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Smoke and mirrors. All is not what it seems with this Sn2 reaction!

Thursday, April 4th, 2019

Previously, I explored the Graham reaction to form a diazirine. The second phase of the reaction involved an Sn2′ displacement of N-Cl forming C-Cl. Here I ask how facile the simpler displacement of C-Cl by another chlorine might be and whether the mechanism is Sn2 or the alternative Sn1. The reason for posing this question is that as an Sn1 reaction, simply ionizing off the chlorine to form a diazacyclopropenium cation might be a very easy process. Why? Because the resulting cation is analogous to the cyclopropenium cation, famously proposed by Breslow as the first example of a 4n+2 aromatic ring for which the value of n is zero and not 1 as for benzene.[1] Another example of a famous “Sn1” reaction is the solvolysis of t-butyl chloride to form the very stable tertiary carbocation and chloride anion (except in fact that it is not an Sn1 reaction but an Sn2 one!)

Here is the located transition state for the above, using Na+.6H2O as the counter-ion to the chloride. The calculated free energy of this transition state is 3.2 kcal/mol lower than the previous Sn2′ version (FAIR data collection, 10.14469/hpc/5045), with an overall barrier to reaction of 26.5 kcal/mol. This compares to ~24.5 kcal/mol obtained by Breslow for solvolysis of the cyclopropenyl tosylate. Given the relatively simple solvation model I used in the calculation (only six waters to solvate all the ions, and a continuum solvent field for water), the agreement is not too bad.

The animation above is of a normal vibrational mode known as the transition mode (click on the image above to get a 3D rotatable animated model). The calculated vectors for this mode (its energy being an eigenvalue of the force constant matrix) are regularly used to “characterise” a transition state. I will digress with a quick bit of history here, starting in 1972 when another famous article appeared.[2] The key aspect of this study was the derivation of the first derivatives of the energy of a molecule with respect to the (3N) geometrical coordinates of the atoms, using a relatively simply quantum mechanical method (MINDO/2) to obtain that energy. Analytical first derivatives of the MINDO/2 Hamiltonian were then used to both locate the transition state for a simple reaction and then to evaluate the second derivatives (the force constant matrix) using a finite difference method. That force constant matrix, when diagonalized, reveals one negative root (eigenvalue) which is characteristic of a transition state. The vectors reveal how the atoms displace along the vibration, and should of course approximate to the path to either reactant or product.

Since that time, it has been a more or less mandatory requirement for any study reporting transition state models to characterise them using the vectors of the negative eigenvalue. The eigenvalue invariably expressed as a wavenumber. Because this comes from the square root of the mass-weighted negative force constant, it is often called the imaginary mode. Thus in this example, 115i cm-1, the i indicating it is an imaginary number. The vectors are derived from quadratic force constants, which is a parabolic potential surface for the molecule. Since most potential surfaces are not quadratic, it is recognized as an approximation, but nonetheless good enough to serve to characterise the transition state as the one connecting the assumed reactant and product. Thousands of published studies in the literature have used this approach.

So now to the animation above. If you look closely you will see that it is a nitrogen and not a carbon that is oscillating between two chlorines (here it is the lighter atoms that move most). The vectors confirm that, with a large one at N and only a small one at C. So it is Sn2 displacement at nitrogen that we have located? 

Not so fast. This is a reminder that we have to explore a larger region of the potential energy surface, beyond the quadratic region of the transition state from which the vectors above are derived. This is done using an IRC (intrinsic reaction coordinate). Here it is, and you see something remarkable.

The Cl…N…Cl motions seen above in the transition state mode change very strongly in regions away from the transition state. On one side of the transition state, it forms a Cl…C bond, on the other side a Cl…N.

It is also reasonable to ask why the paths either side of the transition state are not the same? That may be because with only six explicit water molecules, three of which solvate the sodium ion, there are not enough to solvate equally the chloride anions either side of the transition state. As a result one chlorine does not behave in quite the same way as the other. The addition of an extra water molecule or two may well change the resulting reaction coordinate significantly.

The overall message is that there are two ways to characterise a computed reaction path. One involves looking at the motions of all the atoms just in the narrow region of the transition state. Most reported literature studies do only this. When the full path is explored with an IRC, a different picture can emerge, as here. The Cl…N…Cl Sn2 mode is replaced by a Cl…C/N…Cl mode. This example however is probably rare, with most reactions the transition state vibration and the IRC do actually agree!

References

  1. R. Breslow, "SYNTHESIS OF THE s-TRIPHENYLCYCLOPROPENYL CATION", Journal of the American Chemical Society, vol. 79, pp. 5318-5318, 1957. https://doi.org/10.1021/ja01576a067
  2. J.W. McIver, and A. Komornicki, "Structure of transition states in organic reactions. General theory and an application to the cyclobutene-butadiene isomerization using a semiempirical molecular orbital method", Journal of the American Chemical Society, vol. 94, pp. 2625-2633, 1972. https://doi.org/10.1021/ja00763a011

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The Graham reaction: Deciding upon a reasonable mechanism and curly arrow representation.

Monday, February 18th, 2019

Students learning organic chemistry are often asked in examinations and tutorials to devise the mechanisms (as represented by curly arrows) for the core corpus of important reactions, with the purpose of learning skills that allow them to go on to improvise mechanisms for new reactions. A common question asked by students is how should such mechanisms be presented in an exam in order to gain full credit? Alternatively, is there a single correct mechanism for any given reaction? To which the lecturer or tutor will often respond that any reasonable mechanism will receive such credit. The implication is that a mechanism is “reasonable” if it “follows the rules”. The rules are rarely declared fully, but seem to be part of the absorbed but often mysterious skill acquired in learning the subject. These rules also include those governing how the curly arrows should be drawn.† Here I explore this topic using the Graham reaction.[1]‡

I start by noting the year in which the Graham procedure was published, 1965. Although the routine representation of mechanism using curly arrows had been established for about 5-10 years by then, the quality of such representations in many articles was patchy. Thus, this one (the publisher will need payment for me to reproduce the diagram here, so I leave you to get it yourself) needs some modern tidying up. In the scheme below, I have also made a small change, using water itself as a base to remove a NH proton, rather than hydroxide anion as used in the article (I will return to the anion later). The immediate reason is that water is a much simpler molecule to use at the start of our investigation than solvated sodium hydroxide. You might want to start with comparing the mechanism above with the literature version[1] to discover any differences. 

