysis of the interactions within the system, a QTAIM analysis is shown below.

Left helix. Bond critical points in green. Click for 3D.

Right helix. Click for 3D

Whilst the overall conclusion is that theory agrees well with the experimental observation that peptide sequences tend to coil into right rather than left handed helices,  the reasons they do so is a little more subtle than simple model building alone can reveal.  As the AIM shows, a plethora of unusual and weaker interactions occur within these helices, a full analysis of which must await presentation elsewhere.

An NCI analysis reveals strong hydrogen bonds as blue-shaded surfaces.

NCI surface. Click for 3D.

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The colour of purple

Thursday, February 24th, 2011

One of my chemical heroes is William Perkin, who in 1856 famously (and accidentally) made the dye mauveine as an 18 year old whilst a student of August von Hofmann, the founder of the Royal College of Chemistry (at what is now  Imperial College London). Perkin went on to found the British synthetic dyestuffs and perfumeries industries. The photo below shows Charles Rees, who was for many years the Hofmann professor of organic chemistry at the very same institute as Perkin and Hofmann himself, wearing his mauveine tie. A colleague, who is about to give a talk on mauveine, asked if I knew why it was, well so very mauve. It is a tad bright for today’s tastes!

Charles Rees, wearing a bow tie dyed with (Perkin original) mauveine and holding a journal named after Perkin.

The first thing to note about mauveine is that it is not a single compound; actual samples can contain up to 13 different forms! These all vary in the number of methyl groups present which range from none up to four, in various positions. These compounds all have absorption maxima λmax in the range 540-550nm, the colour of purple. The structure of one of these, known as mauveine A, is shown below.

Mauveine A. Click to load 3D

You can see from this that something is missing. The so-called chromophore is a cation, and an anion needs to be provided to balance the charge. We will now attempt to predict the color of purple using purely the power of quantum mechanics (for many years, accurate prediction of colour was a holy grail amongst dye chemists for obvious reasons). The anion can be chloride, and the colour is often measured in methanol as solvent. So the first task is to calculate this ion-pair. This used to be easier said than done (and in the past, the anion was often simply neglected). But using the ωB97XD density functional procedure (to get the van der Waals interactions modelled correctly) and a 6-311++G(d,p) basis set, coupled with a smoothed-cavity continuum solvation procedure, and two molecules of water (standing in for methanol, which is a bit bigger) as explicit solvent molecules, we get the structure apparent when you click on the diagram above (DOI: 10042/to-7320). Application of time-dependent density function theory (TD-DFT) gives a measure of the UV-optical spectrum (below, loaded as a scaleable SVG image. If you are using a modern browser, it should display. If not, try the latest FireFox, Chrome, Safari etc).

 

 

This has several noteworthy aspects.

  1. The visible (right hand side) part of the spectrum is very monochromatic, with λmax ~440nm. In other words, mauveine has a pure and intense colour.
  2. This λmax is hardly affected by the presence of the counterion.
  3. The electronic transition responsible for this band is a simple HOMO (highest-occupied-molecular-orbital) to LUMO (lowest-unoccupied-molecular-orbital) excitation of an electron.
  4. These orbitals are shown below.
    LUMO HOMO

    Mauveine A. LUMO. Click for 3D

    Mauveine A. HOMO. Click for 3D
  5. Note how the excitation involves the central region of the molecule, and one of the pendant aryl groups, but not the other. One might presume that tuning the colour would only work if changes are made to the first of these aryl groups.
  6. There is a real mystery about the calculated value of λmax, which differs from the observed value by about 100nm (the wrong colour, making mauveine orange rather than purple). Normally, this sort of time dependent density functional theory has errors no greater than 15-20nm. The calculated value of λmax is not sensitive to the basis set, or the presence or not of the counter ion and solvent. Clearly, a discrepancy of this magnitude must have some other explanation. Watch this space!

So this post ends with a bit of a mystery. The fanciest most modern computational theory gets the colour of mauveine wrong by ~100nm. Why?

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The handedness of DNA: an unheralded connection.

