Posts Tagged ‘watoc11’

The inner secrets of an ion-pair: Isobornyl chloride rearrangements.

Sunday, May 29th, 2011

Observation of the slow racemization of isobornyl chloride in a polar solvent in 1923-24 by Meerwein led to the recognition that mechanistic interpretation is the key to understanding chemical reactivity. The hypothesis of ion pairs in which a chloride anion is partnered by a carbocation long ago entered the standard textbooks (see DOI 10.1021/ed800058c and 10.1021/jo100920e for background reading). But the intimate secrets of such ion-pairs are still perhaps not fully recognised. Here, to tease some of them them out, I use the NCI method, which has been the subject of several recent posts.

NCI analysis of the iod-pair transition state for methyl migration in isobornyl chloride. Click for 3D.

To remind, the colour coding of the NCI surface is blue=strongly attractive, red=strongly repulsive, green=weakly attractive, yellow=weakly repulsive. Shown above is the ion-pair transition state for [1,2]methyl migration. Note how the hydrogen bonds between the chloride anion and the water molecules are clearly blue. Only slightly weaker (with a turquoise tint) is a pair of hydrogen bonds between the oxygen atoms and H-C bonds in the isobornyl cation. Such C-H…O bonding in ion-pairs seems to be particularly important. There are other blue regions, between an H…H pair, and a C-H bond and the carbon of the migrating methyl group. Also noteworthy is that many atom pairs have multi-coloured NCI regions, suggesting the interaction is not homogenous, and can be both attractive AND repulsive between any pair of atoms.

The NCI plot below shows the competing 1,6-hydride shift in isobornyl chloride, again involving an ion-pair transition state.

NCI surfaces for the 1,6 hydride migration transition state in isobornyl chloride. Click for 3D.

Notice in this example how the migrating hydrogen supports an attractive hydrogen bond to the chloride anion (ostensibly between a hydride atom and an anionic chloride?), and again how there are a number of blue regions elsewhere.

Modelling is increasingly focusing on these weaker interactions, that probably mediate much (stereo)selectivity in organic reactions. How long before such approaches themselves enter the text-books?

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The inner secrets of the DNA structure.

Wednesday, May 18th, 2011

In earlier posts, I alluded to what might make DNA wind into a left or a right-handed helix. Here I switch the magnification of our structural microscope up a notch to take a look at some more inner secrets.

A fragment of a single chain of DNA, taken from a Z-helix. Click for 3D.

The 3D coordinates of this fragment were obtained by taking a crystal structure of a Z-d(CGCG)2 containing oligomer, editing (to remove water, and superfluous bases) and subjecting it to ωB97XD/6-311G(d,p)/SCRF=water geometry refinement. This should be accurate enough to recover dispersion attractions, and various electronic and electrostatic interactions. Z-d(CGCG)2 was then reduced to the fragment you see above, which is large enough to capture the essence of the Z-helical wind, but small enough to be able to spot things which a larger fragment might overwhelm.

