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An unusually small (doubly) aromatic molecule: C4.

Tuesday, March 15th, 2022

When you talk π-aromaticity, benzene is the first molecule that springs to mind. But there are smaller molecules that can carry this property; cyclopropenylidene (five atoms) is the smallest in terms of atom count I could think of until now, apart that is from H3+ which is the smallest possible molecule that carries σ-aromaticity. So here I have found what I think is an even smaller aromatic molecule containing only four carbon atoms. And it is not only π-aromatic but σ-aromatic.

Let me go through the analysis (using a CCSD(T)/Def2-TZVPPD calculation, DOI: 10.14469/hpc/10226).

  1. Four carbons contain 16 valence electrons for bonding.
  2. Eight of these are conventional, forming four C-C single bonds around the 4-ring.
  3. Eight are left over, and these partition into a set of six and a set of two.
  4. The set of two are in p-π atomic orbitals and form a 4n+2 (n=0) aromatic system
  5. The set of six are in σ-sp AOs and form a 4n+2 (n=1) aromatic system.
  6. The three σ-MOs all contribute to the central C-C bond, particularly σ3 and σ2 in different ways.
  7. σ2 also reminds of [1.1.1]-propellane, where the two σ-electrons are in effect external to the central C-C bond, but spin coupled to form what might be called a σ exo-bond. There is also similarity to the exo bond in C2.
  8. The dissociation energy of the central bond can be estimated at 28 kcal/mol from the triplet state energy.
Bonding MOs for C4.
Click image to load 3D model
π1
σ3 σ2
σ1

So this little molecule carries a lot of diversity in its chemical bonding; an ideal candidate perhaps for a tutorial in bonding theory of organic molecules?

The post has DOI: 10.14469/hpc/10252

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First came Molnupiravir – now there is Paxlovid as a SARS-CoV-2 protease inhibitor. An NCI analysis of the ligand.

Saturday, November 13th, 2021

Earlier this year, Molnupiravir hit the headlines as a promising antiviral drug. This is now followed by Paxlovid, which is the first small molecule to be aimed by design at the SAR-CoV-2 protein and which is reported as reducing greatly the risk of hospitalization or death when given within three days of symptoms appearing in high risk patients.

The Wikipedia page (first created in 2021) will display a pretty good JSmol 3D model of this; the coordinates being generated automatically on the fly from a SMILES string, which specifies only what atoms are connected in the structure by bonds. Given that the structure of this molecule as embedded in the SARS-CoV-2 main protease[1] has been determined (and can be viewed here), I thought I might display those coordinates as an alternative to the Wikipedia/JSmol generated structure.

Click to get 3D model

I extracted the ligand from the PDF file and then added hydrogens manually to obtain the above result.‡ There are two noteworthy points about these representations:

  1. A mystery concerns the nominal C≡N group on the top right, which displays an angle at the carbon of 117°. A cyano group is of course linear (180°). This is not a defect of the crystal structure determination, but an indication of a rather stronger interaction occurring (as indeed noted[1]). The distance between the carbon of the cyano group and an adjacent sulfur is 1.814Å, which indicates a covalent bond has formed to the cyano group. The nitrogen of the erstwhile cyano group is 3.013Å away from an adjacent NH group, which suggests it is stabilised by a hydrogen bond.
  2. Crystal structure searching of units with S…C…N in which the N has only one bond reveals zero hits, but searches of S…C…NH reveal nine hits, with S…C distances in the range 1.74 – 1.80Å and C…N distances in the region 1.25-1.27&Aring. The reported CN distance is 1.251&ARing, confirming that when bound to the protein, the cyano group is replaced by an S-C=NH group and hence is clearly an important component of the mode of action of Paxlovid.
  3. The conformation of Paxlovid is in one respect not fully represented by the Wikipedia diagram, as shown below. This implies the t-butyl group (on the left) as being well separated from the pyrrolidinone ring system at the right of the molecule.

    In fact the two groups are adjacent, being held in that conformation by probably a combination of weak dispersion forces and a contribution from the surrounding protein in the crystal structure. This is more graphically shown by the NCI (non-covalent-interaction) diagram below (DOI: 10.14469/hpc/9964), where the green areas in the region between the two groups (ringed in red) represent stabilising interactions between them. You might also spot other green/cyan regions indicating additional weak hydrogen bonds between C-H groups and oxygen!

PAXLOVID NCI analysis

There are only a small number of crystal structures of small molecules containing the S-C=NH motif. I will try to find out how common this is in protein-ligand structures.

