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The thermal reactions … took precisely the opposite stereochemical course to that which we had predicted. A non-covalent-interaction view of the model.

Wednesday, February 3rd, 2021

Another foray into one of the more famous anecdotal chemistry “models”, the analysis of which led directly to the formulation of the WoodWard-Hoffmann (stereochemical) rules for pericyclic reactions. Previously, I tried to produce a modern computer model of what Woodward might have had to hand when discovering that the stereochemical outcome of a key reaction in his vitamin B12 synthesis was opposite to that predicted using his best model of the reaction.

Vitamin B12 synthesis

Such computer models generate quite accurate 3D coordinates of the transition state for the reaction and this can be most simply analysed for finding e.g. steric clashes. These are when two atoms (mostly hydrogen) approach too close to one another. But we now know that in the region 1.9 – 2.4Å these close approaches can be attractive as well as repulsive and so distances alone are not the complete story. Here I analyse these models using a technique known as non-covalent-interactions (NCI). This is based on the electron density and its reduced density gradients♥ and it explores not merely simply distances between atoms but the non-bonded or weakly interacting regions of a molecule, generating a colour coded surface of interaction rather than pairwise distances. The colour coding goes from red (strongly destabilising, or repulsive regions) to blue (stabilising or attractive regions), with green representing weakly stabilising and yellow weakly destabilising. It gives a much more rounded picture of the entire molecule.

Disrotatory TS for G to H, Click for 3D

Conrotatory “TS” for G to J, Click for 3D

The NCI surfaces are shown above and are best expanded into a rotatable 3D model by clicking on either image. Regions of interest are shown with arrows. The region of the “steric clash” identified for the (thermal) transition state G to H (the one actually found by experiment) can be seen with the arrow in the top right.‡ It is colour coded light blue (attractive; note the very attractive dark blue for the O…HO hydrogen bond in the system), but it is immediately next to a yellow/orange region (repulsive). This again reminds us that “stabilising” and “destabilizing” regions of a molecule can be adjacent to each other, something that physical models cannot convey. The steric clash for the “transition state” G to J (in quotes because it is actually a transition state calculated for the excited triplet state and not the ground state) is indicated with the arrow, being a clash of two methyl groups. It is coded green, indicating weak NCI stabilization.

So, in this analysis, steric clashes become more complex as indicators of reaction outcomes, since it is the overall balance of stabilisation and destabilisation that determines this. You might argue that Woodward would have found this modern analysis far too woolly to be useful in the sense he used, which is as an alert for the possibility of a new principle in organic reaction mechanisms and certainly a Nobel prize for his collaborator Hoffmann!

‡The region of the C-C bond which is forming in this transition state has a very non-standard electron density, to which this analysis cannot really be applied. So that region should be disregarded for the “non-covalent” analysis being done here. ♥Plots a reduced density isosurface, colour mapped with ABS(ρ)*SIGN(λ2), where λ2 is the middle eigenvalue of the Hessian matrix of the electron density. A web page for generating such surfaces can be found at DOI: ftkt.

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The thermal reactions … took precisely the opposite stereochemical course to that which we had predicted

Wednesday, January 20th, 2021

The quote of the post title comes from R. B. Woodward explaining the genesis of the discovery of what are now known as the Woodward-Hoffmann rules for pericyclic reactions.[1] I first wrote about this in 2012, noting that “for (that) blog, I do not want to investigate the transition states”. Here I take a closer look at this aspect.

Vitamin B12 synthesis

I will start by explaining my then reluctance to discuss transition states. Woodward in describing this discovery (in Chem. Soc. Special Publications (Aromaticity), 1967, 21, 217; a historic article which unfortunately remains off-line) notes the “steric preference for attack below the plane for C-5 and a gentle spiral for the cyclization to achieve the required stereochemistry at C-6″. In reference to the diagram above, he is talking about the reaction G to J which he thought was favoured over G to H on steric grounds. We must now try to judge what criteria might have been used to establish these steric grounds. He might have been referring to the relative thermodynamic stabilities of H vs J, which is the aspect I addressed in my earlier blog. But it has now been pointed out to me‡ that Woodward is more likely to have been thinking about the transition state for the reaction, in referring to a “gentle spiral” for the reaction path as inferred by model building. So why my reluctance in 2012 to look at this aspect? As Woodward himself quickly came to realise, the transition state for G to H is electronically “allowed” but the transition state for G to J is electronically “forbidden”. Let me qualify that. The latter is only forbidden on the ground state electronic surface, but it is allowed on an open shell excited state (photochemical) surface. It is very difficult (if not impossible) to directly compare the energies of these two electronic states for any steric differences that might be hidden or embedded within them. So how did Woodward initially infer a “steric preference” between these two reactions?

