Posts Tagged ‘Reaction Mechanism’

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The “unexpected” mechanism of peroxide decomposition.

Sunday, November 18th, 2012

A game chemists often play is to guess the mechanism for any given reaction. I thought I would give it a go for the decomposition of the tris-peroxide shown below. This reaction is known to (rapidly, very rapidly) result in the production of three molecules of propanone, one of ozone and a lot of entropy (but not heat).[1]

The conventional approach might be to try to push some sensible arrows (an approach not always followed up it has to be said, by a reality check using quantum mechanics). I found the arrows that emerged from my playing interesting for the following reasons. 

  1. One scheme might be a process involving six arrows (twelve electrons), which leads directly to the products.
  2. Or, one might try to group the arrows into two sets of three (shown in green and red above). A moment’s consideration suggests that the green set has to precede the red set (if not concurrent), resulting in the initial production of two molecules of propanone and the tetraoxapentane derivative shown. This new molecule then suffers a simple 2+4 pericyclic cycloelimination as the second stage.
  3. It is possible of course that the process may simply consist of homolytic O-O cleavages via biradicals. I will defer discussing this point until later. 

The reality check would then consider whether the two processes are consecutive or concurrent. The following is computed at the wB97XD/6-311G(d,p) level, and corresponds clearly to the three green arrows shown above (no motion corresponding to the red arrows is discernible) and hence would be a consecutive process with a distinct intermediate on the path. The IRC seems to support this.

Saddle point for decomposition. Click for first imaginary vibration.

Saddle point for decomposition. Click for second imaginary vibration.

IRC for apparent concerted decomposition.

The diagram is shown twice above, because this geometry is in fact not a transition state but a second-order saddle point, with two imaginary vibrations. The first corresponds to the green arrows, but the second represents an asymmetric diversion to a quite different path. This second imaginary vibration can be followed in two directions, each potentially leading to a new lower energy saddle point. I was only able to locate one of these, shown below (if I track down the other,  I will append it).

Transition state for initial fragmentation. Click for 3D.

IRC for blue arrows. Click for 3D

IRC for orange arrows. Click for 3D.

As it happens, this corresponds to a rather different partitioning of the electron arrows, into a group of two first (blue) followed by four (orange). The first (proper) transition state is 5.0 kcal/mol lower in ΔG than the second order saddle point. The second transition state is 16.3 kcal/mol lower than the first. The intermediate in this process is actually different from the one shown earlier, but it can also eliminate ozone and two molecules of propanone.

What have we shown thus far? That one’s naive arrow pushing may in fact not come up with the goods. But how about that reality check? Whoops! Look at that activation barrier. The free energy (which is lower than the barrier itself because of the large +ve entropy of the reaction) is still a whopping 70 kcal/mol. 

So the conclusion from all of this? Well, that homolytic pathways, involving a cleavage of an O-O bond to produce a biradical, are very probably the real mechanism after all. Something like the below perhaps? (OK, so you might have told me that at the outset!).

As milestones go, this is my 250th post.

References

  1. F. Dubnikova, R. Kosloff, J. Almog, Y. Zeiri, R. Boese, H. Itzhaky, A. Alt, and E. Keinan, "Decomposition of Triacetone Triperoxide Is an Entropic Explosion", Journal of the American Chemical Society, vol. 127, pp. 1146-1159, 2005. https://doi.org/10.1021/ja0464903

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Thalidomide. The role of water in the mechanism of its aqueous racemisation.

Saturday, November 10th, 2012

Thalidomide is a chiral molecule, which was sold in the 1960s as a sedative in its (S,R)-racemic form. The tragedy was that the (S)-isomer was tetragenic, and only the (R) enantiomer acts as a sedative. What was not appreciated at the time is that interconversion of the (S)- and (R) forms takes place quite quickly in aqueous media. Nowadays, quantum modelling can provide good in-silico estimates of the (free) energy barriers for such processes, which in this case is a simple keto-enol tautomerism. In a recently published article[1], just such a simulation is reported. By involving two explicit water molecules in the transition state, an (~enthalpic) barrier of 27.7 kcal/mol was obtained. The simulation was conducted just with two water molecules acting as solvent, and without any additional continuum solvation applied. So I thought I would re-evaluate this result by computing it at the ωB97XD/6-311G(d,p)/SCRF=water level (a triple-ζ basis set rather than the double-ζ used before[1]), and employing a dispersion-corrected DFT method rather than B3LYP.

Keto-enol tautomerisation occupies a unique position in the history of mechanistic chemistry[2]. In 1889, Beckmann got the whole field rolling by proposing an inferred enol intermediate (which he did not observe) to explain the isomerism of menthone to iso-menthone in conc. sulfuric acid. In modelling the enolisation of thalidomide, I have used both implicit and explicit solvents acting in a self-consistent manner. This approach is not yet much adopted in the wider literature[3]. I have deployed it extensively in this blog as an encouragement to others (selected examples are listed at the bottom of this post). It is worth noting at the outset that the transition state reported previously[1] has a computed dipole moment of ~10D. My experience[3] suggests that any geometry with a dipole moment of this magnitude (or greater) is likely to relax when placed into a continuum field, and this relaxation becomes an important perturbation of both the computed geometry of the transition state and the intrinsic reaction coordinate profile computed from that starting point.