  1. The 3D model (click on above to obtain it) reveals that the oxygen of one of the five-membered (tetrahydrofuran) rings has a close contact to the guanine base of 2.85Å. This is some 0.3Å shorter than the combined van der Waals radii, and very typical of oxygen…electrophilic carbon interactions (see discussion here for more details). We can reasonably assume its real. It is supported by a small NBO perturbation term (~1.1 kcal/mol) corresponding to donation of the oxygen lone pair into a C-N π* orbital.
  2. The next interaction detected comes from a furanose C-H bond, in which the hydrogen approaches to within 2.48Å of the oxygen on the furanose the other side of the phosphate. This is ~0.14Å shorter than the combined van der Waals distances (remember, even at the actual vdW sum, the attraction is still attractive). Why would an apparently inert C-H bond do that? Such bonds are not normally considered in such analyses. Well, this one is special.
  3. It may well be (slightly) more acidic than normal due to a C-Hσ/C-Oσ* anti-periplanar interaction (E2 5.8, magenta bonds in 3D model) into the CH2-OH bond of the furanose. Hence the acidified H can form a weak(ish) hydrogen bond to the oxygen. The NBO E2 energy is 1.4 from the Olp to the C-H* bond (larger E2 interactions normally occur through bonds, but this one is through space, which is why it is smaller).
  4. These two interactions in turn set up a good orientation for the guanine to create a strong anomeric effect between it and the ribose; NLp/C-Oσ*; E2 11.6 (violet bond in 3D model, blue bond b in above diagram). To calibrate this interaction, anomeric effects in sugars are of the order of 14-16 kcal/mol. These stereoelectronic effect helps to slightly rigidify the relationship between the guanine base and the furanose it is connected to.
  5. In contrast, the cytosine-furanose link avoids the classical anomeric effect, and instead sets up a weaker one with a C-C bond instead (E2 6.8, indigo bond, blue bond a in above diagram). The Nlp is not as good a donor, because it is sequestered into the adjacent carbonyl group on the cytosine. The guanine has no such adjacent group, and so its Nlp is a better donor. The outcome of all of this is that the two bases, C and G end up having a different geometrical relationship to the furanose they are each connected to.
  6. Notice the gauche-like conformation of the ethane-1,2-diol fragment (gold bond in 3D model), which is again due to stereoelectronic alignments.
  7. Notice the Nlp …H-C distance of 2.51Å, which like 2 above, is around the sum of the vdW radii. It might be slightly more than just a dispersion attraction, since the NBO E2 Nlp/C-H* through space interaction is ~2 kcal/mol.
  8. There are some other relatively close atom-atom approaches, but I do not list them here. Do explore them yourself (they are labelled 8 in the diagram below).

To complete the present analysis, I include an ELF diagram. This can locate lone-pairs (as monosynaptic basins) as well as bond pairs (disynaptic basins) and so is useful for visualising the anti-periplanar anomeric effects between a lone pair and a bond (connecting a mono and a disynaptic basin if you like). Some of the interactions described in the list above are shown below with dotted lines (note that some of the lone pairs appear as two basins, distributed either face of the aromatic base).

ELF analysis. Click for 3D.

Well, cranking up the magnification on a microscope will always reveal new details. You might ask if these new details matter? Well, since DNA is such a very long polymer, repeating even a very weak (but predictable) interaction millions of times is bound to have some sort of cumulative effect. Who knows which of the ones above might play an important role in the super-winding of DNA, or its packing into a cell, or interaction with proteins, and so on. I do wonder how many of the terms I have identified above have been previously considered for such roles. Anyone know?

Postscript: Shown below is a  non-covalent-analysis (NCI,  see earlier post). A reminder that the interaction surface is colour coded with orange or red tinge if repulsive, blue if attractive, and green for weaker interactions. These surfaces pretty much recapitulate what it itemised above, adding also other interactions not listed above (labelled 8 in diagram).

NCI analysis for Z-CG fragment. Click for 3D.

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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 thermodynamic energies of left and right handed DNA.

Saturday, March 5th, 2011

In this earlier post, I noted some aspects of the calculated structures of both Z- and B-DNA duplexes. These calculations involved optimising the positions of around 250-254 atoms, for d(CGCG)2 and d(ATAT)2, an undertaking which has taken about two months of computer time! The geometries are finally optimised to the point where 2nd derivatives can be calculated, and which reveal up to 756 all-positive force constants and 6 translations and rotations which are close to zero! This now lets one compute the thermodynamic relative energies using ωB97XD/6-31G(d) (for 2nd derivatives) and 6-31G(d,p) (for dispersion terms). All geometries are optimized using a continuum solvent field (water), and are calculated, without a counterion, as hexa-anions.