Model building reached its peak as an essential tool for understanding chemistry in the 1950s, with the likes of Pauling and Watson + Crick making Nobel-prize winning discoveries using this technique. By the 1960s, one could buy commercial model building kits, such as Dreiding stereomodels (1958) which focused on the bonds themselves and CPK or spacefilling models (~1952[2]) based on the size of the atom (a technique pioneered by Loschmidt as long ago as 1860). I would point out that such models are constructed for molecules in their presumed ground electronic state! So Woodward must have been constructing models for G to H and G to J with the implicit assumption that they were in the ground electronic state. Clearly he noticed something which led him to conclude that these models predicted G to J over G to H. I do not know if his models have survived to posterity and are now in a museum somewhere; the chances are we will never know exactly what it was that alerted him that the formation of G to H was so unexpected that it triggered a Nobel-prize winning theory!

Having declined to build TS models in my original musings on this topic, I now decided to bite the bullet and try to now locate at least approximate models for both possible stereochemical outcomes. The disrotatory transition state for G to H is relatively trivial. Here I used the PM7 method, which I noted previously nicely absorbs dispersion corrections which may be important! It also allows a full IRC for the reaction path to be constructed in just a few hours (a DFT approach would take quite a lot longer). The FAIR data for my models can be found at DOI: 10.14469/hpc/7806

I then realised that the electronically “forbidden” transformation G to J (something that makes locating a transition state on the ground state surface unlikely) was in fact allowed for an open shell triplet state (a excited state). In this state, transition state location actually proceeds without issue to find a nice conrotatory transition state.

The two key transition state models are each shown below in two representations. The clashes noted are approaches of two atoms closer than the sum of the van der Waals radii. First, I note that transition state G to H clashes a hydrogen with the adjacent methyl group (H…H contact 1.937Å using the PM7 semi-empirical method, 1.942Å using the ωB97XD/6-311G(d,p) density functional method).†

G to H, ball and stick representation. Click to view 3D♥

G to H, spacefilling representation

G to J also exhibits a clash, albeit a lesser one, between the hydrogens of two methyl groups (2.01Å for PM7, 2.03Å for ωB97XD/6-311G(d,p)). So one could argue that G to J is indeed favoured on steric grounds over G to H, but only by about 0.07Å in the close approach of pairs of non-bonded hydrogen atoms. I also note that Woodward’s gentle spiral or spiral of low pitch is in fact a left-handed one!

G to J, ball and stick representation. Click to view 3D

G to J, spacefilling representation.

To get another perspective on what this means in reality, I conducted a search of the CSD (Cambridge structure database) for the sub-structure shown below:

The results show H…H contacts down to about 2.03Å, which suggests that the steric clash for G to H probably is slightly repulsive, whilst that for G to J could be on the verge of being attractive.

We might conclude that there is probably only a small steric difference between the two quantitative reaction models G to H and G to J as evaluated here, probably favouring the latter and assuming that the sterics are expressed entirely by van der Waals distances and have not been absorbed into bond angles etc. Of course much of what I have done and explained here was not common in the 1960s. The details of how Woodward’s models were actually constructed and how quantitative they were may never be discovered. It matters not of course, since the surprise of finding the actual product was H and not J went on to catalyse one of the great theories of organic chemistry!

‡My thanks to Jeff Seeman and Dean Tantillo for contacting me about this, inspiring the above revisitation and much interesting discussion; J. Seeman and D. Tantillo, “On the Structural Assignments Underlying R. B. Woodward’s Most Personal Data Point That Led to the Woodward-Hoffmann Rules. Related Research by E. J. Corey and Alfred G. Hortmann.”, Chem. Euro. J., 2021, in press. †As noted elsewhere on this blog, H…H contacts as short as 1.5Å have been measured experimentally. ♥To turn the 3D view of the molecule into a spacefill model, right-click in the model window and invoke Scheme/CPK Spacefill as shown below:

References

  1. R.B. Woodward, and R. Hoffmann, "Stereochemistry of Electrocyclic Reactions", Journal of the American Chemical Society, vol. 87, pp. 395-397, 1965. https://doi.org/10.1021/ja01080a054
  2. R.B. Corey, and L. Pauling, "Molecular Models of Amino Acids, Peptides, and Proteins", Review of Scientific Instruments, vol. 24, pp. 621-627, 1953. https://doi.org/10.1063/1.1770803

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Trimerous pericyclic reactions: what is the effect of changing the electron count by two?