‡ There are many tools for performing this operation. I used the following procedure. I downloaded the PDB file (https://files.rcsb.org/download/7vh8.cif), opened it in CSD Mercury, selected the ligand (by identifying the CF3 group and clicking on one atom), inverted the selection so that everything but the ligand was then selected and using edit/structure, I deleted the selected atoms, leaving only the ligand.

Postsript

The cyanopyrrolidine group such as in Paxlovid is well known as a specific probe.[2],[3],[4] CovalentInDB is a comprehensive database facilitating the discovery of such covalent inhibitors[5] and is available here. There is also a program called DataWarrior that is potentially able to find such probes.

References

  1. Y. Zhao, C. Fang, Q. Zhang, R. Zhang, X. Zhao, Y. Duan, H. Wang, Y. Zhu, L. Feng, J. Zhao, M. Shao, X. Yang, L. Zhang, C. Peng, K. Yang, D. Ma, Z. Rao, and H. Yang, "Crystal structure of SARS-CoV-2 main protease in complex with protease inhibitor PF-07321332", Protein & Cell, vol. 13, pp. 689-693, 2021. https://doi.org/10.1007/s13238-021-00883-2
  2. N. Panyain, A. Godinat, A.R. Thawani, S. Lachiondo-Ortega, K. Mason, S. Elkhalifa, L.M. Smith, J.A. Harrigan, and E.W. Tate, "Activity-based protein profiling reveals deubiquitinase and aldehyde dehydrogenase targets of a cyanopyrrolidine probe", RSC Medicinal Chemistry, vol. 12, pp. 1935-1943, 2021. https://doi.org/10.1039/d1md00218j
  3. N. Panyain, A. Godinat, T. Lanyon-Hogg, S. Lachiondo-Ortega, E.J. Will, C. Soudy, M. Mondal, K. Mason, S. Elkhalifa, L.M. Smith, J.A. Harrigan, and E.W. Tate, "Discovery of a Potent and Selective Covalent Inhibitor and Activity-Based Probe for the Deubiquitylating Enzyme UCHL1, with Antifibrotic Activity", Journal of the American Chemical Society, vol. 142, pp. 12020-12026, 2020. https://doi.org/10.1021/jacs.0c04527
  4. C. Bashore, P. Jaishankar, N.J. Skelton, J. Fuhrmann, B.R. Hearn, P.S. Liu, A.R. Renslo, and E.C. Dueber, "Cyanopyrrolidine Inhibitors of Ubiquitin Specific Protease 7 Mediate Desulfhydration of the Active-Site Cysteine", ACS Chemical Biology, vol. 15, pp. 1392-1400, 2020. https://doi.org/10.1021/acschembio.0c00031
  5. H. Du, J. Gao, G. Weng, J. Ding, X. Chai, J. Pang, Y. Kang, D. Li, D. Cao, and T. Hou, "CovalentInDB: a comprehensive database facilitating the discovery of covalent inhibitors", Nucleic Acids Research, vol. 49, pp. D1122-D1129, 2020. https://doi.org/10.1093/nar/gkaa876

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The chemistry of scents: Vetifer oil.

Sunday, February 28th, 2021

I have occasionally covered the topic of colours here, such as those of flowers and minerals, since it is at least possible to illustrate these using photographs or colour charts to illustrate the theme. But when Derek Lowe took a break from his remarkable coverage of the COVID pandemic to highlight a recent article on the active smelling principle in Vetifer oil[1] I could not resist adding a tiny amount to his must-read story.

It would be great to illustrate this with an example of the scent, but digital scent technology has not yet taken off to the point of delivering these to the home.‡  So we will have to make do with a 3D model of the most active ingredient in Vetifer oil, which is species 10 in the scheme below[1]

But first a bit of history. I wrote about one of my chemical heroes William Perkin, whose factory first produced synthetic dyes in quantities that reduced the cost of colourful fabrics♥ to the point of affordability by most people. Less well known is that when he retired from running his factory, he devoted much of the rest of his life to experimenting in his home laboratory, where he discovered a simple and cheap synthesis of coumarin. This substance is an essential component of the so-called fougère genre of perfume and as with his discovery of synthetic dyes, the introduction of synthetic coumarin was to revolutionise the scent industry (although in this case, for other reasons, synthetic components did not reduce the price of perfumes as much as they did that of colourful clothes).