Wednesday, December 29th, 2010

Science is about making connections. Plenty are on show in Watson and Crick’s famous 1953 article on the structure of DNA (DOI: 10.1038/171737a0), but often with the tersest of explanations. Take for example their statement “Both chains follow right-handed helices“. Where did that come from? This post will explore the subtle implications of that remark (and how in one aspect they did not quite get it right!).

The right handed helix is illustrated in the article cited above as perhaps the most famous scientific diagram of the 20th century (as recounted in the TV program by Marcus du Sautoy). It was drawn by Odile Crick, a professional artist, and it is easily her best known work (the original, sadly, appears lost). Many say it has never been bettered; I do not reproduce it here for fear of copyright infringement, but you can see Odile (who died only recently) and her diagram here. One however has to go to the Watson-Crick (WC) full paper (DOI: 10.1098/rspa.1954.0101) for an explanation of why they decided the helix was right-handed, or (P)- in CIP terminology. In my opinion (as a chemist), this is a far better read than the short and more famous note in Nature. There (on page 87) one finds the immortal statement “we find by trial and error that the model can only be built in a right-handed sense”. They follow that remark with another which I will quote later in this post. But the preceding observation is footnoted, and that footnote must rank as one of the most unheralded in science (unlike e.g. Fermat’s). For this footnote notes another article, published just two years earlier (DOI: 10.1038/168271a0) in which the absolute handedness of a small molecule was finally confirmed after ~50 years. The molecule is shown below, and again in modern CIP terminology, the two chiral carbon atoms both have (R) configurations rather than (S). Until this point, the (R) configuration had merely been a guess with an evens chance of it being right (and had it been wrong, imagine how many textbook diagrams would have needed changing!).

The absolute configuration of natural tartaric acid.

Chemists had, in the preceding 50 years, by synthesis and transformation, connected the configuration of tartrate to the ribose sugars that form the linker in DNA, and so Watson and Crick built their famous model of DNA assured in the knowledge that the absolute configuration of their ribose sugar was correct. But that assurance, it is important to remember, had only come two years earlier! The (correct) structure of DNA was very much a discovery of its time, and this connection between tartrate and DNA I think deserves the accolade of great connections in science (I write this in the Semantic Web sense).

On to another statement to be found in the full WC article: “Left handed helices can only be constructed by violating the permissible van der Waals contacts” Given the nature of the molecular model building tools that WC had at their disposal,* I suspect we must forgive them this assertion. But of course, building models using the van der Waals constraints (amongst others of course) is what modern computers are really very good at. So what might a modern visitation of this very issue yield? Shown below is a small DNA duplex, named d(CGCG)2 (DOI: 10.2210/pdb1zna/pdb) This uses only the CG base-pairing motif (the other of course is AT). Well, it turns out that DNA constructed from CG-rich duplexes does NOT necessarily adopt a right handed helix after all! WC (for this particular condition) were in fact wrong, and clearly the van der Waals contacts are not after all objectionable. Left-handed helices (as a left hander myself, I am naturally drawn to them) are also known as Z-DNA (the right handed form is called B-DNA), although many left-handed representations have in fact been drawn in error.

The DNA duplex d(CGCG) showing a left handed helix. The ribose is in the 2E conformation. Click for 3D and see if you can find any objectionable van der Waals contacts!

The model when stripped of its water molecules, is then of a size (250 atoms) which is easily amenable to a modern quantum-mechanical DFT calculation. Importantly, this has to include dispersion corrections (the van der Waals contacts referred to above) to get the correct geometry, and one can use e.g. ωB97XD/6-31G(d) + continuum water solvation correction to compensate for the missing waters (see DOI: 10.1039/C0CC04023A for an example of its use for a large molecule, or indeed this post). In truth, this combination of characteristics in a model has only recently become possible for a molecule of such size.

 

Well, now that a good accuracy wavefunction for e.g. d(CGCG) is possible, what might one do with it? Well, the chiro-optical properties might be calculated (see DOI: 10.1002/chir.20804), including the optical rotation at a specified frequency, or e.g. the electronic circular dichroism spectrum. Such properties are normally computed only for much smaller molecules. Watch this space (or the journals).

* Note added in proof (as the saying goes): This article by Derek Barton published in 1947, some six years before WC claimed “violation of  the permissible van der Waals contacts“, established clearly the principles behind the model building by WC and in many ways could be described as the start of quantitative molecular model building. The very same equation used by Barton to model dispersion attractions is still used in e.g. the ωB97XD DFT method noted above.