The next stage is to compute all of this using quantum mechanics, which will tell us about the energy of the system as it evolves and also identify the free energy of the transition states for the reaction. I am not going to go into any detail of how these energies are obtained, suffice to say that all the calculations can be found at the following DOI: 10.14469/hpc/5045 The results of this exercise are represented by the following alternative mechanism.♥

How was this new scheme obtained? The key step is locating a transition state in the energy surface, a point where the first derivatives of the energy with respect to all the 3N-6 coordinates defining the geometry (the derivative vector) are zero and where the second derivative matrix has just one negative eigenvalue (check up on your Maths for what these terms mean). Each located transition state (which is an energy maximum in just one of the 3N-6 coordinates) can be followed downhill in energy to two energy minima, one of which is declared the reactant of the reaction and the other the product, using a process known as an IRC (intrinsic reaction coordinate). The coordinates of these minima are then inspected so they can be mapped to the conventional representations shown above. New bonds in the formalism above are shown with dashed lines and have an arrow-head ending at their mid-point; breaking bonds (more generally, bonds reducing their bond order) have an arrow starting from their mid-point. The change in geometry along the IRC for TS1 can then be shown as an animation of the reaction coordinate, which you can see below.

Don’t worry too much about when bonds appear to connect or disconnect, the animation program simply uses a simple bond length rule to do this. The major difference with the original mechanism is that it is the chlorine on the nitrogen also bearing a proton that gets removed. Also, the N-N bond is formed as part of the same concerted process, rather than as a separate step.

Shown above is the computed energy along the reaction path. Here a “reality check” can be carried out. The activation free energy (the difference between the transition state and the reactant) emerges as a rather unsavoury ΔG‡=40.8 kcal/mol. Why is this unsavoury? Well, according to transition state theory, the rate of a (unimolecular) reaction is given by the expression: Ln(k/T) = 23.76 – ΔG‡/RT where T is temperature (~323K in this example), R = is the gas constant and k is the unimolecular rate constant. When you solve it for ΔG‡=40.8, it turns out to be a very slow reaction indeed. More typically, a reaction that occurs in a few minutes at this sort of temperature has ΔG‡= ~15 kcal/mol. So this turns out to be an “unreasonable” mechanism, but based on the quantum mechanically predicted rate and not on the nature of the “curly arrows”. And no, one cannot do this sort of thing in an examination (not even on a mobile phone; there is no app for it, yet!) I must also mention that the “curly arrows” used in the above representation are, like the bonds, based on simple rules of connecting a breaking with a forming bond with such an arrow. There IS a method of computing both their number and their coordinates “realistically”, but I will defer this to a future post. So be patient!

The next thing to note is that the energy plot shows this stage of the reaction as being endothermic. Time to locate TS2, which it turns out corresponds to the N to C migration of the chlorine to complete the Graham reaction. As it happens, TS2 is computed to be 10.6 kcal/mol lower than TS1 in free energy, so it is not “rate limiting”.

To provide insight into the properties of this reaction path, a plot of the calculated dipole moment along the reaction path is shown. At the transition state (IRC value = 0), the dipole moment is a maximum, which suggests it is trying to form an ion-pair, part of which is the diazacylopropenium cation shown in the first scheme above. The ion-pair is however not fully formed, probably because it is not solvated properly.

We can add the two reaction paths together to get the overall reaction energy, which is no longer endothermic but approximately thermoneutral. Things are still not quite “reasonable” because the actual reaction is exothermic.

Time then to move on to hydroxide anion as the catalytic base, in the form of sodium hydroxide. To do this, we need to include lots of water molecules (here six), primarily to solvate the Na+ (shown in purple below) but also any liberated Cl–. You can see the water molecules moving around a lot as the reaction proceeds, via again TS1 to end at a similar point as before.

The energy plot is now rather different. The activation energy is now lower than the 15 kcal/mol requirement for a fast reaction; in fact ΔG‡= 9.5 kcal/mol and overall it is already showing exothermicity. What a difference replacing a proton (from water) by a sodium cation makes!

Take a look also at this dipole moment plot as the reaction proceeds! TS1 is almost entirely non-ionic!

To complete the reaction, the chlorines have to rearrange. This time a rather different mode is adopted, as shown below, termed an Sn2′ reaction. The energy of TS2′ is again lower than TS1, by 9.2 kcal/mol. Again no explicit diazacylopropenium cation-anion pair (an aromatic 4n+2, n=0 Hückel system) is formed.



Combing both stages of the reaction as before. The discontinuity in the centre is due to further solvent reorganisation not picked up at the ends of the two individual IRCs which were joined to make this plot. Note also that the reaction is now appropriately exothermic overall.

So what have we learnt?