If you read Derek’s blog on the topic and peruse the diagram above, you will appreciate that Vetifer grass is the source of many essential oils and forms the basis of more than ⅓ of all fragrances. So, like Perkin, to have a synthesis of the most odiferous component, species 10 above, is a major breakthrough and one can only wonder whether new entirely synthetic variants might produce entirely new perfumes! As with flowers, changing a methyl group here or a stereochemistry there can have profound effects on the resulting properties!

2-epi-ziza-6(13)-en-3-one. Click for 3D model

The absolute configuration of 10 is not in doubt in any way, but it was done indirectly via another compound. As as an additional check (and because it is very quick to do) I add here the calculated optical rotation (at 589nm; a ωB97XD/Def2-TZVPP/SCRF=chloroform calculation) as being +106°. The measured value is +132° which is considered reasonably good agreement and certainly confirms the absolute configuration. For good measure, the calculated 13C spectrum (mpw1pw91/aug-cc-pVDZ/SCRF=choroform calculation) also matches that reported (For FAIR data of this analysis, see 10.14469/hpc/7965).

So as I noted, its a shame that the scent of 10 cannot be delivered here. But perhaps there would be health and safety issues if that were to be possible!

‡Around 1993 I was interested in how information about digital scents might be delivered to computers using the Media (or MIME) standard and went as far as informally proposing it be added to the seven existing primary Media types. Rather too tongue-in-cheek I fear, and as far as I know, no olefactory media type has been added to this day! However, an article relating to all of this has recently appeared.[2] ♥ The John Bright collection illustrates the colourful aspects of clothes over the ages. Colours were not absent during e.g. the Victorian era as the collection shows, but one may presume that they were also not affordable by most of the population. In the same manner that in earlier times, eg Tyrian Purple was available only to Roman Emperors and other elites.

References

  1. J. Ouyang, H. Bae, S. Jordi, Q.M. Dao, S. Dossenbach, S. Dehn, J.B. Lingnau, C. Kanta De, P. Kraft, and B. List, "The Smelling Principle of Vetiver Oil, Unveiled by Chemical Synthesis", Angewandte Chemie International Edition, vol. 60, pp. 5666-5672, 2021. https://doi.org/10.1002/anie.202014609
  2. A.B. Wiltschko, "Building an interdisciplinary team set on bringing the sense of smell to computers", iScience, vol. 24, pp. 102136, 2021. https://doi.org/10.1016/j.isci.2021.102136

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Question for the day – Einstein, special relativity and atomic weights.

Saturday, July 25th, 2020

Sometimes a (scientific) thought just pops into one’s mind. Most are probably best not shared with anyone, but since its the summer silly season, I thought I might with this one.

Famously, according to Einstein, m  = E/c^^2, the equivalence of energy to mass. Consider a typical exoenergic chemical reaction:

 A → B, ΔG -100 kJ/mol.  

According to the above, the molecule looses 100 kJ ≡ 1.112650056053618e-18 g after transformation from A to  B. Not much, but possibly measurable using today’s very best technology.

Now for the questions that might arise.

  1. What sort of energy applies above?  If its a free energy, then thermal (zero point and entropic vibrational) energy must clearly contribute. Or is it total energy without thermal and entropic contributions? 
  2. Is the mass loss distributed equally amongst all the atoms. In other words, how much mass does any particular atom lose after reaction or is this question meaningless?
  3. Since clearly the atoms must each lose some mass, that must mean that their atomic weight is a function of the energy content of the molecule they are part of.  A molecule with a lot of internal energy (lets say octanitrocubane, which decomposes to carbon dioxide and nitrogen) must have heavier atoms in the form of cubane than as nitrogen gas.
  4. And to recapitulate the question above, how many orders of magnitude away (if any) might we be from being able to measure this? Or, one can repose this question by asking whether one can measure the mass lost by a battery after discharging?

As with most spontaneous questions, the answers are probably all out there somewhere. Just a matter of finding them!

Here is a real-world example. At the large hadron collider at CERN, about 1011 protons are accelerated to almost the speed of light. During this process, they acquire a mass approaching kgs (I do not recollect the exact value). It certainly is a surprisingly large mass! And it is a surprisingly large amount of energy that has to be injected to achieve this. And when the beam is quenched, that mass is very quickly lost (and a lot of heat is generated in the quenching tunnel).

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A tourist trip around London Overground with a chemical theme.