 

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Gravitational fields and asymmetric synthesis

Saturday, November 20th, 2010

Our understanding of science mostly advances in small incremental and nuanced steps (which can nevertheless be controversial) but sometimes the steps can be much larger jumps into the unknown, and hence potentially more controversial as well. More accurately, it might be e.g. relatively unexplored territory for say a chemist, but more familiar stomping ground for say a physicist. Take the area of asymmetric synthesis, which synthetic chemists would like to feel they understand. But combine this with gravity, which is outside of their normal comfort zone, albeit one we presume is understood by physicists. Around 1980, chemists took such a large jump by combining the two, in an article spectacularly entitled Asymmetric synthesis in a confined vortex; Gravitational fields and asymmetric synthesis (DOI: 10.1021/ja00521a068). Their experiment was actually quite simple. They treated isophorone (a molecule with a plane of symmetry and hence achiral) with hydrogen peroxide and then measured the optical rotation.

Asymmetric synthesis of Isophorone oxide

Conventional wisdom is that the oxygen can be delivered with equal probability to either face of the alkene, resulting in a racemic (equal) mixture of the two enantiomers of the epoxide. But if one enantiomer is formed in slightly greater amount than the other, the reaction is said to proceed asymmetrically, and the product will exhibit an optical rotation. Normally, such asymmetry is induced by carrying out the reaction in the presence of a chiral molecule or catalyst. Light too can be chiral, but these brave chemists decided to use gravity. More specifically, the earth’s gravitational field. In the Northern Hemisphere. The reaction was conducted in a centrifuge in three ways. With the spun tube horizontally, and then vertically spinning clockwise or anticlockwise. The first of these produced product which exhibited no optical rotation within experimental error (e.g +0.2 ± 0.3 mdeg). The second gave results with a positive rotation (e.g. 12.8 ± 0.3 mdeg) and the third a negative rotation (-2.2 ± 0.2 mdeg). They considered that the reaction was occurring in e.g. a clockwise vortex constituting a P-helix (the vortex in other words was chiral) interacting with the earth’s coriolis force.  They speculated (but did not do the experiment) that the reverse effect would be seen in the Southern Hemisphere. Their paper concluded with the grand speculation that prebiotic organic synthesis could have been partially asymmetric as a result of being conducted in a chiral gravitational field (nothing like aiming high!).

Shortly after this was published, a rebuttal appeared (DOI: 10.1021/ja00544a051) penned not by a synthetic chemist but a physicist. In truth, most of the four-paragraph article presents arguments few chemists are familiar with (and probably do not understand). Only one sentence, the very last, made the impact (and it sounds as if it was added as a throw-away afterthought). It simply stated that the magnitude of the earth’s field (in so-called natural units) suggested that a parameter ω related to the spinning velocity was ~10-21 and that the corresponding value that would be required to induce the asymmetry observed (which can be computed from e.g. ΔG = -RT Ln K) was 10-14. Put in rather plainer English, the earth’s magnetic field was seven orders of magnitude too weak to have the effect claimed for it. That last sentence on its own pretty much sunk the theory, and it is no longer thought that gravitational fields can induce asymmetry in reactions. I tell this story (which, as it happened thirty years ago is now largely forgotten), since seven orders of magnitude is quite a large mismatch! Chemists rarely have the opportunity to be so spectacularly wrong when they propose a theory. In reality, even two orders of magnitude is unusual.

It’s when you approach factors of say less than one order of magnitude (the nuances) that arguments about which interpretation is correct may break out. So which category might the subject of this post belong to? As I there noted, it’s all about whether the two carbon atoms separating carbon dioxide and cyclobutadiene in a crystalline lattice by a distance of 1.5Å are interacting by a covalent bond, or a van der Waals attraction. In terms of energies, most chemists agree that these differ by around two orders of magnitude. This, I suggest, does not come into the category of nuance!

For a nice review of asymmetric synthesis under physical fields, see here.

