Posts Tagged ‘energy profile’

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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The mechanism of silylether deprotection using a tetra-alkyl ammonium fluoride.

Wednesday, May 25th, 2016

The substitution of a nucleofuge (a good leaving group) by a nucleophile at a carbon centre occurs with inversion of configuration at the carbon, the mechanism being known by the term SN2 (a story I have also told in this post). Such displacement at silicon famously proceeds by a quite different mechanism, which I here quantify with some calculations.

Trialkylsilyl is often used to protect OH groups, and as shown in the diagram above is specifically used to enforce the enol form of a ketone by replacing the OH with OTMS. The TMS can then be removed when required by utilising nucleophilic addition of e.g. fluoride anion from tetra-alkyl ammonium fluoride to form a 5-coordinate silicon intermediate, followed by collapse of this intermediate with expulsion of the oxygen to form an enolate anion. Before starting the calculations, I searched the crystal structure database for examples of R3SIF(OR), as in the search query below.

There were 55 instances of such species, and show below are their geometric characteristics. In all cases, the two electronegative substituents occupy the axial positions of a trigonal bipyramidal geometry. This of course is the orientation adopted by the two electronegative substituents in the SN2 mechanism for carbon, but with silicon this carbon "transition state" can be replaced by a stable (and as we see often crystalline) intermediate!

Turning to calculations (ωB97XD/6-31+G(d)/SCRF=thf), one can locate three transition states for the silicon process (there is only one for the SN2 reaction with carbon).

  1. TS1 represents attack of fluoride anion along the axial position of the forming 5-coordinate silicon.[1],[2] The oxygen in this instance occupies an equatorial position, and this close proximity between the incoming F(-) and the about to depart OR groups represents a retention of configuration at the Si. Note that the reaction is endo-energic. (c.f. [3]).


  2. The next step, TS2[4],[5]  is to move the F ligand to an equatorial position and the OR group from equatorial to its own axial position so that it can depart in the manner the F adopted to arrive. This requires what is called a Berry pseudorotation, an essentially isoenergic process.



    You might note a "hidden intermediate" at IRC ~-7 (the "bump" in the energy profile). This is caused by re-organisation of the ion-pair geometry, with the tetra-alkyl ammonium cation moving its orientation.
  3. TS3[6],[7] now eliminates the –OR group to complete the deprotection.


The free energies are summarised below. Key points include:

  1. The overall free energy of deprotection is appropriately exo-energic.
  2. The highest energy barrier is actually for pseudo-rotation! This suggests that tuning the deprotection with alternative alkyl or aryl groups on the silicon may be a matter of controlling the Berry pseudorotation process.
  3. TS1-3 proceed with the attacking and leaving groups in close proximity (the angle between an axial and an equatorial group is ~90° of course, whereas for a di-axial relationship (the inversion of the SN2 mechanism) it is instead 180°. This close proximity of nucleophile and nucleofuge minimises the required reorganisation of the ammonium counter-ion in the ion-pairs, and possibly also the dipole moments induced by the reactions, the changes of which for the three reactions are shown below:


  4. The 5-coordinate intermediate where both F and O are axial is in fact significantly lower in energy (a cooperative effect) than when only one of them is axial, which matches the orientations identified above in the 55 crystal structures. For a substitution to occur, the cooperative strengthening of the Si-O and Si-F bonds must be removed; hence the retention of configuration.
System Relative free energy DataDOI
Reactants 0.0 [8]
TS1 7.9 [1]
Int F(ax), O(eq) 5.1 [9]
TS2 10.2 (9.2)* [4]
Int F(eq), O(ax) 5.1 [10]
TS3 5.2 [6]
Products -4.0 [11]
Int F,O(ax) -2.5 [12]

*A lower energy orientation of the ion-pair has subsequently been found.[13]

This analysis shows just how different the carbon and the silicon substitution reactions are and how it is the pseudorotation interconverting two 5-coordinate intermediates that appears to be a key step. But questions remain unanswered. What is the energy of the pseudorotation interconverting an intermediate with ax/eq electronegative groups to one with di-axial electronegative groups? Are there transition states starting from the diaxial intermediate and resulting in elimination, and if so what are their relative energies? I leave answers to a follow up post. 

