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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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A historical detective story: 120 year old crystals

Wednesday, November 17th, 2010

In 1890, chemists had to work hard to find out what the structures of their molecules were, given they had no access to the plethora of modern techniques we are used to in 2010. For example, how could they be sure what the structure of naphthalene was? Well, two such chemists, William Henry Armstrong (1847-1937) and his student William Palmer Wynne (1861-1950; I might note that despite working with toxic chemicals for years, both made it to the ripe old age of ~90!) set out on an epic 11-year journey to synthesize all possible mono, di, tri and tetra-substituted naphthalenes. Tabulating how many isomers they could make (we will call them AW here) would establish beyond doubt the basic connectivity of the naphthalene ring system. This was in fact very important, since many industrial dyes were based on this ring system, and patents depended on getting it correct! Amazingly, their collection of naphthalenes survives to this day. With the passage of 120 years, we can go back and check their assignments. The catalogued collection (located at Imperial College) comprises 263 specimens. Here the focus is on just one, specimen number number 22, which bears an original label of trichloronaphthalene [2:3:1] and for which was claimed a melting point of 109.5°C. What caught our attention is that a search for this compound in modern databases (Reaxys if you are interested, what used to be called Beilstein) reveals the compound to have a melting point of ~84°C. So, are alarm bells ringing? Did AW make a big error? Were many of the patented dyes not what they seemed?

1,2,3-trichloronaphthalene

The story starts to get murky when Reaxys reports the earliest literature for this compound as being 1941 (DOI: 10.1039/JR9410000243), the authority being Wynne himself (now a sprightly 80). The collection of 263 specimens was thought to go back to the 1890s, so how could it contain a compound only made about 50 years later? Time to do an X-ray determination. Remarkably, the 120 year old crystals of specimen 22 were still in good shape, but the determined structure held an initial surprise. The compound was in fact 1,6,7-trichloronaphthalene, quite a different species from the label.

1,6,7-trichloronaphthalene

So, did AW get things badly wrong, and were all those patents based on these structures potentially invalid? A little more detective work using Reaxys reveals that the 1,6,7 isomer melts at 109.5°C, the same as reported by AW in 1890 (Chem. News J. Ind. Sci., 1890 , 61, p. 273). So how did the 1,6,7-compound come to be mistaken for a 1,2,3,-isomer? The culprit turns out to be one prime (‘).

1,6,7 = 2:3:1' Click for 3D

Updated (see comment) Click for 3D

The numbering system in 1890 was different from what it is now. Then, primes were used to distinguish the numbering on each ring. When the collection was catalogued (in the 1990s), the 1′ was mistaken for 1 (you can see the prime on the original label). AW were correct all along, and the patent owners for all those naphthalene dyes can rest easy.

Sample 22 from AW collection

What this teaches us is that crystallography on 120 year old organic compounds is perfectly viable. Indeed, can anyone else claim to have solved the structure of such an old compound? And that those old chemists knew what they were doing, despite not having any instrumentation to help them. Oh, and a final comment. Precious few collections of molecules made by the original scientists exist nowadays. Many a collection has literally been skipped because of health and safety concerns. The AW collection itself was rescued from oblivion by the narrowest of margins. And we have permanently lost the opportunity for any detective work of the type described above. You can see that I am very upset by this. Heritage conservation should not just be old buildings, paintings etc, but the chemical heritage collections as well.

Thanks to Andrew White for the crystal structures (of this and three other samples, but their stories are for another day).

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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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The weirdest bond of all? Laplacian isosurfaces for [1.1.1]Propellane.

Wednesday, July 21st, 2010

In this post, I will take a look at what must be the most extraordinary small molecule ever made (especially given that it is merely a hydrocarbon). Its peculiarity is the region indicated by the dashed line below. Is it a bond? If so, what kind, given that it would exist sandwiched between two inverted carbon atoms?