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Bio-renewable green polymers: Stereoinduction in poly(lactic acid)

Saturday, July 24th, 2010

Lactide is a small molecule made from lactic acid, which is itself available in large quantities by harvesting plants rather than drilling for oil. Lactide can be turned into polymers with remarkable properties, which in turn degrade down easily back to lactic acid. A perfect bio-renewable material!

Lactide

The starting point for ring opening polymerisation is racemic lactide, or rac-LA. This is an equal mixture of the R,R and S,S enantiomers, and it is now treated with a catalyst based on a metal M. If M=Mg, there is a rather remarkable stereochemical outcome for the resulting polymer. The catalyst selects alternating enantiomers for the assembly, resulting in a chain (R,R),(S,S),(R,R),(S,S), etc, the name for which is a heterotactic polymer. It could instead have created a blend of equal proportions of (R,R),(R,R),(R,R) and (S,S),(S,S),(S,S) which is an isotactic polymer. Needless to say, these two polymers have quite different properties, and it very much matters which is formed. Without such a catalyst, a random atactic polymer is created rather than a stereoregular arrangement.

Poly (lactic acid)

The question is how does the catalyst manage to assemble the polymer with such stereoinduction? The origins of this depend on a detailed understanding of the mechanism of the reaction, and in 2005 we suggested one which offered an explanation for the stereospecificity (see E. L. Marshall, V. C. Gibson, and H. S. Rzepa, DOI: 10.1021/ja043819b and an interactive storyboard).

Mechanism for stereoregular polymerisation

The key features of this rational were:

  1. Two possible transition states may control the reaction, TS1 and TS2. Which one depends on which is the higher in energy.
  2. The smallest model for this process involves loading two molecules of lactide onto the catalyst. The first has already been ring opened, and will control the stereochemistry of the second, which is the one suffering the ring opening bond formations/breakings shown above (the first is lurking in the group R).
  3. This leads to four different possibilities, (R,R)-(R,R)*, (S,S)-(S,S)*, (R,R)-(S,S)*, and (S,S)-(R,R)* (where the * denotes the reacting lactide, as in the diagram above). These are all diastereomers, and hence will be different in energy. If one of the first two is the lowest, then isotactic polymer will result; if the latter two then a heterotactic polymer.

Back in 2004, we had constructed a model based on B3LYP and of necessity a mixed basis set, being 6-311G(3d) on the Mg, 6-31G on the lactide and only STO-3G on the catalyst. This was done because the complete system was actually rather large. Even so, a transition state calculation would regularly take at least 10 days to find using the fastest computers available to us at that time. Using this procedure, we found that the rate limiting kinetic step  was in fact TS2 for all four possibilities noted above. Of these, the (R,R)-(S,S) transition state turned out to represent the lowest energy pathway, thus confirming the observed heterotacticity for this particular catalyst.

Well, times have moved on:

  1. Six years later, computers are around 20 times faster! We can now afford to improve the basis set to 6-31G(d,p) on all the atoms, including the catalyst (the Mg stays at 6-311G(3d) however; improving it to 6-311G(3d,2f) makes little difference).
  2. We can now include the solvent (thf) as a continuum field.
  3. In the last five years the B3LYP functional has been shown to underestimate the energies of globular molecules. A modern functional such as ωB97XD, which includes dispersion energy corrections, should be expected to do much better.

It is the purpose of this blog to report an update to the modelling. Quoting relative free energies (including the solvation correction), the results come out as;

  1. (R,R)-(S,S) 0.0 kcal/mol for the TS1 geometry (see DOI: 10042/to-4950)
  2. (S,S)-(S,S) 1.8 for the TS2 geometry
  3. (S,S)-(R,R) 5.5 for the TS1 geometry
  4. (R,R)-(R,R) 9.1 for the TS1 geometry.

Well, there are surprises! Using the gas phase B3LYP model the key transition state was TS2; now its TS1 (for in fact three of the four possible transition states). The bottom line (almost) is that the same stereoisomer as before comes out the winner! The take home lesson is that in six years of progress, modelling can now encompass solvent and dispersion corrections. Many mechanisms with > ~100 atoms investigated in the past without inclusion of these effects could probably do with a re-investigation, especially if the transition states are “globular” in nature. Any by now you are probably wondering what the transition state looks like. Well, here it is (and see it in all its glory by clicking on the diagram below).