Saturday, August 29th, 2015

Most visitors to London use the famous underground trains (the “tube”) or a double-decker bus to see the city (one can also use rivers and canals). So I thought, during the tourism month of August, I would show you an alternative overground circumnavigation of the city using the metaphor of benzene.

Benzene you see is a ring, comprising three “HCCH” segments. The so-called Kekule vibration in benzene  (the b2u mode for anyone interested) induces three pairs of carbon atoms to repeatedly travel towards each other and then reverse and travel away from each other. One can also travel in this manner using the London Overground train system. The three segments connect Clapham Junction (yes, more or less the same Clapham of Kekule’s omnibus) to Willesden Junction.  A second segment goes from there to  Highbury and Islington, and a third from there on to Clapham again to complete the cycle in the clockwise direction. Since trains travel in both directions on each of the three segments, one can (like a carbon atom) oscillate to and fro in any segment, or (like an electron) circulate all the way round (no doubt either diatropic or paratropically with respect to the earth’s magnetic field). Yes, the metaphors are rather contrived; sorry but it is August after all. 

Here are some photos. The first is along the Clapham/Willesden Junctions section, showing the new chemistry building at Imperial College in the early stages of construction. This will be part of the new White City campus about 5km west of the  original South Kensington one. The completed buildings on the right are residences, and the whole site used to be where BBC Enterprises first marketed its productions worldwide and not far from where the BBC television studios broadcast from until recently.

Scheme

This is at Clapham junction itself, platform 1 of 18.

Scheme

This is also along this segment (Imperial’s very own station :-). Way out indeed!

Scheme

And the Thames finally, looking east. On the left is the very exclusive Chelsea harbour apartment complex, some of the most expensive in London. Residents commute by boat rather than train. In the distance somewhere are London and  Tower bridges.

Scheme

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A congruence of concepts: conformations, configurations, amides and enzymes

Sunday, February 9th, 2014

This is the time of year when I deliver two back-2-back lecture courses, and yes I do update and revise the content! I am always on the look-out for nice new examples that illustrate how concepts and patterns in chemistry can be joined up to tell a good story. My attention is currently on conformational analysis; and here is an interesting new story to tell about it.

atrop

Above is a seven-membered ring benzolactam[1]‡, and it caught my eye because of the number of concepts (the semantic density if you like) contained in its chemistry.

  1. The title contains the phrase amide-based axial chirality
  2. and active
  3. conformation
  4. recognised by enzymes and receptors

All the above also implies:

  1. chirality is associated with configurations, whilst conformation is associated with isomerism about single bonds
  2. when conformational analysis is transplanted into a cyclic ring, it can morph magnificently into the land of configuration, via a process known as atropisomerism.
  3. Amides themselves sit in the land between conformation and configuration. Pauling famously used this transition to help devise his helical structures for peptides by deducing that the apparent single N-C bond in an amide (= conformation?) is actually a partial double bond by resonance (= configuration).
  4. The difference between a conformation and a configuration is simply kinetics. An approximate guideline is that if a particular pose in a system is prevented from exchanging with another pose by a half life of at least 1000 seconds, it is classified as a configuration, and if its half-life is less it is a conformation.
  5. Of course enzymes and receptors recognise individual configurations, and hence respond differently. Again the vexed issue of lifetime rears its head. Thus the configuration of thalidomide turned out to have a very short half-life, and so in vivo, the enzymes were exposed to both configurations (one of which turned out to be toxic).

The enantiomeric equilibrium shown above for the benzolactam in fact qualifies as that for configurations, since both enantiomers can be isolated (their half-life is clearly > 1000s) and separately tested for recognition by enzymes.

How can I add any value to the above chemistry? Well, I decided to perform a search of the crystal structure database, and I added two geometric parameters;

  1. The torsion about the 2-3 bond (1-2-3-4)
  2. the torsion about the 3-5 bond (4-3-5-7).

The sign of the first is critical, since the two possible atropisomers have opposite torsion angles. The value of the second relates to Pauling’s assertion that rotation about the amide bond is indeed restricted to two values, either 0 or 180°. So these two concisely blend atropisomerism and configuration. I start with a search of the above system using just the first torsion angle. It shows a nice clustering into those with strongly -ve and those with strongly +ve values; configurational atropisomers! Of course, it does not tell us what the barrier to interconvert them is; that has to be measured (or calculated) separately.