  1. That a “reasonable” mechanism as shown in a journal article, and perhaps reproduced in a text-book, lecture or tutorial notes or even an examination, can be subjected in a non-arbitrary manner to a reality check using modern quantum mechanical calculations.
  2. For the Graham reaction, this results in a somewhat different pathway for the reaction compared to the original suggestion.
    1. In particular, the removal of chlorine occurs from the same nitrogen as the initial deprotonation
    2. This process does not result in an intermediate nitrene being formed, rather the chlorine removal is concerted with N-N bond formation.
    3. The resulting 1-chloro-1H-diazirine does not directly ionize to form a diazacyclopropenium cation-chloride anion ion pair, but instead can undertake an Sn2′ reaction to form the final 3-chloro-3-methyl-3H-diazirine.
  3. A simple change in the conditions, such as replacing water as a catalytic agent with Na+OH–(5H2O) can have a large impact on the energetics and indeed pathways involved. In this case, the reaction is conducted in NaOCl or NaOBr solutions, for which the pH is ~13.5,♣ indicating [OH–] is ~0.3M.
  4. The curly arrows here are “reasonable” for the computed pathway, but are determined by some simple formalisms which I have adopted (such as terminating an arrow-head at the mid-point of a newly forming bond). As I hinted above, these curly arrows can also be subjected to quantum mechanical scrutiny and I hope to illustrate this process in a future post.

But do not think I am suggesting here that this is the “correct” mechanism, it is merely one mechanism for which the relative energies of the various postulated species involved have been calculated relatively accurately. It does not preclude that other, perhaps different, routes could be identified in the future where the energetics of the process are even lower. 

†This blog is inspired by the two students who recently asked such questions. ‡In fact, you also have to acquire this completely unrelated article[2] for reasons I leave you to discover yourself. ♥You might want to consider the merits or demerits of an alternative way of showing the curly arrows. Is this representation “more reasonable”? ♣I thank Ed Smith for measuring this value for NaOBr and for suggesting the Graham reaction in the first place as an interesting one to model.

References

  1. W.H. Graham, "The Halogenation of Amidines. I. Synthesis of 3-Halo- and Other Negatively Substituted Diazirines<sup>1</sup>", Journal of the American Chemical Society, vol. 87, pp. 4396-4397, 1965. https://doi.org/10.1021/ja00947a040
  2. E.W. Abel, B.C. Crosse, and D.B. Brady, "Trimeric Alkylthiotricarbonyls of Manganese and Rhenium", Journal of the American Chemical Society, vol. 87, pp. 4397-4398, 1965. https://doi.org/10.1021/ja00947a041

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Dyotropic Ring Expansion: more mechanistic reality checks.

Sunday, October 1st, 2017

I noted in my WATOC conference report a presentation describing the use of calculated reaction barriers (and derived rate constants) as mechanistic reality checks. Computations, it was claimed, have now reached a level of accuracy whereby a barrier calculated as being 6 kcal/mol too high can start ringing mechanistic alarm bells. So when I came across this article[1] in which calculated barriers for a dyotropic ring expansion observed under mild conditions in dichloromethane as solvent were used to make mechanistic inferences, I decided to explore the mechanism a bit further.

Shown in blue above is the reported outcome, a dyotropic transposition of a OMs group with a ring CH2 group. Shown in red are my additions.

The observed product is a 6,6-bicyclic ring system, for which various calculated mechanistic pathways were reported (R=H)[1].

  1. The first involved dyotropic-like [1,2] transposition of the neutral molecule, for which barriers >39 kcal/mol were calculated[1]. These are certainly too high to be viable and the warning bells were certainly heeded.
  2. These bells led the authors to the hypothesis that protonation of the OMs group would facilitate the reaction (Figure 7[1]). Their model included the proton, but did not include any counter-ion. A barrier of 5.6 kcal/mol for this system was estimated and considered “fully compatible with the mild experimental conditions“. However, as they also noted, “a singular transition structure could not be located due to the topology of the potential energy surface” and “A nudged elastic band method (was) employed to explore how the reaction proceeds“. This latter method was new to me, but in fact since I now thought the barrier might be too low; warning bells started to ring for me now.
  3. I thought the answer might relate to the lack of a negative counter-ion to the positive proton and so I added HCl instead of H+ (red above) to create a more physically realistic model of an acid catalyst; an isolated cation is an un-physical model, unless found in e.g. a mass spectrometer. Also included were two explicit water molecules, waters that were also included in the reported models[1], to help stabilise what was likely to be an ion-pair like system, labelled HI in the diagram above. I will explain what HI means shortly.
  4. I used the same ωB97XD/Def2-SVPP/SCRF=DCM method as originally reported[1]. The inclusion of explicit HCl instead of H+ now readily allowed a transition state to be located and an IRC (intrinsic reaction coordinate) could be computed (FAIR data DOI: 10.14469/hpc/3016) as a replacement for nudged elastic bands! This profile turned out to have some remarkable features, as I will discuss below.
    • I also recomputed the reactant and transition state at the Def2-TZVPPD basis set level, which allows for a better description of negative ions (FAIR data DOI: 10.14469/hpc/3095,10.14469/hpc/3140)  and this results in a calculated ΔG‡195 of ~16 kcal/mol, less than the original computed transition state barriers of >39 kcal/mol and closer to the barrier required for mild experimental conditions at -78°C.
  5. An animation of the IRC at the ωB97XD/Def2-SVPP/SCRF=DCM level (10.14469/hpc/3016) is shown below. It is a concerted formally dyotropic process, albeit very asynchronous in nature in which C-OMs bond breaking precedes C migration, which in turn precedes C-OMs bond formation.
  6. The energy profile is shown below. 