The (re)computed geometry of the aqueous transition state for enolisation of thalidomide is shown below, and for which the entropy-corrected ΔG†298 is 31.0 kcal/mol (the barrier for the prototypical enolisation of propanone is computed as 34.4 kcal/mol). The value in the literature[1] is given as 27.7 kcal/mol for the zero-point-energy corrected total energy barrier, but this value notably does NOT include any entropic corrections. The measured literature value for ΔG†298 is reported as 24.3 kcal/mol at pH 8, a value which probably also includes contributions from both the pure water catalysed route and those from hydroxide anion catalysis (see below). At this point, I should remind that the free energy of activation for a bi- or termolecular reaction in solution must be obtained by correcting the value obtained for a standard state of 1 atmosphere (the state used for the value quoted above). According to Alvarez-Idaboy and co-workers[4], this amounts to a total correction of -4.5 kcal/mol for a bimolecular reaction, and -8.73 kcal/mol for a termolecular reaction. Where one of the components of a termolecular reaction is also the solvent, these corrections probably need to be themselves reduced. But this does achieve a reduction in the computed value of 31.0 kcal/mol to something quite close to the experimental value! 

Aqueous transition state for enolisation of thalidomide. Click for 3D.

Next, I want to consider the base-catalysed enolisation pathway. As with the reaction of dichlorobuteneone with tolyl-thiolate about which I wrote in another post, the authors of the thalidomide study[1] modelled this route by introducing a solvated hydroxide anion, “OH–·H2O” into the structure without any accompanying counter-ion. In other words, their total system has an overall negative charge. I argued before, and I argue again here, that there is no real need to have to do this. Why not for example introduce NaOH•H2O instead? One might argue that the cationic counter-ion so introduced cannot be properly modelled, but the combination of explicit first-sphere water molecules coupled with a continuum model actually handles these counter-ions reasonably well. So may I introduce you to my version of the base-catalysed reaction, involving a contact-ion-pair:

Base-catalysed (NaOH) enolisation of thalidomide. Click for 3D.

This has ΔG†298 4.7 kcal/mol, much lower than the neutral water catalysed reaction. This value is of course for a standard state for [Na+OH–] (1 atm). At pH 8, [OH–] is at least six orders of magnitude less, which may rationalise why the experimental rate is so much slower than this barrier might imply. The IRC corresponds to proton transfer.

I would like to end by noting that many mechanisms which would otherwise involve the development of charge-separation may well borrow a protic solvent molecule in the manner shown here to reduce the degree of charge-separation needed.  Further examples of this are listed below.

  1. Oxime formation from hydroxylamine and ketone. Part 2: Elimination.
  2. Oxime formation from hydroxylamine and ketone: a (computational) reality check on stage one of the mechanism.
  3. Transition state models for Baldwin dig(onal) ring closures.
  4. Transition state models for Baldwin’s rules of ring closure.
  5. The mechanism (in 4D) of the reaction between thionyl chloride and a carboxylic acid.
  6. Mechanism of the diazomethane alkylation of a carboxylic acid.
  7. The mechanism of the Baeyer-Villiger rearrangement.
  8. Stereoselectivities of Proline-Catalyzed Asymmetric Intermolecular Aldol Reactions.
  9. Secrets of a university tutor: tetrahedral intermediates.

References

  1. C. Tian, P. Xiu, Y. Meng, W. Zhao, Z. Wang, and R. Zhou, "Enantiomerization Mechanism of Thalidomide and the Role of Water and Hydroxide Ions", Chemistry – A European Journal, vol. 18, pp. 14305-14313, 2012. https://doi.org/10.1002/chem.201202651
  2. E. Beckmann, "Untersuchungen in der Campherreihe", Justus Liebigs Annalen der Chemie, vol. 250, pp. 322-375, 1889. https://doi.org/10.1002/jlac.18892500306
  3. J. Kong, P.V.R. Schleyer, and H.S. Rzepa, "Successful Computational Modeling of Isobornyl Chloride Ion-Pair Mechanisms", The Journal of Organic Chemistry, vol. 75, pp. 5164-5169, 2010. https://doi.org/10.1021/jo100920e
  4. J.R. Alvarez-Idaboy, L. Reyes, and J. Cruz, "A New Specific Mechanism for the Acid Catalysis of the Addition Step in the Baeyer−Villiger Rearrangement", Organic Letters, vol. 8, pp. 1763-1765, 2006. https://doi.org/10.1021/ol060261z

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Secrets revealed for conjugate addition to cyclohexenone using a Cu-alkyl reagent.

Sunday, November 4th, 2012

The text books say that cyclohexenone A will react with a Grignard reagent by delivery of an alkyl (anion) to the carbon of the carbonyl (1,2-addition) but if dimethyl lithium cuprate is used, a conjugate 1,4-addition proceeds, to give the product B shown below. The standard explanation is that the alkyl copper is a “soft” nucleophile attacking the soft conjugate carbon, whereas the alkyl magnesium is a “hard” nucleophile attacking the hard carbonyl carbon. Is this the best explanation? 