7-ring-amides

Next, I am showing a 2D map of both torsion angles. This shows again the first distribution, but reminds us that the torsion 4-3-5-6 stays resolutely at ~0 for all the compounds (the amide in other words is planar). 7-ring-amides-heat

Oh, a practical point. I mentioned a calculation could be done to estimate the barrier to enantiomerising the two atropisomers. This takes hours, and days if the transition state is awkward (and atropisomers can be so). But the above plots literally took perhaps 2 minutes each! Very cheap insight!

‡Note the use of the word conformation in its title. It could equally validly be configuration! Which is better?

References

  1. H. Tabata, "Chemistry of Amide-based Axial Chirality: Elucidation of the Active Conformation Recognized by Enzymes and Receptors", YAKUGAKU ZASSHI, vol. 133, pp. 857-866, 2013. https://doi.org/10.1248/yakushi.13-00169

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A curly-arrow pushing manual

Wednesday, December 4th, 2013

I have several times used arrow pushing on these blogs. But since the rules for this convention appear to be largely informal, and there appears to be no definitive statement of them, I thought I would try to produce this for our students. This effort is here shared on my blog. It is what I refer to as the standard version; an advanced version is in preparation. Such formality might come as a surprise to some; arrow-pushing is often regarded as far too approximate to succumb to any definition, although it is of course often examined.