    • Between IRC -13 and IRC -6, the reaction prepares for a proton transfer from HCl to the mesityl oxygen, which occurs ~IRC -4.
    • From IRC -3 to IRC +1, the profile is very flat, which probably is the cause of the original failure[1] to locate a transition state.
    • The region IRC -3 to +2 is where the CH2 group starts to migrate, reaching the half way point at ~ IRC 0, the transition state.
    • At IRC +4, the alkyl [1,2] migration is complete and a hidden ion-pair intermediate has formed.
    • From IRC +5 to +17, this hidden ion-pair collapses to form the final non-ionic product. In the process a second proton transfer occurs back to the chloride anion (~IRC +5).
  7. The hidden ion-pair intermediate can be seen more clearly in this plot of the energy derivative gradient norm at IRC +4. The two proton transfers can be seen very clearly as sharp features at IRC -4 and +5. 
  8. The zone of the hidden ion-pair intermediate can also be seen in this dipole moment plot.
  9. This next plot charts the changes in the length of the bond labelled (a) in the diagram above. As the CH2 migration starts to create a carbocation-mesityl anion pair, the bond connecting the two rings is now tempted to also migrate. Doing so would create a more stable tertiary carbocation centre.
  10. This is mirrored by the length of the bond labelled (b). As (a) lengthens, so (b) contracts. But then at IRC +4, the aspirations of both bonds are cruelly frustrated. The methane sulfonic acid has just lost its proton (which has returned to its original home, the chloride anion) and, as an anion, is now voraciously seeking a cation. It out-competes bond (b) and forms a C-O bond. The rejected bond (b) rapidly retreats.
  11. The knock-on effects of this battle between two electron donors can be see further afield. Here is a plot of one C-H bond length (shown above as R-C; R=H). In the expectation that bond (b) will depart, it starts to increase its hyperconjugation with the adjacent carbon, but then retreats along with bond (b).

There are lots more fun to be had with these IRC plots, but I will stop there and try to summarise. This [1,2] dyotropic transposition only has a reasonably low barrier if an ion-pair can be formed. This in turn requires a proton as catalyst, which starts off life attached to Cl, then migrates to O to enhance the ion-pair formation, and finally returns back home to the Cl. By using just a proton (without chloride) in the original study[1], in effect only the region of the reaction coordinate not involving the proton transfers was studied, i.e. IRC -4 to IRC +5. That would indeed give the misleading impression of a very small barrier for the reaction. By including a larger region of the reaction coordinate with the addition of chloride, we get a more realistic model for the reaction.

More importantly, we learn a lot more about the reaction from this better model. The most important new insights are:

  1. Beyond the transition state at IRC = 0, we have pathways for both the formation of a 6,6 bicyclic ring (the blue route in the scheme above) and an alternative 5,7 bicyclic ring product (red route above). The 6,6 product was isolated in 70% yield, which leaves open the possibility that some 5,7 product was formed but was not identified. It would be worth repeating the original synthesis to see if any such product could in fact be detected.
  2. The fact that remote substituents such as R have a response to the reaction suggests that they could be used to mediate between 6,6 and 7,5 ring formation. Perhaps some modification could be found that would lead to only 5,7 product? I will explore this computationally and report my results back presently.
  3. This may represent yet another example where reaction dynamics play a role in determining the product outcome. One transition state but two possible products!  So, as also noted in the previous post, yet another candidate for a molecular dynamics study?

References

  1. H. Santalla, O.N. Faza, G. Gómez, Y. Fall, and C. Silva López, "From Hydrindane to Decalin: A Mild Transformation through a Dyotropic Ring Expansion", Organic Letters, vol. 19, pp. 3648-3651, 2017. https://doi.org/10.1021/acs.orglett.7b01621

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Hydrogen capture by boron: a crazy reaction path!

Thursday, September 21st, 2017

A recent article reports, amongst other topics, a computationally modelled reaction involving the capture of molecular hydrogen using a substituted borane (X=N, Y=C).[1] The mechanism involves an initial equilibrium between React and Int1, followed by capture of the hydrogen by Int1 to form a 5-coordinate borane intermediate (Int2 below, as per Figure 11).‡ This was followed by assistance from a proximate basic nitrogen to complete the hydrogen capture via a TS involving H-H cleavage. The forward free energy barrier to capture was ~11 kcal/mol and ~4 kcal/mol in the reverse direction (relative to the species labelled Int1), both suitably low for reversible hydrogen capture. Here I explore a simple variation to this fascinating reaction.∞


This variation involves transposing X and Y such that Y=N+ and X=C– to form a carbon ylide such that X=C becomes much more nucleophilic than the original nitrogen nucleophile. An animation of the full IRC† (intrinsic reaction coordinate computed at ωB97XD/cc-pvtz; FAIR data doi: 10.14469/hpc/2704) is shown below.

The profile shows that the reaction is concerted between the species labelled React and Prod; no sign of Int1 and Int2!

  1. The region IRC -12 to -5 involves B-C bond cleavage. Because the C is so very nucleophilic, the 4-ring species labelled React becomes very stable and opening it requires a high barrier.
  2. Between IRC -5 and 0, the BH2 group rotates, losing its original interaction with the C to slowly create an empty acceptor orbital on the boron which can then interact with the incoming hydrogen.
  3. At IRC= 0 (the transition state) the hydrogen has been captured by the boron to form a 5-coordinate species, in a manoeuvre that reminds one of the orbital capture of satellites by planets on their way to the outer reaches of the solar system. If the barrier to this capture is computed from IRC= -4 (the region of Int2) it is very much lower than the original system[1], again a reflection of the higher nucleophilicity of X=C–.
  4. The fly past continues until IRC= +7, at which point one end of the bound hydrogen has become suitably orientated to interact with the nucleophilic carbon via lone-pair donation into the acceptor H-H σ* orbital, thus helping to break it.
  5. By IRC= +9, the H-H cleavage is complete.
  6. By IRC= +13 the reaction has reached Prod, being overall ~ -12 kcal/mol exothermic.
  7. The overall thermochemistry is dominated by the potent carbon nucleophile in the reactant, which in turn makes this modification entirely useless for the purposes of a hydrogen-capture system!