1.1.1 Propellane

One (of the many) methods which can be used to characterize bonds is the QTAIM procedure. This identifies the coordinates of stationary points in the electron density ρ(r) (at which point ∇ρ(r) = 0) and characterises them by the properties of the density Hessian at this point. At the coordinate of a so-called bond critical point or BCP, the density Hessian has two negative eigenvalues and one positive one. The sum, or trace of the eigenvalues of the density Hessian at this point, denoted as ∇2ρ(r), provides in this model a characteristic indicator of the type of bond, according to the following qualitative partitions:

  1. ρ(r) > 0, ∇2ρ(r) < 0; covalent
  2. ρ(r) ~0, ∇2ρ(r) > 0; ionic
  3. ρ(r) > 0, ∇2ρ(r) > 0; charge shift

The third category of bond was first characterised by Shaik, Hiberty and co. using valence-bond theory1 and they went on to propose [1.1.1] propellane (above, along with F2) as an exemplar of this type.2 Matching the conclusions drawn from VB theory was the value of the Laplacian. As defined above, for the central C-C bond, both ρ(r) and  ∇2ρ(r) have been calculated to be positive, supporting the identification of this interaction as having charge-shift character.3

The Laplacian represents one of those properties where quantum mechanics meets experiment, in that its value (and that of ρ(r) itself) can be measured by (accurate) X-ray techniques.4 This was recently accomplished for propellane,5 with the same conclusion that the Laplacian in the central C-C region has the significantly positive value of +0.42 au. The electron density ρ(r) at this point was measured as 0.194 au. Calculations5 at the B3LYP/6-311G(d,p) level report ρ(r) as ~0.19 and ∇2ρ(r) as +0.08 au. Whilst the former is in good agreement with experiment, the latter is calculated as rather smaller than expected. This was originally interpreted as indicating that the “the experimental bond path has a stronger curvature [in ρ(r)] than the theoretical” although more recent thoughts are that both experimental and theoretical uncertainty may account for the discrepancy.5,6 An experiment worth repeating?

A hitherto largely unexplored aspect of characterising a bond using the Laplacian is whether the value at the bond critical point is fully representative of the bond as a whole. The Laplacian is related to two components of the electronic energy by the Virial theorem;

2G(r) + V(r) = ∇2ρ(r)/4; H(r) = V(r) + G(r)

where G(r) is the kinetic energy density, V(r) is the potential energy density and H(r) the energy density. Charge-shift bonds exhibit a large value of the (repulsive) kinetic energy density, a consequence of which is that ∇2ρ(r) is more likely to be positive rather than negative. The relationships above hold not just for the specific coordinate of a bond critical point, but for all space. Accordingly, another way therefore of representing the Laplacian ∇2ρ(r) is to plot the function as an isosurface, including both the negative surface (for which |V(r)| > 2G(r)) and the positive surface [for which |V(r)| < 2G(r)].

Such an analysis is the purpose of this post, using wavefunctions evaluated at the CCSD/aug-cc-pvtz level (see DOI: 10042/to-5012). The values of ρ(r) and ∇2ρ(r) at the bcp for the central bond are 0.188 and +0.095 au, which compares well with previous calculations. The values for the wing C-C bonds are 0.242 and -0.491 respectively (and were measured5 as 0.26 and -0.48). Laplacian isosurfaces corresponding to ± 0.49 (the value at the wing C-C bcp), ± 0.47 and ± 0.2 (which reveals prominent regions of +ve values for the Laplacian) can be seen in the figures below (and can be obtained as rotatable images by clicking).


Laplacian isosurface contoured at ± 0.49

 –

Laplacian isosurface contoured at ± 0.47. Red = -ve, blue= +ve.

Laplacian isosurface contoured at ± 0.20

A significant feature is the isosurface at -0.47, which corresponds to the lowest contiguous Laplacian isovalued pathway connecting the two terminal carbon atoms (and which coincidentally is similar in magnitude to that reported5 as measured for these two atoms). Three such bent pathways of course connect the two carbon atoms. The energy density H(r) shows a minimum value of -0.21 au along any of these pathways. It is significantly less negative (-0.13) for the direct pathway taken along the axis of the C-C bond.

Energy density H(r) @-0.21

Energy density H(r) @-0.13

ELF isosurface @0.7

A useful comparison with this result is the ELF isosurface. This too is computed at the correlated CCSD/aug-cc-pVTZ using a new procedure recently described by Silvi.7 Contoured at an isosurface of +0.7, the ELF function is continuous between the two terminal atoms, much in the manner of Laplacian. Significantly, the ELF function at the bcp appears at the very much lower threshold value of 0.54, and forms a basin with a tiny integration for the electrons (0.1e). Since both methods provide a measure of the Pauli repulsions via the excess kinetic energy, the similarity of the Laplacian to the ELF function is probably not coincidental.