  • How the conventions arose
    1. These were established largely by textbook authors. The first with a noticeably modern look was Hunter (1934). Here he is explaining using his notation why an ester group is meta-directing towards aromatic electrophilic substitution. The convention of the time was to represent benzene as a simple hexagon, without the additional bonds
      180px-Hunter
    2. Gould in 1959 (“Mechanism and structure in organic chemistry”, reviewed[1] adopted a clearly modern form. In this example, we have a curly arrow starting at the mid-point of a C-H (hydride) bond, and ending at the nucleus of (an electrophilic) carbon atom. His arrows also start at lone pairs rather than negative charges, but at some stage the convention has evolved to dispense with the : indicating a lone pair, and to start the arrow at the charge instead.300px-Gould
    3. Sykes (“A guidebook to mechanism in organic chemistry” in 1961, reviewed [2] is very similar to Gould, but in his example he shows a nitrogen lone pair heading towards the mid-point of a N-N forming bond, rather than ending at the nucleus of the (electrophilic) nitrogen atom as Gould would have done. Nowadays, we clarify Sykes convention a bit further by adding a dotted line to the forming bond so that the arrow can both start and end on either a lone pair or a line. This dotted line is distinct from dotted or dashed lines used to represent resonance.300px-Sykes
  • The rules :This set can be referred to as following the Sykes convention, and its main points are summarised here:
    1. There are two main types of mechanistic arrows, linear and cyclic (there is a very rare third type[3]. The former have a one clear start and end, the latter can circulate in two directions (clockwise or anticlockwise).
      1. Some reactions may involve using a combination of linear and cyclic arrows (for example the bromination of an alkene or alkene epoxidation by peracid).
    2. The most common mechanism (non-radical) involves just a single arrow either originating or ending at a bond/atom. Normally, no pair of atoms undergo a bond order change between them of more than one.
      1. There are rare exceptions involving two, or even three arrows starting or ending at a bond). The bond order for these can involve changes of 2 or even 3.
    3. Arrows will start at a centre with readily released electrons (nucleophilic for linear reactions). Types of readily released (nucleophilic or nucleus seeking) electron pairs are:
      1. Lone pairs ( : ) associated with an atom. Here, the order of nucleophilicity is C > N > O > F for the first row. The arrow by convention starts at the :.
      2. Bonds. We have to take into account the type of bond.
        1. σ-bonds. Such electron pairs are relatively non-nucleophilic (the s-character of the bond orbital is high) and so only bonds to less electronegative elements can release electrons. Thus a B-H bond can release an electron pair more readily than a C-H bond (in both cases this is called a hydride transfer). Another type of σ-bond which can more easily release electrons is that of cyclopropane (largely because the degree of s-character is lower than a normal σ-bond).
        2. π-bonds. Because these involve only p-AOs (no s-character) they can release electrons relatively easily. Again, this release is easier with less electronegative elements; (B=B) > C=C > C=N > C=O.
        3. δ-bonds, as found in high-bond order metal-metal bonds. Very rarely used in arrow pushing.
    4. Arrows will end at electron accepting sites (electrophiles), to either form a lone pair or a new bond.
      1. The arrow can end at an : associated with an atom. The order of electrophilicity is Halogen > O > N > C > B.
      2. The arrow can end at a bond. Again, a new σ-bond (with high s-character) is a better acceptor of electrons than a π-bond (no s-character), and new bonds associated with more electronegative atoms are the better acceptors. A (formal) positive charge on an atom helps make it a good acceptor (such as a carbocation).
    5. There are four potential combinations of the above rules:
      1. Bond → bond
      2. Bond → lone pair
      3. Lone pair → bond
      4. Lone pair → lone pair. This latter is very rare.
    6. The symmetry of the electrons involved must conform to group theory/symmetry. For example, if the reactant and product of a reaction maintain a plane of symmetry which allows one to distinguish between π- and σ-electrons, one cannot convert a π-pair into a σ-pair during the reaction (or vice versa) if its group-theoretical symmetry has to change. An example of falling foul of this rule is in fact the very first arrows ever pushed in the literature! An elaboration of this rule is used to define whether any particular pericyclic reaction (a reaction with cyclic arrows) is allowed or forbidden.
      1. The convention above makes no attempt to imply symmetry, and as such therefore can result in incorrect mechanisms, as noted above. There are no plans at the moment to add symmetry notation to arrow pushing.
    7. The coordinates of the arrows. This has in the past been very imprecisely defined, but having a precisely defined start and end for each (double-headed, electron pair) arrow could be regarded as being helpful. It is also ascertainable:
      1. Arrows starting or ending at bonds. These coordinates can be computed from the topology of the electron density of either the reactant (the starting point) or the product (the arrow endpoint). Electron density is an experimental observable (using e.g. crystallography) as well as a computable property using quantum mechanics. Its topology (curvatures if you like) can be obtained by appropriate analysis. The key topological property is the bond-critical-point or BCP, which generally can be located at approximately the mid-point of the line connecting the two nuclei (its precise position depends on the relative electronegativities).
      2. Arrows starting or ending at lone pairs (:). Here too topological analysis of the electron density can result in defining the centroid of a lone pair, with again precise coordinates.
      3. Practically, no-one is ever going to perform topological analysis of the electron density in order to push arrows! So a good approximation is to assume that a BCP is located at the mid-point of a bond and a lone pair is located at an atom (mindful this is NOT coincident with the nucleus, since we know a lone pair has p-character). This approximation leads directly to the Sykes convention.Arrows
    8. These points can be summarised in the diagram above, involving reaction between butene (as the electron releasing molecule) and HBr (as the electron accepting molecule).
      1. The green dots represent mid-points of bonds (either breaking or making), and more formally correspond to the BCPs described above.
      2. The green : represents a lone pair being formed, more formally corresponding to the lone pair centroid.
      3. A dotted line is drawn to the forming bond. This is not strictly part of the Sykes convention; it can be optionally omitted and left as implied (in much the same way that most hydrogen atoms in molecules are implied).
      4. There are two (optional) red dots also shown. These are another convention which here is explicit, but is often left implicit. One can regard the red dots as the location of hinges, and regard the arrows as rotating about these hinges. A metaphor might be a hinged door, which is opening (bond breaking) by rotating around one hinge, and closing (bond or lone pair forming) by rotating about the next hinge. In this metaphor a covalent bond is a closed-door and a lone pair is an open door. Adding these hinges allows one to define a simple checking-rule.
        1. For reactions where no atom undergoes a valency change, the hinges MUST be located on alternating atoms. No two adjacent atoms can have hinges.
          1. An exception might be where linear and cyclic arrows are mixed.
        2. For reactions where one atom undergoes a valency change (the most common examples are 4-valent carbon changing to 2-valent carbon, ie a carbene, or 3-valent nitrogen forming 1-valent nitrene, but it also includes changes in oxidation states of transition metals etc), there must be one occurrence of adjacent atoms (ie bonded atoms) each having a hinge.
    9. Most reactions involve more than one arrow (electron pair). The question can then arise as to the relative timing of the various arrows.
      1. If no explicit intermediate is involved, the arrows are said to be concerted, they all operate at the same time.
      2. Any concerted reaction however need not be synchronous, ie the arrows need not all occur at exactly the same time. Sometimes, the arrows can occur in phases.
      3. To determine either the concertedness or synchronicity of any arrow pushing mechanism is however way beyond our current ability to measure (although there are prospects of doing so). Such properties can be computed, but again doing so requires a very sophisticated calculation. Even if these properties can be ascertained, representing them in the convention shown above is also going to be a challenge. So these attributes are currently not attempted using the conventions above.
    10. Radical reactions. These differ from the electron pair reactions since one arrow is assigned to each electron.
      1. Normally, all the arrows used are single-electron fish-books, but there are some rare cases where both fish-book and normal arrows can be combined (the Birch reduction for example).
      2. In general two fish-hook arrows from different sources will both head off to a bond-mid-point (the BCP of the forming bond).
      3. Although the fish-hook implies an electron spin, there is no convention to ensure that the spin-pairing in any formed new bond is correct (strictly, two fish-hooks of opposite spin should combine).
      4. Because two fish-hook arrows derive from an electron pair, there is no sense of direction (the two arrows head off in opposite directions). Radical arrows tend not to be nucleophilic/electrophilic.
    11. Arrows for reactions involving excited states (photochemistry). These are by and large regarded as beyond the scope of arrow pushing, although one could regard them as triplet state reactions involving fish-hook arrows.