References

  1. H. Rzepa, "trimethyl silyl enol + Me4N(+).F(-) 5-coordinate intermediate F axial TS", 2016. https://doi.org/10.14469/hpc/554
  2. H. Rzepa, "trimethyl silyl enol + Me4N(+).F(-) 5-coordinate intermediate F axial TS IRC", 2016. https://doi.org/10.14469/hpc/564
  3. L. Wozniak, M. Cypryk, J. Chojnowski, and G. Lanneau, "Optically active silyl esters of phosphorus. II. Stereochemistry of reactions with nucleophiles", Tetrahedron, vol. 45, pp. 4403-4414, 1989. https://doi.org/10.1016/s0040-4020(01)89077-3
  4. H. Rzepa, "trimethyl silyl enol + Me4N(+).F(-) 5-coordinate intermediate Berry pseudorotation TS", 2016. https://doi.org/10.14469/hpc/551
  5. H. Rzepa, "trimethyl silyl enol + Me4N(+).F(-) 5-coordinate intermediate Berry pseudorotation TS IRC", 2016. https://doi.org/10.14469/hpc/553
  6. H. Rzepa, "trimethyl silyl enol + Me4N(+).F(-) TS", 2016. https://doi.org/10.14469/hpc/539
  7. H. Rzepa, "trimethyl silyl enol + Me4N(+).F(-) TS IRC", 2016. https://doi.org/10.14469/hpc/552
  8. H. Rzepa, "enol + Me4N(+).F(-) Reactant", 2016. https://doi.org/10.14469/hpc/565
  9. H. Rzepa, "enol + Me4N(+).F(-) 5-coordinate intermediate F axial", 2016. https://doi.org/10.14469/hpc/555
  10. H. Rzepa, "trimethyl silyl enol + Me4N(+).F(-) 5-coordinate intermediate", 2016. https://doi.org/10.14469/hpc/540
  11. H. Rzepa, "enol + Me4N(+).F(-) Product", 2016. https://doi.org/10.14469/hpc/563
  12. H. Rzepa, "trimethyl silyl enol + Me4N(+).F(-) 5-coordinate intermediate F/O axial", 2016. https://doi.org/10.14469/hpc/550
  13. H. Rzepa, "5-coordinate intermediate Berry pseudorotation TS2 New conf?", 2016. https://doi.org/10.14469/hpc/577

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A computed mechanistic pathway for the formation of an amide from an acid and an amine in non-polar solution.

Wednesday, November 12th, 2014

In London, one has the pleasures of attending occasional one day meetings at the Burlington House, home of the Royal Society of Chemistry. On November 5th this year, there was an excellent meeting on the topic of Challenges in Catalysis, and you can see the speakers and (some of) their slides here. One talk on the topic of Direct amide formation – the issues, the art, the industrial application by Dave Jackson caught my interest. He asked whether an amide could be formed directly from a carboxylic acid and an amine without the intervention of an explicit catalyst. The answer involved noting that the carboxylic acid was itself a catalyst in the process, and a full mechanistic exploration of this aspect can be found in an article published in collaboration with Andy Whiting’s group at Durham.[1] My after-thoughts in the pub centered around the recollection that I had written some blog posts about the reaction between hydroxylamine and propanone. Might there be any similarity between the two mechanisms?

amide

That mechanism can be represented as above, which (as per the hydroxylamine mechanism) comprises three transition states and two intermediates. The original study[1] reported just the one TS1. Editing out the starting coordinates from the PDF-based supporting information (the process is not always easy) enabled an IRC (intrinsic reaction coordinate) for TS1 to be easily computed.[2]

origa

origa
This reveals that TS1 is not the complete story, there is still much of the reaction left to complete. The energy profile is charted (using the ωB97XD/6-311G(d,p/SCRF=p-xylene method) according to the scheme above as reactants ⇒ TS1 ⇒ Intermediate 1 ⇒ TS2 ⇒ Tetrahedral intermediate ⇒ TS3 ⇒ products. Computed properties for this more detailed pathway are transcluded here from the digital repository[3] and appear at the end of this post.