The issue then is whether a bond must be defined by the characteristics of the electron density distribution along the axis connecting that bond, or whether other, non-least-distance pathways can also be considered as being part of the bond.8 The former criterion defines a pathway involving a positive Laplacian (+0.095) and would be interpreted as indicating charge shift character for that bond. The latter involves three (longer) pathways for which the Laplacian is strongly -ve, and which would therefore per se imply more conventional covalent character for the interaction. Considered as a linear (straight) bond, it has charge shifted character; considered as three “banana” bonds, it may be covalent. Weird!

  1. Shaik, S.; Danovich, D.; Silvi, B.; Lauvergnat, D. L.; Hiberty, P. C., “Charge-Shift Bonding – A Class of Electron-Pair Bonds That
    Emerges from Valence Bond Theory and Is Supported by the Electron Localization Function Approach,” Chem. Eur. J., 2005,
    11, 6358-6371, DOI: 10.1002/chem.200500265 and references cited therein.
  2. W. Wu, J. Gu, J. Song, S. Shaik, and P. C. Hiberty, “The Inverted Bond in [1.1.1]Propellane is a Charge-Shift Bond,” Angew. Chem. Int. Ed., 2008,
    DOI: 10.1002/anie.200804965; 10.1002/cphc.200900633
  3. S. Shaik, D. Danovich, W. Wu & P. C. Hiberty, “Charge-shift bonding and its manifestations in chemistry”, Nature Chem, 2009, 1, 443-3439. DOI: 10.1038/nchem.327
  4. P. Coppens, “Charge Densities Come of Age”, Angew. Chemie Int. Ed., 2005, 44, 6810-6811. DOI: 10.1002/anie.200501734
  5. M. Messerschmidt, S. Scheins, L. Grubert, M. Pätzel, G. Szeimies, C. Paulmann, P. Luger. “Electron Density and Bonding at Inverted Carbon Atoms: An Experimental Study of a [1.1.1]Propellane Derivative, Angew. Chemie Int. Ed., 2005, 44, 3925-3928. DOI: 10.1002/anie.200500169
  6. L. Zhang, W. Wu, P. C. Hiberty, S. Shaik, “Topology of Electron Charge Density for Chemical Bonds from Valence Bond Theory: A Probe of Bonding Types”, Chem. Euro. J., 2009, 15, 2979-2989. DOI: 10.1002/chem.200802134
  7. F. Feixas , E. Matito, M. Duran, M. Solà and B. Silvi, submitted for publication. See also this abstract.
  8. See for example the work of R. F. Nalewajski

Rzepa, Henry S. The weirdest bond of all? Laplacian isosurfaces for [1.1.1]Propellane. 2010-07-21. URL:http://www.ch.ic.ac.uk/rzepa/blog/?p=2251. Accessed: 2010-07-21. (Archived by WebCite® at http://www.webcitation.org/5rOFp6EuM)

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Capturing penta-coordinate carbon! (Part 2).

Wednesday, September 23rd, 2009

In this follow-up to the previous post, I will try to address the question what is the nature of the bonds in penta-coordinate carbon?

This is a difficult question to answer with any precision, largely because our concept of a bond derives from trying to define what the properties of the electrons located in the region between any two specified atoms are. Such a local picture is somewhat at variance with the idea of electrons being delocalized across the entire molecule. Two procedures for analyzing the local electronic behaviour which we have been using recently are AIM (Atoms-in-Molecules) and ELF (the topology of the Electron localization function). There are many useful published articles which elaborate these concepts; if you want to read some of them, start at DOI 10.1021/ct8001915 and follow the cited articles.

Firstly, the AIM analysis of the system below, where X=cyclopentadienyl anion and Y=CN.

The Sn2 transition state

The Sn2 transition state

This is shown below. If you click on the image, you will see a rotatable version of this diagram. The coloured (red, yellow and green) dots represent so-called critical points in the curvature of the electron density function ρ(r). The red dots are known as bond critical points, or BCPs. These (almost) always are found along the line connecting two atoms which we tend to refer to as a bond. You will see two that have been circled in the diagram below, and these appear to show a bond connecting the central 5-coordinate carbon atom and a carbon of each of the cyclopentadienyl rings (which themselves are revealed as rings by the presence of a yellow dot). Indeed, that central carbon atom does seem to have five red dots radiating out along lines connecting it to five carbon atoms.