Relative thermodynamic energies (kcal mol-1) of DNA duplexes.
system Total energy (duplex) Dispersion term ΔΔH298 Δ(-T.ΔS298) ΔΔG298 duplex ΔG298 single chain ΔΔG298 (Duplex)
Z-CGCG 0.0 0.0 0.0 0.0 0.0 0.0 -60.3
B-CGCG 6.2 -4.2 8.0 3.9 11.9 +3.1 -54.7
Z-ATAT 0.0 0.0 0.0 0. 0.0 0.0 -44.9
B-ATAT -7.6 -12.8 -7.0 2.7 -4.3 -1.8 -45.7

Note how the CGCG duplex is more stable as a Z-helix, whilst the ATAT duplex prefers the B-helix. I will discuss the precise reasons for this elsewhere.

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Do electrons prefer to move in packs of 4, 6 or 8 during proton exchange in a calixarene?

Friday, January 7th, 2011

This story starts with a calixarene, a molecule (suitably adorned with substituents) frequently used as a host to entrap a guest and perchance make the guest do something interesting. Such a calixarene was at the heart of a recent story where an attempt was made to induce it to capture cyclobutadiene in its cavity.

The basic skeleton of a calixarene

At the base of the calixarene are four hydroxyl groups, arranged in either a left or right handed manner. The molecule, in other words is chiral (C4 symmetry to be precise). As a chiral molecule, it might trap left and right-handed guests in a slightly different manner (forming two possible diastereomeric host-guest complexes).  As it happens, the guest in the cyclobutadiene story was just such a chiral molecule. But an essential question to ask is what the barrier to enantiomerization of such a calixarene might be?  One can envisage several ways of accomplishing such a conversion.

Enantiomerization pathways for a chiral calixarene

All four hydrogens can be moved in a single step, one might move two at a time in two steps, or one might move one at a time in four steps. These processes would involve respectively 8, 6 or 4 electrons in each step. There is a fundamental difference between the first pathway and the last two;  the latter involve  ionic intermediates (zwitterions) whereas the first is neutral. As such one might imagine the process would depend on the ability of the solvent to stabilize any such zwitterion.

Let us start with a gas phase model (ωB97XD/6-311G(d,p)), and a transition state with one negative force constant is indeed found with  C4v symmetry. The free energy barrier ΔG† for the process is 14.0 kcal/mol, which means the reaction will occur rapidly, even at lower temperatures of  ~200K. A pack size of 8 seems preferred for this model. This is hardly a surprise since the formation of ionic intermediates would not be expected. One might however speculate thus. In the schematic above, n=1 and one might be tempted to ask if higher values of n (lets say  n=2, a pack size of 10, or n=3, a pack size of 12, etc ) might exhibit similar behaviour. Is there any limit to the ring/pack size for this type of proton exchange?

Transition state for enantiomerization of a calixarene in the gas phase. Click for 3D.

What about in solution? Well, let us apply the mildest of solvents, benzene as a so-called continuum field. This has a very low dielectric (2.3) and you might imagine it would have hardly any effect. Well click on the below. The C4v geometry now has three computed negative force constants; the two additional ones are shown below (they are degenerate with a wavenumber of 101i cm-1).

C4v symmetric geometry for calixarene in benzene solvent, with three negative force constants. Click for animation of E mode.

C4v geometry for calixarene in benzene. Click for animation of second E mode.

Each of these additional two negative force constants shows a displacement heading towards the zwitterion shown in the scheme below. As one increases the polarity of the solvent, so the force constant becomes more negative. Thus for dichloromethane, it is now 322i cm-1 and with water it is 376i cm-1

So now the question is what happens when either of the two additional negative force constants is followed downhill? Will it form a true zwitterion (which would have Cs symmetry), in which case it would be (two) 6 electron processes to enantiomerize the calixarene instead of one 8 electron one.

True transition state for proton exchange in solution phase calixarene

In fact this geometry of Cs symmetry, which does resemble the zwitterion shown in the scheme above, is NOT a minimum but a true transition state itself (the free energy barrier hardly changed from the value for the gas phase). So the answer seems to be that a calixarene enantiomerizes via transition state not of C4v but of Cs symmetry, and which resembles a zwitterion but is not actually one. The 8-packof electrons was tempted to take a short rest-break on their way to shifting the four protons, but in the end did it in a single journey! So we have an unusual zwitterionic but nevertheless concerted transition state for the process.