The evolution of the dipole moment along the IRC shows very non-linear behaviour (such plots are rarely shown in most published IRC analyses; they should be!), ending of course with the ionic zwitterion that is the imminium borohydride Prod. Indeed the entire reaction coordinate is an unusually vivid example of a non-least motion path!

This simple atom transposition has given us a very instructive exercise in reaction paths, by-passing entirely both  Int1 and Int2 (making them hidden intermediates), and converting React → Prod into a concerted reaction. It would be great to probe this convoluted journey using reaction dynamics!

∞Archived as DOI: 10.14469/hpc/3096

‡ Such a species can be seen as a hidden intermediate in the mechanism of reduction of a carboxylic acid by diborane.

†None were shown in the original study.[1]

References

  1. L. Li, M. Lei, Y. Xie, H.F. Schaefer, B. Chen, and R. Hoffmann, "Stabilizing a different cyclooctatetraene stereoisomer", Proceedings of the National Academy of Sciences, vol. 114, pp. 9803-9808, 2017. https://doi.org/10.1073/pnas.1709586114

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Conference report: an example of collaborative open science (reaction IRCs).

Thursday, May 25th, 2017

It is a sign of the times that one travels to a conference well-connected. By which I mean email is on a constant drip-feed, with venue organisers ensuring each delegate receives their WiFi password even before their room key. So whilst I was at a conference espousing the benefits of open science, a nice example of open collaboration was initiated as a result of a received email.‡

Steven Kirk  contacted me with the following query: Do you know of any open-access database of calculated IRCs with coverage of as broad a range of classes of chemical reactions as possible? I recollected that about six years ago, I was exploring the use of iTunesU as a system for delivering course content in a rich-media format. I produced animations for about 115 reactions (many of which as it happens were taken from this blog, but quite a number were also unique to that project) and placed them into iTunesU, and now sending the URL https://itunes.apple.com/gb/course/id562191342 to Steven.

I should at this point explain something of the structure of such an iTunesU course.

  1. An essential feature is the course icon, seen below on the left. Since the course is hosted by Imperial College, it had to be an officially approved icon. I am sure you can believe me if I tell you that this took a month or so to obtain, with a fair bit of persistence required!
  2. I also had to get approval to place the iTunes app on all the teaching computers so that students could open the course. Believe me again when I tell you that I had to persuade the Apple lawyers in Cupertino to release a special license for this app to persuade our administrators here to install it on the Windows teaching clusters. Another few months had passed by.
  3. When creating an entry (using e.g. https://itunesu.itunes.apple.com/coursemanager/ ) one has to specify values for various descriptors, also often called metadata. Thus any one entry has fields for name and description, with the popularity added by Apple. Only a few words are visible in the description field, which can be expanded in iTunes using the i button.
  4. Steven meanwhile had replied asking if the original data that was used to generate the IRC might be available. Specifically his second question was “So the DOIs are only stamped into the animation’s bitmaps, or are they also somewhere in the metadata?“. That little i button is not easy to spot, and there is no indication, in the event, of what information it might actually contain.
  5. Here it is expanded. The contents are unstructured text, into which I have placed the required DOI.
  6. The lesson here is that I had fortunately had the foresight to include a link to the IRC data in anticipation of just such a question from someone in the future. But black mark to Apple here; the text cannot be selected and copied into a clipboard! It is fairly unFAIR data, since it can only be inter-operated (the I of FAIR) by a human re-typing it by hand. And the human has also to recognise the pattern of a DOI; a machine could not obtain this information easily. Moreover Steven is a Linux user; he does not readily have access to the iTunes app on this operating system!
  7. Also, there were 115 such entries, and now the prospect was rearing that each would have to be hand processed. Moreover, because the text was unstructured, there was no guarantee that I would have adopted the same pattern for all 115 entries.
  8. Fortunately Steven was on the ball. I quote again: it turns out iTunes isn’t needed at all. A service I found on the web http://picklemonkey.net/feedflipper-home/ takes an ITunes URL and converts it to an RSS feed. Opening this feed in Firefox and RSSOwl respectively let me save the feed as XML and HTML (both attached).
  9. This is currently where we stand (Steven’s first email was two days ago), but it’s not finished yet. Depending on how assiduous I was five years ago, some DOIs to the data may be acquired from the list. Sometimes I simply wrote e.g. See http://www.ch.imperial.ac.uk/rzepa/blog/?p=6816 knowing that the links to the data were there instead. I can already see that some descriptions have neither a DOI nor a link to the blog. More detective work will be needed, unfortunately.

How might the situation described above been avoided? Well, Apple in iTunesU only provided in effect one metadata field, and this was an unstructured one. Anything went in that field. Had they provided (or had the course creator been able to configure it themselves) there might have been another field entitled say “data source“. This could moreover been made a mandatory field and a structured one. Thus it might have only accepted known types of persistent identifier, such as a DOI. Further, the system could have checked that the DOI was actually resolvable. Before you ask, I did log a “bug” with Apple asking this be done, but nothing ever was. With such a tool to hand, I might have achieved data sources for all the 115 entries. The resulting XML (as generated above) could have been used to automate the retrieval of all 115 datasets describing this course. 

At this stage then, Steven can follow-up his interest in building a reaction IRC library and analysing it. I will do all I can to encourage Steven not to make the mistakes I did and to ensure that any further data that is required to augment the library does not suffer the problems above. On the other hand, I console myself that in two days, much of the data for the course I created five years ago was salvageable; I wonder how many other iTunesU courses there are for which that can be said!

I will let (with some blushing) the final word be Steven’s: You are one of the few chemists who has both pioneered and built the principles of ‘open chemistry’ into their actual scientific work. I visit your blog occasionally knowing that there is a very high probability I could download and tinker with the results of real calculations.