In 2007, one of those wonderfully simple experiments was done[1]. The dimethyl lithium cuprate reagent (dissolved in THF) was injected into an NMR sample tube at -100°C containing A, and the spectrum measured immediately. The species identified as 4 (the numbering as used in the reference) has two 1H methyl resonances[2] at ~ -0.04 to – 0.23 ppm (assigned to Meβ) and -1.08 to -1.11ppm (assigned to Meα), and the copper coordinates to the alkene as a π-complex. If TMS cyanide is added, 4 is immediately converted to complex 1, in which the π-complex is replaced by a simple C-Cu σ-bond. Compound 4 upon heating gives B, whilst 1 gives the silyl enol ether of B.

How does this match quantum simulation[3]? First, the 1H NMR result for 4 (at the wB97XD/6-31G(d,p)/SCRF=THF level and with the lithium coordinated to an ether solvent) comes out as -1.4 ppm (Meα) and -0.31 ppm (Meβ). The 13C is 76.4 and 60.6 ppm for the vinyl carbons (positions 3 and 4, obs) and 64.5/56.7 (calc). These latter values are affected by spin-orbital coupling to the metal, which can shift the values by up to about 10 ppm[4], but the relative values are also in good agreement. So the reaction must proceed starting from this π-copper complex.

The IRC reveals a concerted transfer of  Meβ to the conjugate 4-position of B, with a reasonable barrier to reaction which indicates that on warming to room temperatures, the complex 4 will readily react. Formally at least, this corresponds to reductive elimination from the Cu(III) species to form a Cu(I) complex (in which however the metal now coordinates to the enol double bond rather than the alkene).

IRC for methyl transfer. Click for 3D transition state.

I will deal with the case of methyl transfer from 1 in a later post. With 4, we can directly see that the origins of conjugate 1,4-addition an α,β-unsaturated ketone are that the Cu reagent forms a π-complex to the alkene, which positions one of the alkyl groups on the metal in the ideal position to attack in conjugate manner. Regarding the different behaviour of the magnesium Grignard reagent, it boils down to asking why it does NOT form a π-complex in this situation (I would note here that Mg-π-complexes are indeed known).

References

  1. S.H. Bertz, S. Cope, M. Murphy, C.A. Ogle, and B.J. Taylor, "Rapid Injection NMR in Mechanistic Organocopper Chemistry. Preparation of the Elusive Copper(III) Intermediate", Journal of the American Chemical Society, vol. 129, pp. 7208-7209, 2007. https://doi.org/10.1021/ja067533d
  2. S.H. Bertz, C.M. Carlin, D.A. Deadwyler, M.D. Murphy, C.A. Ogle, and P.H. Seagle, "Rapid-Injection NMR Study of Iodo- and Cyano-Gilman Reagents with 2-Cyclohexenone:  Observation of π-Complexes and Their Rates of Formation", Journal of the American Chemical Society, vol. 124, pp. 13650-13651, 2002. https://doi.org/10.1021/ja027744s
  3. H. Hu, and J.P. Snyder, "Organocuprate Conjugate Addition:  The Square-Planar “Cu<sup>III</sup>” Intermediate", Journal of the American Chemical Society, vol. 129, pp. 7210-7211, 2007. https://doi.org/10.1021/ja0675346
  4. D.C. Braddock, and H.S. Rzepa, "Structural Reassignment of Obtusallenes V, VI, and VII by GIAO-Based Density Functional Prediction", Journal of Natural Products, vol. 71, pp. 728-730, 2008. https://doi.org/10.1021/np0705918

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Mechanisms of carbon monoxide insertion reactions: A reality check on carbonylation of methyl manganese pentacarbonyl

Sunday, November 4th, 2012

When methyl manganese pentacarbonyl is treated with carbon monoxide in e.g. di-n-butyl ether, acetyl manganese pentacarbonyl is formed. This classic experiment conducted by Cotton (of quadruple bond fame) and Calderazzo in 1962[1] dates from an era when chemists conducted extensive kinetic analyses to back up any mechanistic speculations. Their suggested transition state is outlined below. Here I subject their speculations to a quantum mechanical “reality check“.

The mechanism as above, formally at least is a pericyclic insertion of a carbene into a C-Mn bond. As the preamble to studying the mechanism, the following related reactions are of some interest:

  1. The addition of dichlorocarbene to ethene (see this blog for IRC)
  2. The addition of dichlorocarbene to butadiene (see this blog for IRC)
  3. The addition of carbon monoxide to ethene, for which the IRC is shown below
  4. The even simpler insertion of carbon monoxide to H2, for which the IRC is shown below
  5. And finally the insertion of carbon monoxide to methane, which is the closest analogy for us here.
  6. Notice that all of these reactions are asymmetric, and that the two new bonds forming to the carbon do so very asymmetrically/asynchronously, albeit in a concerted manner.

You might conclude from the above that extending this to identifying the transition state for insertion of carbon monoxide into a C-Mn bond is almost bound to reveal something interesting. Well, I was not able to locate (at the ωB97XD/6-311G(d,p)SCRF=di-n-butyl ether level) the carbon monoxide insertion transition state proposed by Cotton and Calderazzo (which of course does not mean it does not exist). But my efforts instead led to the following different course for the reaction (which is actually covered by the original authors with the statement “a mechanism involving a rapid pre-equilibrium to form MeCOMn(CO)4 cannot be ruled out at this stage“). Thus TS1 expresses that pre-equilibrium.