Still unresolved is whether such cyclic transfer of four protons between four oxygen atoms continues to be concerted for larger rings, or whether the system is finally tempted to break up the transfer by resting with one or more discrete intermediates along the way. I finally note that in the calixarene reported which catalysed the thoughts above, the four oxygens are capped with a guanidinium cation sitting just above them, and this too may have an interesting effect on the proton transfer process.

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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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Can a cyclobutadiene and carbon dioxide co-exist in a calixarene cavity?

Friday, November 19th, 2010

On 8th August this year, I posted on a fascinating article that had just appeared in Science (DOI: 10.1126/science.1188002), in which the crystal structure was reported of two small molecules, 1,3-dimethyl cyclobutadiene and carbon dioxide, entrapped together inside a calixarene cavity. Other journals (e.g. Nature Chemistry, DOI: 10.1038/nchem.823) ran the article as a research highlight (where the purpose is not a critical analysis but more of an alerting service). A colleague, David Scheschkewitz, pointed me to the article. We both independently analyzed different aspects, and first David, and then I then submitted separate articles for publication describing what we had found. Science today published both David’s thoughts (DOI:10.1126/science.1195752) and also those of another independent group, Igor Alabugin and colleagues (DOI: 10.1126/science.1196188). The original authors have in turn responded (DOI: 10.1126/science.1195846). My own article on the topic will appear very shortly (DOI: 10.1039/C0CC04023A). You can see quite a hornet’s nest has been stirred up!

At issue is whether the two bonds (indicated with arrows below) are best described as normally covalent, or very much weaker van der Waals contacts, or essentially non-interacting atoms. The last two interpretations would sustain the claim that 1,3-dimethyl cyclobutadiene and carbon dioxide can co-exist as separate species inside the cavity. The first would argue that they have reacted to form a different molecule. You can inspect the 3D coordinates by clicking on the diagram below.

Reported X-Ray structure. Click for 3D

Barboiu et al originally argued that these two bonds were strong van der Waals contacts, with C-C and C-O distances of 1.5 and 1.6Å respectively, and with a OCO angle of  120°. The various responses to this claim tend to the view that these distances/angles clearly represent new covalent (or partially ionic-covalent) bonds, and that the combined species cannot be described as 1,3-dimethyl cyclobutadiene and carbon dioxide. There is obviously much more to it than that (including a detailed analysis of the errors present in a partially disordered crystal structure). So make your own minds up based on the articles cited above and if it helps, the  original 3D coordinates, for your convenience made available above!

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Reactions in supramolecular cavities – trapping a cyclobutadiene: ! or ?

Sunday, August 8th, 2010

Cavities promote reactions, and they can also trap the products of reactions. Such (supramolecular) chemistry is used to provide models for how enzymes work, but it also allows un-natural reactions to be undertaken. A famous example is the preparation of P4 (see blog post here), an otherwise highly reactive species which, when trapped in the cavity is now sufficiently protected from the ravages of oxygen for its X-ray structure to be determined. A colleague recently alerted me to a just-published article by Legrand, van der Lee and Barboiu (DOI: 10.1126/science.1188002) who report the use of cavities to trap and stabilize the notoriously (self)reactive 1,3-dimethylcyclobutadiene (3/4 in the scheme below). Again sequestration by the host allowed an x-ray determination of  the captured species!

Scheme for production of 1,3-dimethylcyclobutadiene 3 and CO2.

The colleague tells me he has himself already penned an article on the topic and submitted this to a conventional journal. However, their rules decree that whilst it is being refereed, I could not discuss the article here, or indeed even name its author. Assuming his article is published, I will indeed reveal his identity, so that he gets the credit he deserves! Meanwhile, I will concentrate in this blog purely on two other aspects of this reaction which caught my own eye after he brought the article to my attention.