The rules above are terse, and in particular I have not tried to add more than one example, although quite a number are sprinkled throughout this blog.

References

  1. W.M. Schubert, "Mechanism and Structure in Organic Chemistry (Gould, Edwin S.)", Journal of Chemical Education, vol. 37, pp. 379, 1960. https://doi.org/10.1021/ed037p379.2
  2. D.F. Detar, "A guidebook to mechanism in organic chemistry (Sykes, Peter)", Journal of Chemical Education, vol. 40, pp. A224, 1963. https://doi.org/10.1021/ed040pa224.1
  3. B.S. Young, R. Herges, and M.M. Haley, "Coarctate cyclization reactions: a primer", Chemical Communications, vol. 48, pp. 9441, 2012. https://doi.org/10.1039/c2cc34026g

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Molecular Matryoshka dolls

Tuesday, September 20th, 2011

A Matryoshka doll is better known as a Russian nesting doll. They can have up to eight layers. Molecules can only emulate two layers, although see here for a good candidate for making a three-layered example (the inside layer is C60, which itself might encapsulate a small molecule. See also  DOI: 10.1021/ja991747w). These molecular dolls can be created out of quite simple molecules. Here I explore just one, and focus on what is happening inside!

The basic component of a molecular capsule.

The above represents the “tennis ball” component of a molecule first made by Branda, Wyler and Rebek (DOI: 10.1126/science.8122107) in 1994. It has four pairs of carbonyl/NH units, and two of these molecules can stitch together to form an almost spherical capsule. Into this can pop smaller molecules, and in this case methane was persuaded to enter (highlighted with a magenta arrow below).

A molecular Russian doll with methane inside. Click for 3D

Finding out the structure of these dolls can be a tricky business. More often than not, they do not crystallise nicely enough to determine this by X-ray analysis (the structure of this one has never been reported, the structure above is a calculation), and even if the basic container could be analysed, the small molecules inside often rattle around too much (i.e. they are disordered) for their optimum position to be identified. Rebek and co resorted to 1H NMR spectroscopy. If you read their paper, you will find that the chemical shift of the four methane protons comes at -0.91 ppm if inside the cavity, and at +0.23 outside. These sorts of induced shifts (they can be very much larger) makes the identification of more complex molecules which may be inside the cavity a fraught business. Is there another method? Here I suggest that the 1H NMR spectrum can be calculated to sufficient accuracy to be able to comment on that internal structure.

The above is a ωB97XD/6-311G(d,p)/SCRF=dichloromethane calculation (under optimum conditions, this can predict the shifts of protons to an accuracy of < 0.1 ppm!). So it is here, with the calculated methane chemical shift being -0.84 ppm (averaged over the four protons). In fact, the spectrum above is amazingly like the real thing (which can be seen at the DOI above), excepting of course proton couplings. Oh, if you cannot see a spectrum, it is because your browser does not support SVG. Why did I use this format? So that you can expand the view above (zoom in using your browser), and the SVG will rescale the drawing without loss of resolution!

We might presume then that the calculated structure must be a good model for the real thing (the structure of which Rebek and Co were never able to obtain). If you click on the model above, you may notice that the methane is not located exactly in the centre of the cavity, but it is displaced towards the face of one of the benzene rings, and away from the other. Thus these internal dolls do have a preference for where they sit, a phenomenon by the way which Rebek has termed social (molecular) isomerism (DOI: 10.1021/ja020607a).This system has 181 atoms. I estimate that this sort of calculation can readily be done for molecules with up to about 250 atoms nowadays, which would cover a fair sprinkling of these molecular Matryoshka dolls.