AIM analysis (red = bond critical points, yellow = ring, green = cage)

AIM analysis (red = bond critical points, yellow = ring, green = cage)

So is the case proven for pentavalent carbon? Well, no. Firstly, one has to inspect the value of ρ(r) at the circled red dot. This has a (calculated) value of 0.022 au and a calculated bond length of ~2.7Å. We need to calibrate this against a real system as reported in DOI: 10.1021/ja710423d (below):

Hexa-coordinate carbon

Hexa-coordinate carbon. Click for 3D model

Here, the electron density ρ(r) was actually measured using X-ray diffraction, and found to be ~0.017 for bond critical points found connecting the central carbon and each of the four oxygen atoms. The length of these “bonds” was measured as  ~2.7Å. The agreement with our frozen transition state is quite striking.

One can go a little further and inspect the (2nd) derivative of the electron density at the bond critical point, termed the Laplacian, or ∇2ρ, which tells what kind of “bond” one might have. The measured value of ∇2ρ for the system above was ~0.06 au, and the calculated value for our pentacoordinate system is 0.04 au, which again suggests we are dealing with a very similar interaction in both systems (one hypothetical and calculated, the other real and measured). The use of the term  interaction was deliberate.  It is less loaded than the term  bond. Thus the value of ρ(r) for an undisputed C-C single bond is around 0.28 au, around ten times higher than our putative bonds. Since we do not really wish to grace a ρ(r) value of 0.022 with the term decibond (or any other fraction of a single bond) perhaps it is best to call it just an interaction, and leave open the question of how strong that interaction is! So, despite the  AIM analysis  finding a bond critical point, we shall settle for interpreting that merely as an interaction, and not a bond!  Well, is an interaction (or come to that, a decibond) worthy of counting towards a coordination?  Perhaps!

So AIM can provide information about the curvature and density of the electrons in the region of a bond/interaction. But it does not provide any information about another simple question which the term bond implies. How many electrons might be involved? Ever since  G. N. Lewis coined the term two-electron bond in 1916,  we have become used to interpreting bonds in terms of simple (often integer) numbers of electrons.  A carbon-carbon single bond shares two electrons; a double bond four electrons, and so on. We use this concept all the time in the technique known  as arrow-pushing, which helps us delineate mechanisms of reactions. Might it be possible to  identify how many electrons are involved in bonds/interactions of the captured  SN2 species above? Enter the ELF technique. It would not be appropriate to delve into the theory of this method here; suffice to say that  (approximately), the  bond-critical-point of the  AIM analysis in this case would map to a disynaptic basin for ELF. Thus a two-electron single bond will reveal a disynaptic basin (the centroid of which approximately matches the position of the  AIM BCP), which can be integrated to approximately two electrons. Shown below are the centroids of the disynaptic basins calculated for our SN2 species:

ELF basins (purple dots) for the SN2 system

ELF basins (purple dots) for the SN2 system. Click for 3D model

The most striking difference with the AIM analysis is that that the central carbon is surrounded only by three, not five disynaptic basins. The BCPs found for the two di-axial interactions have no counterpart in synaptic basins. Of course, that does not mean that there are no electrons that can be integrated in that region, just that the curvature of the density in that region is not sufficiently well defined to define a bounded volume of space which can be clearly integrated. Perhaps that condition is what we might mean by a bond!

The three disynaptic basins that do surround the central carbon integrate to a total of 7.85 electrons, which is close enough to 8 for us to say that this carbon is NOT hypervalent!

So what is our final conclusion? The frozen SN2 species is not hypervalent. It could reasonably be said to be coordinated by three bonds, and two diaxial substituents that interact with the central carbon weakly. Perhaps rather than penta-coordinate, the central carbon could be described as pentacoordinaloid!

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A molecule with an identity crisis: Aromatic or anti-aromatic?

Monday, April 13th, 2009

In 1988, Wilke (DOI: 10.1002/anie.198801851) reported molecule 1

A [24] annulene. Click on image for model.

A 24-annulene. Click for 3D.