  1. The first stage involves the migration of the methyl group from Mn to an adjacent carbonyl group via TS1 to form Int1.

    TS1. Click for 3D animation of transition mode.

  2. As the methyl group migrates to the adjacent carbonyl, it creates a putative vacant coordination site on the metal. This is re-occupied by the concerted formation of a C-H agostic interaction, exhibited by  Int1. This new interaction now blocks any attempt by free carbon monoxide to insert into that erstwhile vacant site.
    Mn-TS1-IRC
  3. Int1 now rearranges to form an isomer, Int2, in which the agostic C-H interaction is replaced by a Mn-π-interaction from the acetyl group. This creates trigonal bipyramidal coordination at the Mn. Int2 is 6.9 kcal/mol lower in free energy than Int1.

    Int2. Click for 3D.

  4. A free carbon monoxide now attacks this intermediate via TS2 to coordinate onto the metal to reform octahedral coordination and complete the carbonylation reaction, and in the process converting the C=O π-complex into a Mn-C σ-complex.

    TS2. Click for 3D.
  5. TS2, as with the transition state for alkene metathesis, reveals that bond formation between the incoming carbon of the carbon monoxide and the Mn has not yet started (3.05Å). Instead the barrier is largely induced by the need to reorganise the ligands present on the metal before new bonds can form.
  6. Which of TS1 (+ CO) or TS2 is higher in free energy? Using di-n-butyl ether as the simulated solvent, TS2 emerges as the higher by 4.2 kcal/mol.It is so in part because of the greater loss of entropy at the transition state for this latter geometry. In fact, the kinetics reported by Cotton and Calderazzo (ΔG‡303 20.6 kcal/mol, ΔS‡ -21.1 cal/mol) indicate the reaction is first order in [CO], which indeed implies that TS2 must be higher in energy (since TS1 does not depend on [CO]). The theory indicates ΔG‡298 16.4 kcal/mol, ΔS‡ -7.5 cal/mol for TS1 and ΔG‡298 20.6 kcal/mol, ΔS‡ -30.9 cal/mol for TS2. This level of agreement strongly supports the migration/addition pathway over the direct C-Mn insertion route.

I hope that by adding a layer of quantum mechanical interpretation to the original synthetic and kinetic study, we can learn a bit more about what sounds like a very simple reaction, but which has turned out to have wonderful and subtle twists and turns.

References

  1. F. Calderazzo, and F.A. Cotton, "Carbon Monoxide Insertion Reactions. I. The Carbonylation of Methyl Manganese Pentacarbonyl and Decarbonylation of Acetyl Manganese Pentacarbonyl", Inorganic Chemistry, vol. 1, pp. 30-36, 1962. https://doi.org/10.1021/ic50001a008

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

Sunday, October 28th, 2012

The reaction described in the previous post (below) is an unusual example of nucleophilic attack at an sp2-carbon centre, reportedly resulting in inversion of configuration[1]. One can break it down to a sequence of up to eight individual steps, which makes teaching it far easier. But how real is that sequence?

Starting with the first of these steps, the heterolytic cleavage of the C-OTf bond to form a vinyl carbocation.The transition state, located at the ωB97XD/6-31G(d,p)/SCRF=ethanol level, reveals a more complex process in which the alkene assists in the eviction of the triflate leaving group and for which the immediate product is the carbocation precursor of molecule B, not A.

Transition state for C-OTf heterolysis. Click for 3D.

IRC for C-OTf heterolysis. Click for final product.

The IRC shows that the bonds all cleave/form at different times. 

  1. From IRC 12-5, a conformational reorganisation occurs to prepare the alkene for assisting in the …
  2. C-OTf heterolysis, which is largely complete at the transition state (IRC=0.0) with a C-O bond length of 2.7Å (green arrow). The potential energy surface at the transition state is unusually flat; the imaginary reaction mode, νi has the very low value for a reaction involving cleaving bonds of 90 cm-1. The putative C-C bonds which are about to form are still very long (3.0, 3.1Å) and the transition state is quite close to instead being a vinyl carbocation intermediate. Similar behaviour was computed for the purported Sn1 solvolysis of tert-butyl chloride, in which the tertiary carbocation is not an actual intermediate on the reaction path but is instead a transition state for the reaction.
  3. At IRC -4, the first C-C bond is forming (blue arrow), a process largely completed by IRC -7.5.
  4. At IRC -10, the second C-C bond is forming (red arrow).
  5. The initial product of this process is the ion-pair deriving from molecule B.

I want to spend a little more time with the transition state for the substitution process described above.

  1. Firstly, it is worth noting that it represents inversion of configuration at the reacting sp2-hybridised carbon atom, much like that which occurs for substitution reactions of sp3-hybridized carbon.
  2. A vinyl carbocation sounds exotic, but an iso-electronic species related to it in which boron replaces the carbon can in fact be crystallised. This makes for a neutral molecule, rather than the ion-pair involved in our reaction. An example is shown below[2]. As with our transition state, the angle subtended at the central atom is 180°. These types of system are also very reactive, which is why they can only be made if substituted with bulky groups, and one might presume that these boron analogues would also react readily with alkenes.

    VARJED. Click for 3D.

  3. One can go one step further and isolate a stable vinyl carbocationic ion-pair itself, as in the example shown below[3].

    LOKRIN. Click for 3D.