  1. TS1 yields what might be called a zwitterionic intermediate. However, this has a relatively small dipole moment (5.7D). Thus, against accepted wisdom, such apparently ionic intermediates CAN be involved in reactions occurring in non-polar solvents!
  2. TS2 is rather unexpected, involving synchronous proton transfer coupled to anomerically related C-OH bond rotation. This rotation changes the anomeric interactions with the adjacent substituents; in my experience I have never before seen a reaction mode quite like this one!
  3. TS3 collapses the tetrahedral intermediate by synchronous proton transfer and C-O bond cleavage, and is (in this model) the rate determining step.  The free energy barrier corresponds to a half-life at 298K of about half an hour.
  4. The product is calculated as exoenergic with respect to reactants,; the reaction does drive to form an amide (and any catalysis of course will not influence that final outcome, only its kinetics).

If you read the original article[1] you will realise the above only scratches the surface of the many fascinating properties of this apparently very simple reaction. Thus, not addressed above is why amides are only formed in certain solvents (xylene for example) but not others. The solvent may have a specific role to play which is not modelled simply by its continuum dielectric or its boiling point. There is much else that could be said.

References

  1. H. Charville, D.A. Jackson, G. Hodges, A. Whiting, and M.R. Wilson, "The Uncatalyzed Direct Amide Formation Reaction – Mechanism Studies and the Key Role of Carboxylic Acid H‐Bonding", European Journal of Organic Chemistry, vol. 2011, pp. 5981-5990, 2011. https://doi.org/10.1002/ejoc.201100714
  2. H.S. Rzepa, "C21H21NO4", 2014. https://doi.org/10.14469/ch/74636
  3. H.S. Rzepa, "A computed mechanistic pathway for the formation of an amide from an acid and an amine in non-polar solution.", 2014. https://doi.org/10.6084/m9.figshare.1235300

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Patterns of behaviour: serendipity in action for enantiomerisation of F-S-S-Cl

Thursday, September 19th, 2013

Paul Schleyer sent me an email about a pattern he had spotted, between my post on F3SSF and some work he and Michael Mauksch had done 13 years ago with the intriguing title “Demonstration of Chiral Enantiomerization in a Four-Atom Molecule“.[1] Let me explain the connection, but also to follow-up further on what I discovered in that post and how a new connection evolved.FSSF3-gen

The prologue (or prequel). Reaction 2 is the path for decomposing the dimer of SF2 (X=F) to two monomers. In the previous post I (eventually) found the transition state for this process, with a relatively low energy barrier. As a mechanistic type, it is known as a reductive elimination (the reverse would be a oxidative addition) since the S atom on the left is reduced from a formal oxidation state of S(IV) to S(II) (or vice versa). Analogues of this reaction are 1 and 3. But before I managed to locate the transition state for reaction 2, I accidentally found the transition state for reaction 4. This retains the S-S bond (at the transition state, this bond is actually shorter than in reactant/product), and is what might be called a two-electron pericyclic redox reaction, since the S on the left is reduced to S(II) and the S on the right is oxidised to S(IV). I have not yet found whether this actually represents a new mechanistic type or not; it does not appear to have a name (should it be called periredox? Or redoxocyclic?). The lesson to be learnt here is that nature normally indulges in the (more or less) lowest energy route to a given target, but quantum chemists have the advantage that they can discover “chemistry in the clouds”; patterns of behaviour requiring too much energy to be seen in the real world and hence permanently hidden from us. But that does not mean we cannot learn chemistry from them.