‡Might I assure all the speakers that I concentrated totally on their talks rather than incoming emails!

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First, hexacoordinate carbon – now pentacoordinate oxygen?

Saturday, March 25th, 2017

The previous post demonstrated the simple iso-electronic progression from six-coordinate carbon to five coordinate nitrogen. Here, a further progression to oxygen is investigated computationally.

The systems are formally constructed from a cyclobutadienyl di-anion and firstly the HO5+ cation, giving a tri-cationic complex. There are no examples of the resulting motif in the Cambridge structure database. A ωB97XD/Def2-TZVPP calculation (DOI: 10.14469/hpc/2350) shows it is again a stable minimum, with a Kekule mode of 1203 cm-1.

A QTAIM  topological analysis of the electron density shows it differs from the nitrogen analogue in now having the ring topological feature for the basal four carbons, which in turn gives rise to a cage critical point (blue dot). The values of the electron density are lower than for N.

The ELF basin analysis shows the C-C bonds are regular single ones (2.01e), whereas the C-O bonds have a slightly greater electron population than the C-N bonds discussed in the previous post.

I suspect the prospects of making a stable tri-cation in such a small molecule are lower than the crystal di-cation achieved with carbon as the apical atom. But the charge can be reduced to a di-cation by replacing the HO5+  above with S–-O5+; the animation below showing the Kekule mode (1140 cm-1, DOI: 10.14469/hpc/2356).

And for some (negative) loose ends.

  1. The P equivalent constructed from cyclobutadienyl di-anion and HP4+ is now unremarkably 5-coordinate. But in fact it is not a stable minimum (DOI: 10.14469/hpc/2357), having two negative force constants.
  2. as does the system  from cyclobutadienyl di-anion and O=P4+(DOI: 10.14469/hpc/2358)
  3. and the system from cyclobutadienyl di-anion and HS5+(DOI: 10.14469/hpc/2360).
  4. Transposition of S/O to give O–-S5+ likewise (DOI: 10.14469/hpc/2359).

So the family of hyper-coordinate 2nd row main group elements now comprises the experimentally verified C, with N and O now open to such verification.

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Reaction coordinates vs Dynamic trajectories as illustrated by an example reaction mechanism.

Monday, March 20th, 2017

The example a few posts back of how methane might invert its configuration by transposing two hydrogen atoms illustrated the reaction mechanism by locating a transition state and following it down in energy using an intrinsic reaction coordinate (IRC). Here I explore an alternative method based instead on computing a molecular dynamics trajectory (MD).

I have used ethane instead of methane, since it is now possible to envisage two outcomes:

An animation of the IRC starting from the located transition state is shown below (DOI: 10.14469/hpc/2331). This is based purely on the computed potential energy surface of the molecule. The IRC is computed from the forces experienced on the atoms as they are displaced from an initial set of coordinates corresponding to the located transition state and then following the direction indicated by the eigenvectors of the negative force constant required of a transition state. Importantly, there is no time component; the path is based entirely on energies and forces.

Next, a molecular dynamics simulation (ωB97XD/6-31G(d,p), DOI: 10.14469/hpc/2330).  This uses the ADMP method, which requests a classical trajectory calculation using the “atom-centered density matrix propagation molecular dynamics model”. This integrates kinetic energy contributions from the molecular vibrations and so explicitly now includes a time component. In this example the evolution of the system from the transition state is charted over a period of 100 femtoseconds (1000 integrated steps). As it happens this is a relatively short period of evolution; sometimes periods of picoseconds may be required to get a realistic model, especially if one is also dealing with explicit solvent molecules (of which perhaps 500 might be required).

Such explicit inclusion of the kinetic energy from molecular vibrations in effect allows the molecule to “jump” over shallow barriers. In this case, the barrier for a [1,2] hydrogen shift from the methyl group to the adjacent carbene (watch atom 8). Simultaneously, the path taken by two hydrogens no longer corresponds to their transposition but to their elimination as a hydrogen molecule. So this quite different outcome from the IRC is very probably also a much more realistic one.

If the MD method is so much more realistic than the IRC, then why is it not always used? The simple answer is computational time! For this very small molecule and using quite a modest basis set (6-31G(d,p)), the relatively short 1000 time steps took about three times as long to compute as the IRC. The factor gets worse as the size of the molecule increases and the number of time steps for a realistic result increases. Perhaps, as technology gets better and new computer architectures emerge, MD simulations of ever increasingly complex reactions will become far more common. In ten years time, I expect most of the examples on this blog will use this method!

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The smallest C-C-C angle?

Monday, October 31st, 2016

Is asking a question such as “what is the smallest angle subtended at a chain of three connected 4-coordinate carbon atoms” just seeking another chemical record, or could it unearth interesting chemistry?

A simple search of the Cambridge structure database for a chain of three carbons, each bearing four substituents (sp3 hybridized in normal paralance) reveals the following distribution:

ccc

The value 60° is of course a three-membered cyclopropane ring. The tail of the distribution is very small, and there are a few small outliers with values of < 54°. Most of the time such outliers are in fact simple errors, but here we see that they are in fact semibullvalenes, of the type shown below, with the small angle subtended at the central of the three carbon atoms coloured in red.

cazfue

In this diagram I have added my own semantic interpretation of what is going on. Let me itemise this:

  • These molecules can undergo very rapid [3,3] sigmatropic rearrangements, shifting a σ-bond away from the 3-ring to create another such ring.
  • This process elongates one of the C-C bonds and of neccessity this reduces the angle at the associated carbon.
  • I have drawn two types of arrow connecting the two structures. The first is an equilibrium arrow, which implies a transition state connecting the two species. This transition state will have equal bond lengths for the forming/breaking C-C bond, and the transition state will have a rate constant which is slower than the time taken for one molecular vibration (~10-15s)
  • It is also possible however that the second arrow is the correct one, and this implies an electronic resonance rather than a nuclear motion. This would have a rate constant comensurate with electron dynamics (~10-18 s) rather than nuclear vibrations.