The reaction involves imobilising a precursor 1 in a crystalline calixarene network as shown above, and then in situ photolysis to form the Dewar lactone 2. Further photolysis then results in extrusion of carbon dioxide and the formation of 1,3-dimethyl cyclobutadiene 3 and CO2, both still trapped in the host crystals. Thus imobilised, here they both apparently remain (at 175K) for long enough for their X-ray structure to be determined. What attracted me to this chemistry was the potential of this reaction as a nice example of a Diels Alder reaction occuring in a cavity. The first example of such catalysis was reported by Endo, Koike, Sawaki, Hayashida, Masuda, and Aoyama (DOI: 10.1021/ja964198s) and I have used this in my lectures for many years. This latter example however illustrates the promotion of a cycloaddition, which inside a cavity is accelerated by a factor of ~105, rather than of the reverse cycloelimination. I explain this to students by invoking entropy. Normally, when two molecules react together, there is an entropic penalty, which can add 8 or more kcal/mol to the free energy of activation of a bimolecular reaction in the absence of the cavity.

Structure of entrapped 1,3-dimethylcyclobutadiene, obtained from the CIF file provided via DOI: 10.1126/science.1188002

By a strange coincidence, my name is also on a recently published article (DOI: 10.1021/ol9024259) with other colleagues on the use of (Lewis) acid catalysts to accelerate a type of reaction known as the Prins. This involves the addition of an alkene to a carbonyl group. Now as it happens, the reaction in the scheme above showing 4 → 2 happens to combine these features; it is both a Diels-Alder cycloaddition and also involves an alkene adding to a carbonyl compound! It is therefore noteworthy that the claimed reaction 1 → 2 → 3 + CO2 is done in the presence of a strong acid catalyst, the guanidinium cation 5, which is itself part of the structure of the calixarene-based host. It is represented as X in the scheme above, and can also be identified in the above 3D model via the light blue atoms.

There are however crucial differences between these two earlier examples I quoted and the reaction of 2 → 3; the latter is in fact a cycloelimination and not a (cyclo)addition. In other words, according to literature precedent, the guanidinium cation-based cavity should act to accelerate the reverse cycloaddition 4 → 2 rather than the forward cycloelimination. Since the isomerisation 3 → 4 is thought to be fast, the question arises: how rapid is the reverse reaction 4 → 2? In particular, is it slow enough to allow X-ray diffraction data to be collected for 3/4 over the necessary period of 24 hours or more? Legrand, van der Lee and Barboiu do not address this point in their article. Nor is there discussion there of how the cavity and the acid catalyst might influence the position of the equilbrium 2 → 3 + CO2.

This is where calculations can help. At the B3LYP/6-311G(d,p) level four different models were selected.

  1. Model A is a simple gas phase calculation for the singlet state, which reveals the free energy barrier for 4 → 2 is already quite modest for a Diels-Alder reaction (more typical values are ~22 kcal/mol), due no doubt to the instability/reactivity of the cyclobutadiene. However, at 175K, that would still be quite sufficient to prevent the reverse reaction from occurring to any extent over the period of X-ray data collection.
  2. Model B adds a condensed phase (water) to the model. This serves in part to simulate the condensed crystal environment (which is pretty ionic being a tetra ion-pair). The barrier drops to 12.1 kcal/mol.
  3. Adding one guanidinium cation to both these models (C and D) which simulate the Prins conditions, drops the barrier to 8.3 kcal/mol (model 4).
  4. You can inspect details of any of the calculations by clicking on the digital repository entry (shown as dr in the table), where full data is available.

None of these models includes the entropic effects of full constraint in a cavity (which I estimated above as capable of reducing the free energy barrier for reaction by ~8 or more kcal/mol). If this correction is applied to model D, it would reduce the barrier to ~0 kcal/mol! The calculations also reveal that the reverse reaction 4 → 2 is exothermic, and this exothermicity is enhanced by the acid catalyst 5. It would be further enhanced by reducing the entropy of reaction by pre-organizing the reactants in the cavity. The tendency must therefore be for 3/4 to revert to 2 on purely thermodyamic grounds, and only the presence of a significant kinetic barrier would allow them to exist as separate species. This barrier, as one might infer from the calculations shown in the table below, may not be a large one. Even a barrier of 8 kcal/mol might require cooling to significantly lower than 175K to render the reaction slow on a ~24 hour timescale.