(R,R)-(S,S) Transition state for stereoregular lactide polymerisation. Click for animation

And if you are also wondering how one might proceed to analyse the origins of the stereoinduction, the NCI interaction surfaces (as described in this post) are shown below. Note how the extensive degree of green interaction surface is associated with the globular nature referred to above.

Non-covalent interaction (NCI) surfaces for the (R,R)-(S,S) transition state. Click for 3D

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The mysteries of stereoinduction.

Thursday, July 1st, 2010

Stereo-induction is, lets face it, a subtle phenomenon. The ratio of two stereoisomers formed in a reaction can be detected very accurately by experiment, and when converted to a free energy difference using ΔG = -RT Ln K, this can amount to quite a small value (between 0.5 – 1.5 kcal/mol). Can modelling reproduce effects originating from such small energy differences? Well one system that has been argued about now for several decades is shown below as 1.

Norbornene systems

Way back in 1992, we thought that the explanation for attack by an electrophile on the alkene from the syn face was electrostatic (although it did depend on the nature of the electropile; thus we concluded that attack by Hg(OH)2 was electrostatic, but by BH3 was orbital controlled). Recently, a different explanation has emerged, relating to how the fundamental normal vibrational modes of the molecule interact with the transition normal mode for the reaction. A new example of this, relating to reaction of the isomeric 2 with a peracid has recently been discussed on Steve Bachrach’s blog. Here, the peroxide of the peracid is thought to act as an electrophile (although one must bear in mind that it does bear two electron lone pairs!). The conclusion was pretty clear cut; the experimental preference for syn (92%) over the anti isomer (8%, ΔΔG = 1.4 kcal/mol) was NOT due to electrostatic effects, but due to distorsional asymmetry in the vibrational mode that couples/forms the transition state mode.

I could not resist revisiting this system. As in 1992, a molecular electrostatic potential was calculated for 2. The method used was wB97XD/aug-cc-pvdz, and if you want the archive of this calculation to evaluate it yourself, see here).

MEP for 2. Click on diagram for 3D.

A very clear electrostatic bias for syn attack emerges (orange = attractive to a proton=electrophile). This electrostatic picture is not directly related to any distortional asymmetry, although of course both could arise from the same electronic factors. They may indeed be different manifestations of the same underlying nature of the wavefunction. But I would claim here that to make the clear statement that electrostatic effects are NOT responsible for the discrimination in this reaction is perhaps too simplistic (electrostatic potentials were not reported in the original article). The control experiment is 3, which is known to be far less selective. The calculated electrostatic potential likewise shows much less discrimination.

The norbornene with a four-membered ring

Is there another take on 2? Well, how about an NBO (natural bond order) analysis? The interaction energy between the filled C1-C2 orbital and the antibonding C15-C16 π* bond is 3.24. This could be regarded as pushing electrons into the anti-periplanar syn face of the alkene. The corresponding C2-C9/C15-C16 interaction resulting in an anti-preference is less at 2.55 kcal/mol. This effect arises because the C1-C2 bond (localised as an NBO) is a better donor (E=-17.8eV) than C2-C9 (E=-18.1eV). Because C2 is common to both, it must be the difference between C1 and C9 (i.e. the hybridization of each). Perhaps it’s an orbital effect after all?

Norbornene electrostatic potential

I would conclude by saying that it can be ferociously difficult to identify the fundamental origins of stereo-induction. But I leave the argument in the hands of the reader now. What do you think?

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Chemistry with a super-twist: A molecular trefoil knot, part 2.

Tuesday, June 1st, 2010

A conjugated, (apparently) aromatic molecular trefoil might be expected to have some unusual, if not extreme properties. Here some of these are explored.

  1. The first is the vibrational spectrum. With 144 atoms for this molecule, it has 426 vibrational modes, but one is highlighted below. This is the mode that moves the atoms in accord with the Kekulé resonance. If real, this mode resists such alternation. The mode has a value of ~ 1310 cm-1 for benzene, although this is accepted as being lower than expected due to the phenomenon of π-distortivity (DOI: 10.1039/b911817a and also this post). The mode shown below has the value of 1650 cm-1, which is a good deal higher than for benzene. The significant coupling of the CH wagging motions with the C-C/C-N stretching (Duschinsky coupling) makes the interpretation more complex (it also occurs for benzene itself), but the Kekulé mode (there are in fact several) is surprisingly large for so many π-electrons. Perhaps the large degree of writhe noted in the previous post might have something to do with it?