Monday, November 2nd, 2020

In an earlier post, I pondered on how the “arrow pushing” for the thermal pericyclic reactions of some annulenes (cyclic conjugated hydrocarbons) could be represented in terms of either two separate electrocyclic reactions or of one cycloaddition reaction. Each reaction is governed by selection rules which can be stated in terms of the anticipated aromaticity of the pericyclic transition state as belonging to a 4n or a 4n+2 class. This in turn determines whether the topology of the transition state belongs to a class of aromatic species known as either Hückel or Möbius. Here I play with the observation that by adding or removing two electrons from the molecule, the two classes 4n and 4n+2 can be swapped. What happens to the aromaticities of the transition states if that is done?

The test bed is a [20]annulene, which might undertake either a eight electron (4n) 4s+4s cycloaddition in the inner ring, or two eight electron (4n) electrocyclic reactions in the outer rings in which the new bond is formed antarafacially from opposite faces. The selection rules suggest that the former must proceed through an anti or non-aromatic Hückel transition state and the latter through an aromatic Möbius transition state.

We are measuring the aromaticity by using the so-called NICS NMR method, for which an aromatic value is a negative chemical shift for the NICS probe, a non-aromatic value is ~0 and an anti-aromatic value a positive chemical shift. The location of these probes is determined by analysis of the critical points in the electron density of the transition states and placement at either the ring or the cage critical point so determined.

# System Charge ν(s) ν(a) NICS (outer rings) NICS (inner ring) ΔG DOI
1 trans, D2 0 -399 -433 -6.7 -0.3 -774.036424 7483
2 trans, D2 +2 -388 -399 +4.0 +2.1 -773.381567 7490
3 trans, D2 -2 -412 -324 -15.0 -12.9 -774.179873 7526
4 cis, Cs 0 -413 -369 -8.6 -5.4 -774.048172 7482
5 cis, Cs +2 -640 -453 +11.1 +2.1 -773.386424 7493
6 cis, C2 0 -491 -459 -8.3 +1.4 -774.059141 7486
7 cis, C2 +2 -685 -479 +10.5 +2.3/+3.7 -773.392100 7497
8 cis, C2 -2 -926 -533 +8.4 -13.9 -774.2029900 7525

Each of the stationary points located is in fact a saddle point of order 2 (and in some cases 3), with ν(s) corresponding to normal vibrational mode for synchronous formation of both bonds, and ν(a) to formation of one C-C bond but cleavage of the other. The fact that both the force constants for these modes are negative suggests that the two electrocyclic reactions are independent and occur consecutively rather than concurrently. This then argues against it being a synchronous cycloaddition reaction, but could of course still be a highly asynchronous one.

The first three examples are in fact for a [20]annulene with a central trans rather than cis double bond (as illustrated above), resulting in D2 symmetry. The neutral system has the outer ring aromatic (-ve NICS) and the inner ring non-aromatic, as appropriate for the rules stated above. Removing two electrons might you would imagine swap these two, but of course the electrons are removed from the entire [20]annulene as a whole, and not from specific regions. In fact it results in mildly anti-aromatic rings in both regions. Adding two electrons now makes the rings strongly aromatic, behaving as if the two electrons have really only modified the inner cycloaddition reaction.

The reactions with a cis stereochemistry at the central bond again confirm for the rules for the neutral annulene, but now the dianion predicts the outer ring to be anti-aromatic and the inner one aromatic, with a reversal of aromaticity for both sets of rings. Despite the cycloaddition now being an aromatic transition state, the force constants still indicate it to be asynchronous. But the observation that ν(s) is now significantly larger than ν(a) suggests that perhaps the reaction can indeed now be considered as at least in part an asymmetric cycloaddition. 

Click to view vibrational modes

What is the point of doing these calculations, you may well ask? Its unlikely that they could ever be subjected to experimental tests! Well, here we are using quantum mechanical calculations as an experimental procedure in its own right, to try to push the simple pericyclic selection rules beyond anything envisaged by its original formulators.

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Trimerous pericyclic reactions.

Thursday, October 8th, 2020

I occasionally spot an old blog that emerges, if only briefly, as “trending”. In this instance, only the second blog I ever wrote here, way back in 2009 as a follow up to this article.[1] With something of that age, its always worth revisiting to see if any aspect needs updating or expanding, given the uptick in interest. It related to the observation that there can be more than one way of expressing the “curly arrows” for some pericyclic reactions. These alternatives may each represent different types of such reactions, hence leading to a conundrum for students of how to label the mechanism. I had noted in that blog that I intended to revisit the topic and so a mere eleven years later here it is!