  4. One can also learn from looking at the orbitals of our transition state. The NBO (natural bond orbital) shows a very prominent interaction between the alkene acting as a π-donor and the vacant p-orbital on the vinyl carbocation acting as an acceptor; almost a π-complex in fact, and on its way to making a three-membered ring (blue ≡ purple, red ≡ orange).

    Click for rotatable orbitals.

So we have learnt that the breakdown into small steps that I used for pedagogic reasons in order to understand how the reaction proceeds is in fact conflated into one single concerted mechanism forming the product B. But we also now know that although these steps occur in concerted fashion, they do not occur in a synchronous manner. So it is still worth breaking the reaction into these steps, one must simply recognise that they can occur consecutively, and without any explicit intermediates involved.

I will take a break here, and deal with the formation of the other product, molecule A, in the next post.

References

  1. T.C. Clarke, and R.G. Bergman, "Olefinic cyclization at a vinyl cation center. Inversion preference for intramolecular nucleophilic substitution by a double bond", Journal of the American Chemical Society, vol. 94, pp. 3627-3629, 1972. https://doi.org/10.1021/ja00765a062
  2. R. Boese, P. Paetzold, A. Tapper, and R. Ziembinski, "Alkylalkylidenborane R  BC(SiMe<sub>3</sub>)<sub>2</sub>: Isolierbare Moleküle mit zweifach koordiniertem Sextett‐Boratom", Chemische Berichte, vol. 122, pp. 1057-1060, 1989. https://doi.org/10.1002/cber.19891220607
  3. A. Klaer, W. Saak, D. Haase, and T. Müller, "Molecular Structure of a Cyclopropyl Substituted Vinyl Cation", Journal of the American Chemical Society, vol. 130, pp. 14956-14957, 2008. https://doi.org/10.1021/ja8069055

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Secrets of a university tutor. An exercise in mechanistic logic, prequel.

Saturday, October 27th, 2012

The reaction below plays a special role in my career. As a newly appointed researcher (way back now), I was asked to take tutorial groups for organic chemistry as part of my duties. I sat down to devise a suitable challenge for the group, and came upon the following reaction[1]. I wrote it down on page 2 of my tutorial book, which I still have. I continue to use this example in tutorials to this day, some 35 years later.

The challenge is to find a mechanistic explanation for the formation of products A and B. It is an exercise largely in perception and logic, with application of some chemical knowledge of carbocations and their (relative) stability.

  1. The first stage is to try to map the starting molecule to each of the products, and to do this the relevant atoms are numbered (it can be an arbitrary numbering scheme, but it should be consistent across all three molecules). One perceives that the numbers can be anchored to the two methyl groups present in all three molecules; they do not seem to play a role in the mechanism and we also take an informed guess that they do not migrate relative to each other.
  2. At this point, students normally ask what OTf is. It is in fact triflate, derived from triflic acid or trifluorosulfonic acid; CF3SO2OH. One can digress at this point into a discussion of acidity and pKa values. The essential conclusion that emerges is that it must be a very strong acid since the triflate anion is very highly stabilised by the electronegative groups present. In other words, the C-OTf bond must easily dissociate into triflate anion, leaving behind a carbocation.
  3. The next stage is to prepare a list of all the bond changes that must occur during the mechanism.
    1. The most obvious is to declare that C6-0 cleaving bond in the reactant,
    2. replacing it by formation of C5-O bonds in A and B.
    3. Reduce the bond order of C5-C6 to one.
    4. Increase the bond order of C1-C6 from zero to one to form A.
    5. Increase the bond order of C1-C6 from one to two to form A. Note that we do this in two explicit steps since (with only a few exceptions), bonds rarely change their order by more than one in any distinct mechanistic step.
    6. Reduce the bond order of C2-C1 to one.
    7. The above transforms were all overtly explicit; one sees in the diagram what needs to be done. The next two steps require perception of the implicit information in the diagram. It can take a while to spot that C1 has to lose a hydrogen atom to form A.
    8. And that the hydrogen so removed has to be added to C2 to form A.

    A list for B could be constructed along similar lines.

  4. Now it is time to choreograph these changes. One is helped in these decisions by the knowledge that one cannot, even temporarily, increase the valence of any carbon beyond four, but one can decrease it to three if it becomes a carbocation.
    • One will also spot that the list of eight items above can be grouped into pairs. Thus implementing items 4 and 6 as a pair requires just one arrow to be pushed to form intermediate A1. Item 6 defines the start point for the arrow and item 4 the end point.
    • A digression into carbocation stability is now required to explain the driving force for this arrow. The vinyl cation that is formed by loss of the triflate anion is very unstable. This is because the carbon contributes to the C-OTf bond via an sp2 hybrid orbital. The high s character of this hybrid means that the shared electron pair in this bond is more strongly attracted by the carbon nuclear charge, and hence are less easily lost to form a carbocation than would be the case with e.g. a C(sp3)-O bond. This boils down to stating that a vinyl carbocation is less stable than an alkyl carbocation, and hence that forming the latter from the former will be exothermic.
    • Another pair from the to-do list can be selected, 7 and 8. We must convert two implicit into two explicit hydrogen atoms to do this step. Again, a single electron arrow is required, and we get to A2. The driving force for this step is the conversion of a secondary isolated carbocation into a secondary allylic carbocation, which is resonance stabilised with an adjacent bond.
    • This leaves items 3 and 5, but we use them to illustrate the resonance stabilisation. A2 and A3 are resonance forms, and so we do not use the normal reaction arrow, but use a resonance arrow instead. This resonance form is in fact favoured because it converts a secondary carbocation into the more stable tertiary ion.