Model ΔG‡4 → 2
kcal/mol		 ΔGreac 4 → 2 Singlet-triplet
separation
A. Gas phase,X=none dr ts 16.8 dr -3.5dr +5.7 dr
B. Continuum solvent (water),X=none dr ts 12.1dr -6.0 dr +7.7 dr
C. Gas phase,X=guanidinium+ dr ts 6.1 dr -19.5dr +2.1dr
D. Continuum solvent (water),X=guanidinium+ dr ts 8.3 dr -10.1 dr +7.7 dr

So I end my own speculations here on the nature of the reaction reported by Legrand, van der Lee and Barboiu by asking: are the products they claim (1,3-dimethylcyclobutadiene and carbon dioxide) capable of existing as separate species for long enough inside their cavity, even at 175K, to allow for the collection of X-ray data for a structure determination?

I tend to think probably not (? rather than !). But do decide for yourselves.

Archived as http://www.webcitation.org/5rpkn2Z5S on 08/08/2010. See also this post.

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Non-covalent interactions (NCI): revisiting Pirkle

Thursday, July 15th, 2010

NCI (non-covalent interactions) is the name of a fascinating new technique for identifying exactly these. Published recently by Johnson, Keinan, Mori-Snchez, Contreras-Garca, Cohen and Yang, it came to my attention at a conference to celebrate the 20th birthday of ELF when Julia Contreras-Garcia talked about the procedure. It is one of those methods which may seem as if it merely teases out the obvious about a molecule, but it is surprising how difficult seeing the obvious can be sometimes. I have blogged about this previously, in discussing the so-called Pirkle reagent. On that occasion, I used the QTAIM technique to identify so-called critical points in the electron density. NCI goes one stage further in identifying surfaces of interaction rather than just single points, the idea being that this focuses attention on regions in molecules which are primarily responsible for binding, stereoselection and other aspects of molecular selectivity.

The Pirkle reagent

The Pirkle reagent

So I was intrigued as to whether the NCI method might find something that my analysis using the QTAIM procedure might have missed. The required program is available for download. I will not go into the theory behind the program, but like AIM, it uses the properties of the electron density via a combination of the first and second derivatives to concentrate on the non-bonded or weakly interacting regions of a molecule.

NCI interactions in the Pirkle reagent

The results of the analysis (using the SCF option in the program, and a B3LYP/6-31G calculation) are displayed using VMD, and I cannot pull my usual trick of displaying the surface within the page of a blog via Jmol (although it seems Jmol with some effort could probably be persuaded to also render the information). So the above cannot be rotated. I have therefore circled one (there are others) interesting region in red. This encloses two surfaces. I should explain the colour coding adopted by the program. Red would be a repulsive interaction, and blue attractive. Weak interactions are shown in green. In the diagram above, these include the π-π stacking and various hydrogen bonds. But concentrating on the two surfaces inside the red circle, one occurs between the two hydrogens shown below. It catches the eye because there is a blue-tinge to the colour coding! This might mean it is a bit stronger than just “weak”.

A Weak interaction in the Pirkle reagent

The NCI method I do not think is meant to provide a definitive answer to the question; is that interaction real/strong? It serves, as I noted earlier, to spike interest. Here, it does that, since this particular interaction had indeed never previously been identified for attention (the obvious had been missed!). Highlighting such potential regions of a molecule and perhaps then helping in the design of experiments to test if the interactions are real is what the NCI program is meant to do (IMHO)!

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Chemical intimacy: Ion pairs in carbocations

Monday, January 11th, 2010

The scheme below illustrates one of the iconic reactions in organic chemistry. It is a modern representation of Meerwein’s famous experiment from which he inferred a carbocation intermediate, deduced from studying the rate of enantiomerization of isobornyl chloride when treated with the Lewis acid SnCl4.