It was a highly unexpected outcome of a nickel-catalyzed reaction and was described as a 24-annulene with an unusual 3D shape. Little attention has been paid to this molecule since its original report, but the focus has now returned! The reason is that a 24- annulene belongs formally to a class of molecule with 4n (n=6) π-electrons, and which makes it antiaromatic according to the (extended) Hückel rule. This is a select class of molecule, of which the first two members are cyclobutadiene and cyclo-octatetraene. The first of these is exceptionally reactive and unstable and is the archetypal anti-aromatic molecule. The second is not actually unstable, but it is reactive and conventional wisdom has it that it avoids the undesirable antiaromaticity by adopting a highly non-planar tub shape and hence instead adopts reactive non-aromaticity. Both these examples have localized double bonds, a great contrast with the molecule which sandwiches them, cyclo-hexatriene (i.e. benzene). The reason for the resurgent interest is that a number of crystalline, apparently stable, antiaromatic molecules have recently been discovered, and ostensibly, molecule 1 belongs to this select class!

So is 1 actually anti-aromatic? Let us look at some of the ways in which this might be estimated.

  1. One can inspect the bond lengths, measured from X-ray analysis. The longest is 1.463Å, labelled a above, and it corresponds to a single bond (value from the crystal structure).
  2. If the molecule had a bond alternating structure, the adjacent bonds would be expected to be much shorter, in the region of 1.32Å. In fact, they are rather longer, at 1.37Å. Indeed, in the cycloheptatriene part of the molecule, the alternation is much less than one might expect of an anti-aromatic molecule, oscillating between 1.37 and 1.43Å.
  3. One can also inspect aromaticity via a variety of magnetic indices. The simplest of these is the NICS probe. Placed at a ring centroid, a negative value of this index of around -10ppm indicates aromaticity (this is the value for benzene), whilst a strongly positive value (of up to +20 ppm) indicates anti-aromaticity. Molecule 1 has two potential centroids, one placed at the absolute centre of the system, and one placed at the centroid of the ~6-membered ring completed using bond b (in reality, the centroids were computed from the positions of ring critical points obtained from an AIM analysis). The NICS values at these two positions are both ~-4.4 ppm (See DOI: 10042/to-2156 for details of the calculation). These values does not indicate antiaromaticity! They could even be described as mildly aromatic. So what is going on?
  4. What about the chemical shifts of the other protons? All the hydrogens attached to sp2 carbons are predicted to resonate at around 6.7ppm (unfortunately Wilke does not report the experimental spectrum), which is typical of an aromatic system (anti-aromatic systems have high upfield shifts for such protons, at around 2ppm or even -2 ppm, see DOI: 10.1021/ol703129z for examples). The two protons of the methylene bridges are also quite different; 2.9 and 0.8 ppm. The latter is the proton endo to the cycloheptatrienyl ring, and is typical of a proton placed in the anisotropic magnetic shielding region of e.g. benzene. Thus the cycloheptatrienyl ring is itself behaving as if it were aromatic, whereas the overarching 24-annulene ring is certainly not behaving as if it were antiaromatic.

One possible explanation involves a concept known as homoaromaticity. The bond marked as b could be regarded as completing the 6π-electron local aromaticity of that ring (it would be formally considered as a 1π-electron bond, with no underlying σ-framework, see 10.1021/ct8001915 for further detail). Well characterised examples of such neutral homoaromatics are in fact very rare indeed; the phenomenon is thought to manifest mostly through cationic homoaromatics (i.e. the homotropylium cation, see 10.1021/jo801022b for discussion). So has the case been made for 1 being the first clear cut example of a neutral homoaromatic molecule, containing no less than four rings exhibiting this type of aromaticity?

There is one further concept that can be introduced. Clar (for a discussion, see DOI: 10.1021/cr0300946) proposed that benzenoid 6π-electron local aromaticity is preferred to less local or more extended cyclic conjugations, if the two compete. Many examples in a type of compound known as polybenzenoid aromatics are known where the most favourable resonance structure is that which maximises the number of Clar rings. More recently, quite a few ostensibly antiaromatic molecules have been shown to attenuate this unfavourable effect by forming instead groups of aromatic Clar islands containing delocalized benzene like rings (discussion of this point can be found at DOI: 10.1039/b810147g). In molecule 1, we could have a new phenomenon; a homoClar ring, formed to avoid antiaromaticity.