At this stage, the sequence can be completed with step 2. I will leave it to you, the reader, to work out the sequence of events required to form B rather than A if you wish.

Over the years, I have confronted groups of students with the reaction scheme shown at the top of this post, and asked them to work out the mechanism. Most look quite petrified, and certainly mystified, at this stage. Shown as at the top, it is indeed an intimidating mechanism. But by breaking it down into small and very simple steps, and then working out the order in which to implement them, most students come away from this exercise thinking it was actually rather easy! 

But I end this post with my real agenda! Is the above sequence actually supported by the “reality check” of quantum mechanics. Is the reaction likely to happen as I have dissected it above? Well, in all the years I have used it as an example of mechanism in organic chemistry, I had never subjected it to this test. In the next post, I will reveal what I discovered when I did so.

References

  1. T.C. Clarke, and R.G. Bergman, "Olefinic cyclization at a vinyl cation center. Inversion preference for intramolecular nucleophilic substitution by a double bond", Journal of the American Chemical Society, vol. 94, pp. 3627-3629, 1972. https://doi.org/10.1021/ja00765a062

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How is the bromination of alkenes best represented?

Sunday, October 14th, 2012

I occasionally delve into the past I try to understand how we got to our present understanding of chemistry. Thus curly arrow mechanistic notation can be traced back to around 1924, with style that bifurcated into two common types used nowadays (on which I have commented and about which further historical light at the end of this post). Here I try to combine these themes with some analysis of wavefunctions for a particularly troublesome reaction to represent, the dibromination of an alkene, which I represented in the previous post as shown below.

However, that first step in the mechanism (red box above) has been represented in two other ways in the past. The green box used to be common, but is now being superseded by the magenta style (as for example here). 

I should first explain (what I think is) the intent of these three schemes (this is not really declared very formally, and so I am interpreting rather than stating):

  1. The green scheme, showing two arrows, attempts to illustrate a nucleophile (the alkene pπ electrons) interacting with an electrophilic acceptor (the Br-Br σ* bond) in a filled/empty orbital sense.
  2. The magenta scheme, showing three arrows, adopts a notation where a nucleophilic electron pair attacks an electrophilic atom centre to form a new bond between the two atoms.
  3. The red scheme has the nucleophilic electron pair terminating at the (approximate) bond centroid of the newly forming bond rather than at the atom.†

I set out to see what light quantum mechanics might be able to cast. To do so, I subjected the wavefunction of the system shown in the blue box above to analysis, which represents the species being formed as a result of the curly arrows pushed in the schemes above.

Firstly, QTAIM, which determines the topology of the electron density in the molecule. The green dots in this diagram are what are called “bond-critical-points”, or BCPs. The numerical values associated with each green dot are the electron density ρ(r) at that point.

Now, I have pointed out elsewhere that the existence of such a topological feature does not necessarily coincide with what we think of as a bond. With that caveat in mind, one can see that the BCPs reveal a cyclobromonium ring, with one C-C single bond (from the value of  ρ(r) ), two C-Br bonds, and a ring point (shown in red). The slightly weaker bond (again from the value of  ρ(r) ) is the one about to cleave as a result of the tribromide anion attacking the carbon, with inversion of configuration at that carbon. 

This picture does seem to correspond to our intuitive thoughts about mechanism. It offers a way of interpreting the arrow pushing scheme shown in red above. In this sense, an arrow would start at a BCP of a nucleophilic (donor) bond in the reactant, and terminate at the BCP of the acceptor bond formed in the product. Should we need to do so, we could derive precise 3D coordinates of the relevant BCPs, and ensure that our curly arrows either start or end precisely at those coordinates. This method would not allow for example the magenta scheme, since the terminating point of what is after all an electron arrow cannot be at a nucleus but needs to be at a bond (critical point). There is however one aspect un-answered. Both the red and magenta schemes have one arrow starting at an electron “lone pair”, and QTAIM does not give us coordinates for these! I will deal with this aspect last.

Yet another way of looking at it is to interpret the wavefunction in terms of pairs of (doubly) occupied and empty localised orbitals so that a donor-acceptor interaction energy can be derived. On to the NBO technique (natural bond orbitals), which tells us about the donor/acceptor interactions within a molecule. This relates to how the green box above might be viewed. When this is done, two sets of NBO orbital pairs are especially pertinent; each is a (doubly occupied) donor originating from the alkene (purple and orange) and an (empty) acceptor corresponding to the Br-Br cleaving bond (red and blue). In the overlay of two NBOs below, the purple (donor) and blue (acceptor) densities are overlapping in-phase to form a C-Br bond (arrow 1) Equally, overlap of an orange (donor) originating in part from a lone pair on bromine and the red acceptor (from the B-Br anti-bond) are forming the second C-Br bond (arrow 2). This actually corresponds more closely to the magenta than the green box. 

NBO Analysis. Click for 3D.

NBO Analysis. Click for 3D.