Thus isomeric reaction 4 is very much higher in energy than 2. But it is what triggered Paul’s memory. Reaction 5 is related both to 4 in that it involves a [1,2] hydrogen shift of X (retaining the S-S bond) followed by a second [1,2] shift of Y. It is also related to 2 since it involves in effect an oxidative addition (by a lone pair) to an S-X bond to generate S(IV), followed by a reductive elimination back to S(II) to regenerate the enantiomer of the reactant (it is thus a two-step redox reaction). Thus if X and Y are different in 5, then all three of the species shown above are themselves chiral, and hence the reaction is indeed a “Demonstration of Chiral Enantiomerization in a Four-Atom Molecule”. The point here is that enantiomerisations do not necessarily have to proceed through an achiral transition state, but that the entire enantiomerisation pathway can be continuously chiral.

That was the intro! Now follows my calculated intrinsic reaction coordinate (ωB97XD/6-311G(d,p) for reaction 5.[2] My first attempt at the transition state was to use 2 as a template (rather than 4, which was far higher in energy). Well, talk about unexpected! The migration of X=Cl is 16.7 kcal/mol lower than X=F.  No problem there. Next, the IRC for X=F. The overall process certainly enantiomerises the two chiral gauche conformations, but without transposing X and Y, and not involving an intermediate S(IV) species as shown in reaction 5 (i.e. it goes directly, via reaction 6). 

FSSCl

But look at that energy! Way too high (above the clouds in fact). And although the start and end species are identical (apart from being enantiomers) the energy profile is far from being symmetrical. 

FSSClE

As for the gradient norms, where to begin? The TS as always is at IRC =0.0 But in between it and the start and end points one can see no less than THREE “hidden intermediates“. Two of them are in fact exactly cis (IRC=3.5) and trans (IRC = 5.0) planar forms of F-S-S-Cl. At these points, the pathway is clearly achiral! The third (IRC = 1.0) is a fascinating species in which the S-S bond is largely broken and it is bridged by an F. So this pathway involves S-S cleavage, just like 2. It is entirely serendipitous; no-one in their right mind would actually set out to find it! 

FSSClEG

Well, since 2 as a template led to the above, what happens when 4 is used? For F migrating[3] a barrier 11.6 kcal/mol higher is found than for Cl migrating[4], similar to that previously reported.[1]

FSSClpa

The energy and gradient norm profiles, in comparison to the previous, are uneventful.[5] The S-S bond stays intact throughout, and it is shorter at the transition state (1.846Å) than at  the start (1.950Å) or the end (1.874Å). This reaction has got its feet on the ground, rather than its head in the clouds!

FSSClpaG FSSClpaE

I am reminded of stories our crystallographer here tells. Students bring him synthesized molecules for their structures to be determined, and quite frequently it’s not at all the compound that was desired. For not a few highly focused students, the compound is quickly forgotten, even though it may have turned out to be very unusual. Likely it will not be deposited into a repository. And how many compounds that might otherwise have been the catalyst for new and unusual discoveries are thus lost?  So never throw away an unexpected result (yes, even a calculation).  There is probably something you could learn from it! 

References

  1. P.V.R. Schleyer, and M. Mauksch, "Demonstration of Chiral Enantiomerization in a Four‐Atom Molecule", Angewandte Chemie International Edition, 2000. http://doi.org/d8g2nw
  2. H.S. Rzepa, "Gaussian Job Archive for ClFS2", 2013. https://doi.org/10.6084/m9.figshare.801866
  3. H.S. Rzepa, "Gaussian Job Archive for ClFS2", 2013. https://doi.org/10.6084/m9.figshare.803096
  4. H.S. Rzepa, "Gaussian Job Archive for ClFS2", 2013. https://doi.org/10.6084/m9.figshare.802822
  5. H.S. Rzepa, "Gaussian Job Archive for ClFS2", 2013. https://doi.org/10.6084/m9.figshare.802821

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A conflation of concepts: Conformation and pericyclic.

Thursday, January 10th, 2013

This is an interesting result I got when studying the [1,4] sigmatropic rearrangement of heptamethylbicyclo-[3.1.0]hexenyl cations. It fits into the last lecture of a series on pericyclic mechanisms, and just before the first lecture on conformational analysis. This is how they join.