The isomerisation of iso-bornyl chloride

Meerwein himself suggested (in effect, since he lacked the modern terminology used here) that the reaction proceeded via a hydride shift 3, which was acting as the mirror in reflecting 1 onto 1‘. A few years later, isotopic labelling studies demonstrated that another pathway occurs, at more or less the same rate. This alternative proceeds via a series of [1,2] carbon shifts, with the mirror now being 8 rather than 3. I have documented the story in detail in an article that will shortly appear in the J. Chemical Education (DOI: 10.1021/ed800058c). There, calculations reveal that the two transition states, 3 and 8 (which the experiments above suggest should be almost equal in energy) in fact differed by ~8 kcal/mol in favour of the latter for a gas-phase model which does not include the counterion. These calculations were done at a level (B3LYP/cc-pVQZ) which indicates that 8 kcal/mol represents a real discrepancy not so much in the calculation as in the model used for that calculation. I suggested that perhaps the discrepancy might be due to tunneling effects in the hydride transfer reaction, accelerating that pathway compared to methyl transfer.

What was missing from that particular model was the counter-ion, which is supposed to form an intimate ion-pair with the carbocation in moderately polar solvents. How much does the presence of such an object perturb the transition states?  To find out, we need calculate such systems (which by definition have very large dipole moments) with inclusion of solvation corrections. Now that new algorithms for computing transition states with solvation have made this a routine calculation, I can report an update to these results. This was done at the B3LYP/cc-pVTZ (aug-cc-pVTZ-pp for the Sn) level, using dichloromethane as a continuum solvent. Without the SnCl5 counterion, 3 and 8 differ by 5.4 kcal/mol in free energy (this difference now includes all the solvation free energy terms), and in the presence of the counter-ion this remains unchanged at 5.4 kcal/mol (see DOIs 10042/to-3668 and 10042/to-3667 without SnCl5 and 10042/to-3670 and 10042/to-3665 with). The free energy of activation with SnCl5 (see DOI: 10042/to-3695 for starting material) is 16.6 kcal/mol (for the [2,6] H shift) and 11.2 kcal/mol (for the  [1,2] Me shift), which indicates a facile room temperature reaction (as indeed is the case).

TS H-transfer. Click for animation

TS 1,2 Methyl shift. Click for animation

What are the implications for this result?

  1. Modelling an (intimate) ion-pair is different from that of covalent compounds in one respect. Whereas the geometry at covalent atoms is very well established and largely predictable, ion-pairs are potentially much more flexible. In other words, it is nowhere near as obvious where to place the counter-ion. In the above diagrams, the SnCl5 is located at a reasonable position, but there are other positions where it could be. Although what is shown is an energy optimized structure, a full search of all the possible positions that the SnCl5 could adopt has not been undertaken, and the possibility must remain that another pose of the ion might be lower in energy, for either of the two transition states. Indeed, if it turns out there are many positions for the ion of very similar in energy, then the entropy of the system would have to be corrected for these microstates.
  2. Nevertheless, one can draw insight from the two structures shown above (click to animate the transition mode). The counter-ion for the hydride transfer does approach the transferring hydrogen quite closely, and does appear to establish a H-bond between two hydrogens and one chlorine. This would stabilize that structure relative to the methyl shift transition state, where such hydrogen bonds do not appear to form. In this case  however, these interactions do not change the relative stabilties.
  3. These ion-pairs do have very large dipole moments (~23D for 3, ~27D for 8), which suggests that the result might in fact be sensitive to the nature of the solvent (and presumably the counter-ion itself).

Many reactions do take place in which intimate ion-pairs are formed (including a fair number of catalytic systems involving metals). We cannot generalise from the result above, but it may well be that the perturbation induced by such counter-ion may play significant roles in deciding selectivities. I would venture to suggest that increasingly modelling such as reported here will play a significant role in establishing mechanisms accounting for the selectivity of catalytic reactions.

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