This brings us back to a deficiency of QTAIM; it does not tell us what kind of bonds we are dealing with. We might have presumed that the formed C-Br bonds of the bromonium ring (e.g. blue box) were single and hence two-electron bonds.

We have one more way of looking at bonds, and this method also allows us to count the electrons in the bond. Remember, a bond does not have to contain integer numbers of electrons! It can just as easily be fractional, as for example in PF5. ELF (the electron localisation function) is a way of looking at the properties of the electron density to identify localised spin-paired probabilities. The ELF technique partitions the function into discrete basins, and these can then be integrated for the total number of electrons defined by the ρ(r), the electron density. The centroids of these basins then give us something actually quite similar to the bond-critical-points from QTAIM theory, but carry two additional benefits. Firstly, the total electron count associated with each basin. Secondly, it also gives us the centroids of any lone pairs (which we identified as something helpful for defining either a start point or an end point of a curly arrow in arrow pushing). I show below the ELF analysis of the ion-pair intermediate of this bromination (i.e.the outcome of the arrow pushing in the red or magenta boxes). The red dots are basin centroids; there are lots of them but I concentrate only on the two marked with black arrows. They are the result of the donor-acceptor orbital overlaps, the principle one of which was shown above. These two ELF basins each have electron integrations of ~1e. Each C-Br “bond” contains only one shared (i.e. covalent) electron.

Click for 3D.

So which of the three schemes above is the most realistic? Well, the green scheme uses only one curly arrow in the carbon-bromine region, and so it carries the message that the bonds in this region only involve two electrons. The red scheme corresponds closely to the topology of the electron density involved in the reaction, but clearly, its arrows are NOT simple two-electron arrows. Neither are those of the magenta scheme, which seems rather to fall between two stools; it is not accurate topologically, but neither are its arrows simple two-electron arrows.

My conclusion must be a reminder that when we push curly arrows, we may not necessarily be able to associate these arrows with simple pairs of electrons. This is quite a subversive statement to make. But then again,surely the concept of curly arrow pushing, dating as it does from 1924, is overdue a makeover?

† Alan Dronsfield has contacted me with some information about when styles 2 and 3 might have bifurcated. Two particularly influential early text-books on mechanism, one published by Gould in 1959 and another by Sykes in 1961, appear to have adopted respectively the magenta and red schemes.

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Alkyne metathesis: a comparison with alkene metathesis.

Monday, October 8th, 2012

Metathesis reactions are a series of catalysed transformations which transpose the atoms in alkenes or alkynes. Alkyne metathesis is closely related to the same reaction for alkenes, and one catalyst that is specific to alkynes was introduced by Schrock (who with Grubbs won the Nobel prize for these discoveries) and is based on tungsten (M=W(OR)3).

In the previous post, I expressed surprise at the nature of the transition state for the alkene reaction, since the C-C or M-C bond (M=Ru) had hardly started to form by the time the transition state was reached. So what of the nature of the alkyne analogue? Firstly, I should mention that since the intention is to study the intrinsic reaction coordinate, which can be a lengthy calculation, it is necessary to prune the catalyst itself down to bare essentials. Unfortunately, it is now increasingly recognised that those sterically bulky groups that often adorn modern catalysts can in fact dramatically affect the nature of transition state. For one example where e.g. addition of bulky groups can transform a transition state to a minimum, see here[1] (and there may well be other examples of the reverse transformation of changing a minimum into a transition state). So with that caveat in place, take a look at the computed transition state (ωB97XD/Def2-SVPD/SCRF=dichloromethane) for a model where the t-Butoxy ligands of the real catalyst are replaced by simple OH groups.

Transition state for addition of alkyne to Schrock catalyst. Click for 3D

The C-W and C-C forming bonds are respectively 2.45 and 2.59 Å long; both are significantly shorter than those for the alkene transition state. The latter however had four ligands other than the incoming alkene to reorganise, whereas this one has one fewer. With less reorganisation needed, it can start forming bonds earlier.

The transition state leads to a fascinating product, being a metallacyclobutadiene. The carbocycle itself is of course famously transient and unstable (normally ascribed to its being anti-aromatic). In contrast, changing one carbon to tungsten makes the ring stable enough to be isolated as a crystal, one example of which is shown below (with an imine replacing one of the alkoxy groups). 

Crystal structure of a metallacyclobutadiene. Click for 3D.

This is an example where replacing an atom carrying a pπ orbital with one carrying a dπ orbital inverts the aromaticity rules. However, the alternating bond pattern characteristic of cyclobutadiene (and anti-aromaticity) remains visible in this structure. Thus the two C-C lengths in the X-ray structure below are 1.39 and 1.53Å, which perhaps corresponds to something like the following resonance form rather than implicating anti-aromaticity. More analysis is clearly needed here at some future stage. At any rate, the barrier for converting one bond-localized form into the other  (via TS2)  looks likely to be very small, and that the rate-determining-step is going to  be TS1/TS1′.

The intrinsic reaction coordinate appears thus, with the C-C forming only shortly after the W-C bond is formed.

Schrock IRC Schrock IRC

A postscript to the above. The IRC paths for these reactions are particularly difficult to compute; the secret lies in discovering the correct combination of parameters and step size to use. As a result, I have been able to chart a larger proportion of the IRC than initially reported.