14me

The experiment it relates to[1] may well be a contender for the top ten list of most influential experiments ever conducted in chemistry. At -40°C, the 1H NMR spectrum of this species has three peaks, at δ2.06, 1.57 and 1.13 ppm with an integral ratio of 15:3:3. The five basal methyls are averaged to 2.06 ppm, whereas those marked above as Mea and Meb exhibit distinct separate resonances. At -90°C, the five basal methyls split into peaks at δ2.48, 2.02, 1.66, in the integral ratio of 6:3:6. This indicates a process that is slow at the lower temperature but becomes fast (on the NMR time scale) at the higher temperature. The process must retain the individual identity of Mea and Meb.

The explanation is of course that a pericyclic [1,4] sigmatropic shift occurs. As a four electron process, this must have one antarafacial component, and this is by far easier to achieve by inverting the configuration at the migrating carbon centre. To convince oneself that this process does indeed retain the individual identity of Mea and Meb, an IRC of the reaction can be computed (ωB97XD/6-311G).

Click for 3D.

The energy profile is smooth and springs no surprises. The barrier is about right for the temperatures noted above. 14meE

But the RMS gradient norm along the IRC is unexpected. 14meG

  1. Between the limits IRC ± 9, the profile is that of a reaction, involving bonds breaking and forming.
  2. In the range IRC ± (9 – 15), unexpected features appear (hidden intermediates if you check this post). A whole plethora of them. This is the conformational region where the methyl flags start waving (and no bonds are formed or broken). If you watch the animation above very carefully, you will note that the methyl groups start rotating at the start and at the end of the migration, at a stage when the ring has an allyl cation. This delocalised cation has a different impact upon the conformation of the methyl groups from that of the transition state, where the charge now resides largely on the migrating carbon, and the ring now has just a neutral butadiene. This latter imparts a different conformational preference upon the methyl groups. You can see an orbital analysis of these effects at this post.
  3. But perhaps the most surprising aspect of all of this is that each methyl flag waves at a different time from the others; first one waves, then the second and then the third. The two remaining basal methyls (attached to sp3 carbons) do not wave at all.

So this classic reaction is not just a pericyclic exemplar, it also illustrates nicely and concisely the conformational analysis of methyl groups interacting with an unsaturated system. Two for the price of one so to speak.

References

  1. R.F. Childs, and S. Winstein, "Ring opening and fivefold degenerate scrambling in hexa- and heptamethylbicyclo[3.1.0]hexenyl cations", Journal of the American Chemical Society, vol. 90, pp. 7146-7147, 1968. https://doi.org/10.1021/ja01027a059

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Secrets of a university tutor. An exercise in mechanistic logic: second dénouement.

Monday, October 29th, 2012

Following on from our first mechanistic reality check, we now need to verify how product A might arise in the mechanism shown below, starting from B.

This pathway backtracks the original one in reversing the final arrow of that process (shown in red in previous post and in magenta here for the arrow in reverse), to go uphill in energy to reach the secondary (unstabilised) carbocation. This turns out to be a very shallow minimum, almost merely a ledge on the mountainside. It is not difficult to see how the original pathway down to B’ might have missed this Y-fork (= bifurcation).

Transition state for cyclopropyl ring opening. Click for 3D.

This unstable carbocation does not hang around; the barrier to transfer of a hydrogen (orange arrows) is tiny. This motion completes the formation of the product A.

We have seen here a classical analysis of mechanism in terms of an energy profile that has a separate pathway and associated transition state for each product in a reaction. But one should note that there are increasing claims for reactions whose outcome is determined not by an explicit transition state for each reaction pathway, but where the very dynamics of the system as it exits from a single transition state can result in a bifurcation into two (or indeed more) final products. I would like to suggest that the reaction described here might also be such an example. Thus although the mechanism as shown below shows just the single product B, it might be that only a small diversion from that initial pathway would also result in formation of A, and that there would be no need for the explicit transition states to this species as shown above to be actually visited.

It would finish by noting that all the mechanisms above were studied with inclusion of the triflate counter-ion; indeed the first step could not really be studied without it. The system seems a good candidate for a thorough molecular dynamics exploration;  I have certainly come a long way from an introductory tutorial in organic chemistry!

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