What does x-ray crystallography measure? Well the diffraction of photons by electrons. In order to obtain a diffraction pattern, enough photons have to be diffracted to be measured, and even with most modern instruments this still takes minutes or hours. During this period, all the various nuclear positions encountered as a result of vibrations or equilibria are sampled. So if the rate constant for the [3,3] sigmatropic rearrangement is fast, x-ray diffraction will measure the average of the two sets of nuclear positions, which can be distinguished only with some difficulty (if at all) from the structure implied instead by electronic resonance.

If the equilibrium arrow applies, then the small angles of <54° are merely the average of the normal value for a 3-membered ring and a smaller value for a structure where one of the C-C bonds has been removed. In my opening sentence, I noted that the three carbon carbon atoms had to be connected in a chain. This is no longer true; the goalposts have been moved (a lot)!

If its an electron resonance, then the three carbon atoms are still connected, albeit one of the two C-C bonds is no longer a single bond but rather weaker and hence longer. The goalposts have merely been slightly shifted!

A calculation (B3LYP/Def2-TZVPP+D3 dispersion, doi: 10.14469/hpc/1850, [1]) of the structure KUZFUE [2] shows the C2-symmetric species shown below, with an elongated C-C bond and hence a reduced C-C-C angle, as being a true minimum (a resonance) rather than a transition state (an equilibrium). The vibration which shortens one C-C bond and lengthens the other has the real calculated wavenumber 244 cm-1.‡ But the boundary between the two possibilities (often referred to as the boundary between a single and a double minimum in a potential energy surface) is notoriously difficult to capture using calculations.

cazfue

How could experiment definitively settle the issue? Well, the SLAC beam is a unique instrument. Its source of X-rays is so intense that you can get an analysable diffraction pattern from a crystal on a timescale so short that during this period no nuclear motions occur (not even vibrations). Those nuclear positions capture the true equilibrium positions of the atoms in the molecule. Now, how does one get beam time on the SLAC?

‡ Click on the image above to see an animation of this normal mode. If you are running the macOS Safari browser, make sure Preferences/Security/Plug-in settings/Java has the site ch.ic.ac.uk or ch.imperial.ac.uk set to on. If you do not do this, the somewhat unhelpful message You do not have Java applets enabled in your web browser, or your browser is blocking this applet. will appear. Note also that new system installations might tend to switch these settings to off.

References

  1. H. Rzepa, "CAZFUE", 2016. https://doi.org/10.14469/hpc/1850
  2. L.M. Jackman, A. Benesi, A. Mayer, H. Quast, E.M. Peters, K. Peters, and H.G. Von Schnering, "The Cope rearrangement of 1,5-dimethylsemibullvalene-2,6- and 3,7-dicarbonitriles in the solid state", Journal of the American Chemical Society, vol. 111, pp. 1512-1513, 1989. https://doi.org/10.1021/ja00186a064

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A tutorial problem in stereoelectronic control. A Grob alternative to the Tiffeneau-Demjanov rearrangement?

Saturday, November 28th, 2015

In answering tutorial problems, students often need skills in deciding how much time to spend on explaining what does not happen, as well as what does. Here I explore alternatives to the mechanism outlined in the previous post to see what computation has to say about what does (or might) not happen.

TD

I start with posing the question what does the chloride counter-ion do? If you are aware of the literature on computational reaction mechanisms, you may note that where ionic species are involved, one of the ions is often excluded from the calculations. Here for example, the pertinent reacting species is a diazonium cation, but the anion would likely not be mentioned, and the calculation would be performed as a charged cation (the physically unrealistic charge=1 in the input file!). This is because of an awkward difficulty with ion-pairs. There is no formal bond between the two charged fragments (unless a zwitterion) and so it is not entirely obvious quite where to place the counter-ion. In the diagram above, position 1 is where it was in my first exploration, but with knowledge that it might form a hydrogen bond to an acidic hydrogen, one could also perhaps place it into positions 2 or 3. In 2, as shown by the blue arrows and product above, an entirely different reaction occurs known as the Grob fragmentation.[1] In fact as a di-carbonyl compound, it can then participate in an acid-catalysed aldol condensation and this can lead to the same product as the original Tiffeneau-Demjanov rearrangement, albeit with loss of stereochemical integrity. So it might be worth effort in explaining whether this alternative is likely (in other words how robust the likely stereochemical integrity of the product is).

System Relative TS free energy TS Dipole moment DataDOI
1 0.0 17.7 [2]
2 1.4 24.2 [3]
3 3.7 29.3 [4]

The energies of the three located transition states increase with the dipole moment; as the counter-ion moves further from the positive charge, its position becomes less stable. Still, route 2 is not that much higher in energy. Time for an IRC (intrinsic reaction coordinate) to explore what actually does happen during route 2, the possible Grob rearrangement.

grob1

The reaction animation above shows the required Grob characteristic, the green bond breaking. But instead of the OH then de-protonating, the hydrogen stays in place and instead the Tiffeneau-Demjanov migration takes place. This will require removal of a different proton and indeed in the latter stages, the chloride anion starts off in its determined journey to do so.

GrobDM

The variation in dipole moment as the reaction proceeds is fascinating. At IRC -6, it reaches a minimum, but then reverses itself in hunt of a better way of reducing the dipole moment.

What about 3? This is slightly artificial, since the real system has a methoxy group here, which would inhibit this route. One can still learn chemistry though. The hydrogen bond formed from chloride to the OH encourages the anomeric effect to form a partial oxy-anion, which in turn encourages the red bond to break rather than the green one. But in fact no complete proton transfer happens, and the reaction reaches a non-productive cul-de-sac. 