    Molecular trefoil: the Kekulé mode for bond alternation. Click for animation.

  2. The NICS (nucleus independent chemical shift) at the centroid of the trefoil is -16.4 ppm. This is clearly an aromatic value, and confirms our inference that the system is a 4n+2 aromatic molecule. In this example, the aromaticity is not only three-dimensional, but helical as well. The predicted 1H NMR spectrum (below) shows three regions. The upfield region (~ -5 ppm) corresponds to protons pointing directly inwards to the centre, whilst the lowfield region (~ 8ppm) corresponds to protons at the outside edge.

    Predicted 1H NMR spectrum

  3. Shown below is the calculated electronic circular dichroism (ECD) spectrum. It shows a large Cotton effect due to the chiral nature of the trefoil. The electronic transitions extend beyond ~1500nm, approaching the near infra-red. The phase of the Cotton effect at ~600nm calculated for the chiral isomer shown in the 3D model above would certainly suffice to assign the absolute configuration of the system should the experimental spectrum be measurable.

    Calculated Electronic circular dichroism spectrum for the base trefoil.

    The spectrum above shows maximum absorption at ~600nm, which means optical rotation at the sodium D-line (589 nm) cannot be measured (light has to get through to measure its rotation). However, the region of 880nm (the highest value available on commercial spectrometers) is reasonably transparent for such measurement. Calculations may not be much help, since the linear CPHF equations appear unstable. Thus [α]880 shows an enormous dependence on the precise DFT method chosen to compute it (~ +8763°@CAM-B3LYP but the very different -59898°@B3LYP).

Henry Rzepa. Chemistry with a super-twist: A molecular trefoil knot, part 2.. . 2010-06-02. URL:http://www.ch.ic.ac.uk/rzepa/blog/?p=2084. Accessed: 2010-06-02. (Archived by WebCite® at http://www.webcitation.org/5qC4NiFsM)

 

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Anatomy of an asymmetric reaction. The Strecker synthesis, part 2.

Wednesday, May 26th, 2010

In the first part of the post on this topic, I described how an asymmetric sulfoxide could be prepared as a pure enantiomer using a chiral oxygen transfer reagent. In the second part, we now need to deliver a different group, cyano, to a specific face of the previously prepared sulfoxide-imine. The sulfoxide is now acting as a chiral auxilliary, and helps direct the delivery of the cyanide group to specifically one face of the imine rather than the other. After removal of the aluminum carrier for the cyano group and hydrolysis of the cyano group to a carboxylic acid group, we end up with an enantiomerically pure amino acid.

The Strecker synthsis: asymmetric delivery of cyanide anion. Click for 3D model of transition state

Two transition states can be computed (ωB97XD/6-311G(d,p)/SCRF[dichloromethane], see DOI 10042/to-4927) and the S,S(S) diastereomer is found to be  1.35 kcal/mol lower in total free energy than the R,S(S) isomer. This agrees with the observed specificity. Again, a reason for the specificity needs identifying, and again we use  AIM.

AIM analysis for the asymmetric delivery of cyanide to an imine, S,S(S) form.

In the favoured diastereomer, a BCP or bond-critical-point (green arrow above) can be found connecting a hydrogen from an aryl group to the oxygen of the Al-OMe group  via a weak hydrogen bond (H…O distance 2.25Å). In the disfavoured form, this interaction vanishes, and is instead replaced by a repulsive close N=CH…C-aryl contact of 2.49Å (for which there is no  BCP, red arrow below).

Disfavoured transition state. R,S(S) form.

The take home message from these two posts is that quite unusual interactions may often be responsible for asymmetric induction in a stereospecific reaction, and that helpful clues to these interactions may well be derived from an AIM analysis. Indeed, anyone doing stereospecific synthesis in the lab should be familiar with these methods! You have to be a jack-of-all-trades nowadays to keep up!

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