Postscript:  Professor Rebek has kindly sent me the spectrum of both encapsulated methane and ethane which is reproduced below. The NMR of ethane calculated by the same procedure as above is -0.41 ppm.

The 1H NMR spectrum of encapsulated methane and ethane.

Archived on 2011-09-26. URL:http://www.ch.imperial.ac.uk/rzepa/blog/?p=4930. Accessed: 2011-09-26. (Archived by WebCite® at http://www.webcitation.org/61zSZeG7P)

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Secrets of a university tutor: (curly) arrow pushing

Thursday, October 28th, 2010

Curly arrows are something most students of chemistry meet fairly early on. They rapidly become hard-wired into the chemists brain. They are also uncontroversial! Or are they? Consider the following very simple scheme.

Curly arrow pushing

It represents protonation of an alkene by an acid. Two products are of course possible, leading to either a tertiary carbocation as shown in (a), or a primary one (not shown). Either involves two arrows, but how to illustrate this (important) difference in the outcome using the arrows. Most textbooks show (a). The lhs arrow starts at the middle of the bond, and ends at the atom of hydrogen. This unfortunately leads to an ambiguity. It does not define which carbon is involved in forming the new C-H bond.

In recognition of this problem an article has recently appeared (DOI: 10.1021/ed086p1389) which attempts to improve model (a) by using what they call bouncing arrows, as in (b). The arrow starts at the mid point of the C=C bond, but then bounces to one end, before heading off to again to end at the H atom. The idea is that the direction of bounce informs which of the two possible bonds will be formed. Leaving aside the (non-trivial) issue of how to persuade e.g. ChemDraw to produce a bouncing arrow, I note that an alternative system has been in use where I teach for many years; (c).

  1. This starts by addressing the problem of which bond to form by immediately drawing a dotted line where you want the bond to go.
  2. The arrow starts as before, at the mid point of a bond, but this time it ends at the mid-point of the dotted line. If nothing else, Chemdraw has no problem with this notation!
  3. Are there any other advantages? Consider (d). The green dots indicate the results of a QTAIM analysis, revealing bond-critical points (BCP) in either the reactants or the products. The first arrow both starts and ends at such a BCP. The second arrow starts at a BCP, and ends at a lone pair (these are not revealed using QTAIM. If instead, ELF synaptic basin centroids were to be used, then all arrows would start or end at such a basin). This therefore gives (c)/(d) some quantum mechanical reality.
  4. Another advantage is that one can formulate check-sumrules. By this I mean extra rules that can be used to check you have gotten things correct. Take a look at the red dots, one on the oxygen, another on the bromine. The metaphor is that these can be regarded as hinges, about which the bond swivels, the course of the swivel following that of the trajectory of the arrow.
    1. For heterolytic (electron pair) arrow pushing in which none of the centres involved changes its valency, the red dots must be located on alternating atoms.
    2. For heterolytic (electron pair) arrow pushing in which a valency change does occur (e.g. formation of a carbene), two red dots must be on adjacent atoms.
    3. In general, no more than one arrow either starts, or ends, at a bond. This used to be thought of as a fairly hard rule, but in fact its not difficult to come up with reactions which break it. For example, this one, where as many as three arrows either start or end at a given bond. And, as a challenge, can you break the rule by formulating arrow pushing for the (concerted) reaction between an alkyne and a per-acid (avoiding the anti-aromatic oxirene, the ring opening of which may conflate with the peroxidation).
    4. One can interrupt the concerted flow of arrows to form intermediates along the way. One famous example of such interruption is aromatic electrophilic substitution, which can however be persuaded to move all of its arrows more or less synchronously.
  5. The metaphor now is one of doors opening and closing, rather than bouncing arrows.

There must be thousands of tutors around the world, teaching tens of thousands of students the arcane art of arrow pushing. If anyone has yet another schema for doing so, I would be delighted to hear from them.

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And now for something completely different: The art of molecular sculpture.

Sunday, October 17th, 2010

Chemistry as the inspiration for art! The inspiration was the previous post. As for whether its art, you decide for yourself. Click on each thumbnail for a molecular sculpture (the medium being electrons!).

MO 54. Click for 3D

MO 55. Click for 3D

MO 57. Click for 3D

MO 46. Click for 3D

MO 47. Click for 3D

MO 48. Click for 3D

MO 38. Click for 3D

MO 39. Click for 3D

MO 40. Click for 3D

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