Alt1

So, to conclude, there is no Grob fragmentation! Instead, a slightly confused Tiffeneau-Demjanov migration occurs in a rather more roundabout manner than previously. We have explored here just TWO reaction trajectories. A more statistical exploration of the trajectory landscape will give us a more complete picture, but I rather fancy that would be very well above the call of duty required to answer a stereochemical problem!

References

  1. C.A. Grob, and W. Baumann, "Die 1,4‐Eliminierung unter Fragmentierung", Helvetica Chimica Acta, vol. 38, pp. 594-610, 1955. https://doi.org/10.1002/hlca.19550380306
  2. H.S. Rzepa, "C 8 H 13 Cl 1 N 2 O 4", 2015. https://doi.org/10.14469/ch/191653
  3. H.S. Rzepa, "C 8 H 13 Cl 1 N 2 O 4", 2015. https://doi.org/10.14469/ch/191654
  4. H.S. Rzepa, "C 8 H 13 Cl 1 N 2 O 4", 2015. https://doi.org/10.14469/ch/191655

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A tutorial problem in stereoelectronic control. The Tiffeneau-Demjanov rearrangement as part of a prostaglandin synthesis.

Monday, November 23rd, 2015

This reaction emerged a few years ago (thanks Alan!) as a tutorial problem in organic chemistry, in which students had to devise a mechanism for the reaction and use this to predict the stereochemical outcome at the two chiral centres indicated with *.  It originates in a brief report from R. B. Woodward’s group in 1973 describing a prostaglandin synthesis,[1] the stereochemical outcome being crucial. Here I take a look at this mechanism using computation.

TD

The amino group is firstly converted to a diazonium chloride by nitrous acid and the resulting group is then easily eliminated. The problem is easy once you spot that either of the coloured bonds in the reactant is approximately antiperiplanar to the diazonium group, and might migrate to contract the ring. The green bond has a dihedral angle of ~174° with respect to the C-N≡N bond whilst the red bond has a less optimal value of ~166°. This alignment can also be viewed using orbital overlaps, in this case the (localised) NBO corresponding to the green or red bond and the empty antibonding NBO for the C-N bond. Below, the blue phase of the C-C bond is presumed to overlap constructively with the purple phase of the C-N anti bond, and likewise for the red/orange phases for the red bond.

Click for 3D

Click for 3D

Click for 3D

Click for 3D

A transition state (ωB97XD/6-311G(d,p)/SCRF=dichloromethane) can be located[2] and this yields[3] the reaction animation shown below;

Ta

This has lots of interesting features, itemised below. The essence of the mechanism is that the green bond is induced to migrate by the proton removal from the OH bond by the chloride group. The red bond, although also aligned more or less correctly, has no such assistance.

  1. Plot 1 of energy shows a small activation energy (7 kcal/mol), leading to an exothermic reaction by about 34 kcal/mol.
  2. The gradient plot 2 (the derivative of the energy with respect to the geometry) shows several interesting features
    1. The reaction starts at IRC = 1.5 with zero gradients.
    2. It reaches the transition state very early (IRC=0.0), at which point the gradients are again zero.
    3. and then the gradients (almost but not quite) reach zero again (IRC ~-2). This is called a hidden reaction intermediate and corresponds to the cations noted above (as an ion pair, with chloride anion). Because the ion pair has a large dipole moment, one might expect the reaction to be sensitive to the polarity of any solvent, and these hidden intermediates might become real ones in highly polar solvents.
    4. At IRC -5, the gradients become large as the carbon starts to migrate.
    5. The migration (with retention of stereochemistry, it is a cationic [1,2] sigmatropic shift) is induced by the chloride anion starting to abstract the proton from the OH group, in synchrony with the carbon migration.
    6. After IRC -8, we see only conformational changes occurring, which may also be interesting to analyse.
  3. Plot 3 shows the length of the breaking (migrating) C-C (green) bond. It hardly changes up to the transition state; it is only afterwards that it really starts to break/migrate. Curiously, the red bond actually lengthens more than the green one at this stage (watch the animation above carefully) before changing its mind and reforming.
  4. Plot 4 the length of the newly forming (migrating) C-C bond. Note how initially, up to the transition state, this bond also lengthens (rather more than the green one does), before slowly reversing itself to contract at the transition state after IRC -3.
  5. Plots 5 and 6 show the lengths of the O…H and Cl…H bonds as the proton transfer proceeds. This mostly occurs AFTER the transition state is passed, and so the reaction should not exhibit any primary kinetic isotope effect induced by e.g. deuterium substitution.
  6. Plot 7 shows the dipole moment evolving along the reaction. At the start the species is an ion pair (diazonium chloride), but as the reaction proceeds HCl is formed and the dipole moment decreases to that of a less ionic compound.

TSE

TSG

TSBL12

TSBL13

TSBLOH

TSBLClH

TSDM

As a learning tool, I find such animations carry a lot of information about reactions and their mechanism and it does not take more than a day or so to chart their course in the manner above.

References

  1. R.B. Woodward, J. Gosteli, I. Ernest, R.J. Friary, G. Nestler, H. Raman, R. Sitrin, C. Suter, and J.K. Whitesell, "Novel synthesis of prostaglandin F2.alpha.", Journal of the American Chemical Society, vol. 95, pp. 6853-6855, 1973. https://doi.org/10.1021/ja00801a066
  2. H.S. Rzepa, "C 8 H 13 Cl 1 N 2 O 4", 2015. https://doi.org/10.14469/ch/191625
  3. H.S. Rzepa, "C8H13ClN2O4", 2015. https://doi.org/10.14469/ch/191626

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