For further discussion, see the comment posted to Steve Bachrach’s blog.

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How do molecules interact with each other?

Sunday, April 12th, 2009

Understanding how molecules interact (bind) with each other when in close proximity is essential in all areas of chemistry. One specific example of this need is for the molecule shown below.

The Pirkle reagent

The Pirkle reagent

This is the so-called Pirkle Reagent and is much used to help resolve the two enantiomers of a racemic mixture, particularly drug molecules. The reagent binds to each enantiomer of a racemic drug differently, and this difference can be exploited by using e.g. column chromatography to separate the two forms. The conventional wisdom is that such chiral recognition occurs via a three-point binding model. In other words, at least three different interactions must occur between the Pirkle reagent and the drug to allow such chiral recognition.

So how do we identify where these bindings might occur? A good place to start is to look at the self-binding of the Pirkle reagent, in other words, how does it interact with itself in the crystal state? An X-ray structure of the pure enantiomer of the Pirkle reagent shows that it binds with itself to form a loose dimer. We are now in a position to analyze exactly how this binding occurs. To do this, we are going to invoke a technique known as Atoms-in-molecules or AIM. This effectively looks at the curvature of the electron density in the dimer, and from the characteristics of this curvature, identifies a series of so called critical points, or regions where the first derivative of the electron density (referred to as ρ(r) ) with respect to the geometry is zero. These critical points come in four varieties only;

  1. A nuclear critical point, which almost exactly corresponds to where the nuclei are
  2. A bond critical point, which is the key to understanding not only where actual bonds are in the molecule, but also a range of weaker interactions which are conventionally not graced with the term bond, but which nevertheless can be essential in understanding how to molecules interact weakly with each other.
  3. The remaining two types of critical point relate to rings and cages, and we will not be concerned further with them here.

The electron density required for this analysis could in principle come from the X-ray measurements themselves, but it is not easy to acquire this to the required accuracy (although it can be done). In this case, it is easier (and probably no less accurate) to calculate the density from a DFT-based quantum mechanical calculation. The result of this is shown below.

Pirkle dimer. Click on image to obtain model

Pirkle dimer. Click for 3D.


The light blue spheres show the position of selected bond critical points or BCPs in the AIM analysis. So what do they tell us about how two molecules of Pirkle molecule interact with each other? Three different points labelled 1-3 are highlighted for discussion.

  1. Points 1 connect the hydrogen of the OH group with the carbons of the π-face of the anthracene ring (the left ring of the molecule as shown above). This is an unusual type of interaction known as a π-facial hydrogen bond, and it has only been recognized as such in the last 30 years. Note that this interaction is not restricted to occur just between a pair of atoms, but can involve more (in this case almost a whole benzene ring). By finding the value of the electron density ρ(r) at this BCP, one can estimate the energy of interaction resulting from its formation. In this case, ρ(r) ~ 0.014 au, and comparison with other types of hydrogen bond suggests that this value corresponds to an interaction energy of around 2.5 kcal/mol. This is a little weaker than a conventional OH…O hydrogen bond, but is still quite significant. Two of these interactions occur in this Pirkle dimer.
  2. Points 2 are equally unexpected. They connect the oxygen of the same OH group involved in the previous interaction, and one of the ring C-H groups. Again, that C-H…O groups can interact has only been recognized relatively recently. The value of ρ(r) of ~ 0.018 indicates a hydrogen bond strength of ~3 kcal/mol, again hardly insignificant.
  3. There are four specific interactions of the final type 3. These occur in the region of overlap of the two anthracene rings, and these are referred to as π-π stacking interactions. Again, the ρ(r) of ~ 0.005, calibrated against known systems, suggests that each is individually worth around 1 kcal/mol.

So adding up all eight interactions indicates that the two molecules of the Pirkle reagent have an interaction energy of around 15 kcal/mol resulting just from these weak bonds (there are other types of interactions between two molecules known as dispersion forces, which also contribute), and which together provide more than enough free energy to overcome the entropy required to bring the two molecules together.

Armed with tools such as AIM, one can now be more confident in analyzing the various terms that contribute to two molecules interacting with each other, and in the case of chiral molecules, how these interactions may result in chiral recognitions.

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