  • The barrier to addition of ethyne is smaller than found previously for alkene
  • At IRC -5, we start to see several features (amplified in the gradient norm along the IRC) which correspond to conformational reorganisation of the hydroxyl groups attached to the metal
  • The final conformation of these matches the crystal structure shown in the post. This leads one to conclude that the conformation of these ligands may be crucial in determining the catalytic activity of the system
  • In the final conformation, the two C-C bond lengths are predicted as 1.41Å and 1.45Å. The crystal structure shows a rather greater asymmetry, but perhaps we can see the origins of this asymmetry as originating in the conformational re-orientation of the di-axial alkoxy groups. If you look at the IRC very carefully, you will notice that near the end, the W-OH groups start to strongly rotate. As they do so, the relative lengths of the two C-C bonds invert (ie the longer one ends up as the shorter one). This in turn implies that the orientation of the lone pairs on the oxygen controls the relative lengths of the two C-C bonds of the metallacyclobutadiene.
  • So the IRC in the end teaches us some very interesting stereoelectronic features of this catalytic system which deserve to be further investigated.

So this brief foray into metathesis chemistry seems to indicate that the attributes of the alkene and alkyne reactions are indeed rather different, most obviously in the amount of reorganisation in the ligand coordination geometry that each requires. The full story however is bound to only emerge when realistically sized ligands replace the simple small ones here.

References

  1. K. Abersfelder, A. Russell, H.S. Rzepa, A.J.P. White, P.R. Haycock, and D. Scheschkewitz, "Contraction and Expansion of the Silicon Scaffold of Stable Si<sub>6</sub>R<sub>6</sub> Isomers", Journal of the American Chemical Society, vol. 134, pp. 16008-16016, 2012. https://doi.org/10.1021/ja307344f

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Alkene metathesis springs a surprise.

Monday, October 1st, 2012

Alkene metathesis is part of a new generation of synthetic reaction in which a double C=C bond is formed from appropriate reactants where no bond initially exists (another example is the Wittig reaction), with the involvement† of a 4-membered-ring metallacyclobutane ring 1 (again, very similar to the Wittig). I thought it might make a good addition to my collection of reaction mechanisms and so as the first step I set about locating the transition state (TS or TS’) for the reaction, using in this case a model for Grubbs’ catalyst. I have located a fair few transition states in my time, and was frankly not expecting a surprise. This is the story that showed otherwise …

The reaction involves the formation of a C-C bond, and one can normally rely on that bond length being in the range 2.0 – 2.3Å. Thus the thermal 2+2 cycloaddition of two ethenes can have a C-C length of 2.0Å, albeit accompanied by a fascinating trapezoidal geometry. My initial thought was that this reaction might be similar. Using as the metal Ru (the one deployed for the Grubbs catalyst) the hunt proved to be unusual difficult. Eventually, it emerged (ωB97XD/Def2-SVPD/SCRF=dichloromethane) as shown below (I have deployed simple ammine ligands as replacements for the usually used pyridine, and chlorine around the metal; at this stage the subtleties of steric and electronic tuning of the catalyst are not needed). 

Transition state for alkene metathesis. Click for 3D.

The C-C bond is 3.0 Å, well outside the normal limit of forming C-C bonds. Indeed, at this length it has hardly started to form at all (neither has the Ru-C bond, at 3.4Å). So conventionally one would conclude it must be an early (very early) transition state, and such would also have a very small barrier to reaction (thus the barrier for cycloaddition between osmium tetroxide and propene is < 1 kcal/mol for an Os...O length of 2.36Å) But no, the IRC shows the barrier is around 14 kcal/mol (quite reasonable for a thermally facile reaction).

The IRC reveals all. Put simply, the initial Ru complex has a trigonal bipyramidal geometry. Such a shape has no free ligand site large enough to accommodate an incoming alkene. A free site can be however generated by changing the metal coordination to square pyramidal. So the initial approach of an alkene plays that role, by effectively repelling the Cl and Ru=CH2 ligands into the square pyramidal geometry. This process by the way is not dissimilar[1] to pseudorotation in PCl5. No C-C bond formation can happen whilst this geometrical reorganisation takes place (another example of high barriers induced purely by changes in bond angles is atropisomerism in taxol).

Reorganisation of ligands up to TS Formation of bonds after TS

It is only after the transition state is passed that the bond formation can start to take place. So this reaction takes place in two very distinct stages, a reorganisation of the coordination around the metal, and then bond formation. Why might this be interesting? Well, because designing a better catalyst requires knowledge of the intrinsic reorganisations involved, and the order in which they happen. One might imagine that such two-stage behaviour in catalysts is in fact not that unusual.

† Several ruthenium metallacyclobutanes have been isolated as crystalline solids. One example is shown below.

A ruthenium metallacyclobutane. Click for 3D.

Another example is the carbonylation of methyl manganese pentacarbonyl, which I will cover in a future post.

References

  1. M.E. Cass, K.K. Hii, and H.S. Rzepa, "Mechanisms That Interchange Axial and Equatorial Atoms in Fluxional Processes: Illustration of the Berry Pseudorotation, the Turnstile, and the Lever Mechanisms via Animation of Transition State Normal Vibrational Modes", Journal of Chemical Education, vol. 83, pp. 336, 2006. https://doi.org/10.1021/ed083p336.2

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