Annulenes, or cyclic conjugated polyenes can (hypothetically) indulge in transannular cyclisations which can be regarded as either two electrocyclic reactions, or one cycloaddition reaction, or perhaps a chimera of all three which here I describe as trimerous. Locating the transition states for such a trimerous reaction is quite straightforward and here I give the FAIR data DOI for all the examples shown below (DOI: 10.14469/hpc/7440).‡ The calculations are all at the B3LYP+GD3BJ/Def2-TZVPP level.

The central reaction can be represented as a cycloaddition in which two new bonds form between the termini of two conjugated alkenes. The stereochemistry for each alkene component is defined as either suprafacial (the two new bonds form to the same face of that alkene) or antarafacial (the two new bonds form on opposite faces of that alkene). Another way of representing the curly arrow mechanism is to draw to separate electrocyclic reactions, in which one new bond is formed between the termini of a conjugated alkene. If this bond connects at each end to the same face of that alkene, the bond forms suprafacially, if it connects opposite faces of that alkene it forms antarafacially. One must also count the number of cyclic curly arrows used in each representation; the examples above illustrate two, three or four curly arrows, representing four, six or eight electrons. One can now combine these attributes to form some selection rules.

For thermal reactions, one can state that if the total electron count represented by an odd number of curly arrows corresponding to the formula 4n+2 (n = 0,1,2, etc, the n is NOT the same as that shown in the scheme above) and there are either no (or an even number of) antarafacial components, the reaction will be “allowed” and proceed through a “Huckel aromatic transition state“. Alternatively, if the total electron count corresponds to an even number of curly arrows matching the formula 4n (n=1,2, etc) and there is one (or an odd number of) antarafacial components, the reaction will this time proceed through a “Mobius aromatic transition state“. These are in fact a concise alternative statement of the Woodward-Hoffmann selection rules for thermal pericyclic reactions.

Entry # n (scheme only) [ ]-Annulene
TS		  electron count
in each ring		 s/a
components		 NICS for each
ring centroid
1 0 10 endo 4,6,4 a,s+s,a -3.5,-15.3,-3.5
2 0 10 exo 4,6,4 a,s+s,a -2.8,-11.6,-2.8
3 0 12, saddle=1♠ 4,8,4 s,s+a,* -0.1,-10.3,-2.0
4 0 12, saddle=2 4,8,4 *,s+a,* -0.9,-10.7,-0.9
5 1 14 endo 6,6,6 a,s+s,a +2.2,-17.1,+2.2
6 1 14 exo 6,6,6 a,s+s,a +9.7,-11.1,+9.7
7 1 16 6,8,6 a,s+a,a +9.1,-9.6,+9.1
8 2 18 endo, saddle=1 8,6,8 s,s+s,a -2.0,-15.0,-♥
9 2 18 endo, saddle=2 8,6,8 *,s+s,* -0.5,-17.1,-0.5
10 2 18 exo,saddle=1 8,6,8 a,s+s,a -6.2,-4.5,-3.7
11 2 18 exo,saddle=2 8,6,8 a,s+s,a -8.2,-1.4,-8.2
12 2 20,saddle=3 8,8,8 a,s+*,a -8.5,+0.3,-8.5

♥No ring centroid in AIM analysis.♠The symmetrical geometry has two negative force constants (saddle=2), representing an asymmetric distortion to a true transition state (saddle=1).

For the reactions shown in the scheme above, we will determine the NICS (Nucleus independent chemical shift) value at the ring centroid of each reaction to ascertain the aromaticity in that ring. The effective ring centroid in turn is located by performing an AIM analysis of the topology of the electron density and locating the RCP (ring critical points in that density; a critical point itself is one where the first derivatives of the density with respect to the three cartesian coordinates is zero) or in several examples the CCP (Cage critical point). I will discuss some of these systems individually, but in fact there is a wealth of information available for each one and to discover it all, you should go to the data files and inspect all the structures for yourself. Firstly, the colour code in the table above:

  • In the s/a column, blue represents systems where the electrocyclic component forms a bond antarafacially. whereas the cycloaddition component forms both bonds suprafacially to both the alkene and the diene.
  • Red represents systems where the electrocyclic component forms a terminus bond antarafacially and the cycloaddition component forms a bond suprafacially to the alkene but antarafacially to the diene.
  • Where the π-system in the pericyclic transition state has a local orthogonality (i.e. the pericyclic π-system is locally twisted by 90°±6 at one point) it is not possible to confidently distinguish between supra and antarafacial. Such instances are declared non-aromatic and are shown in black.
  • In the NICS column, green represents an aromatic value and red an antiaromatic value. Black is effectively non-aromatic.

Individual entries

The way to read the table above is the following. In the 4th column (electron count in each ring, corresponding to the curly arrows representing the reaction at that ring), determine if the count belongs to the 4n or the 4n+2 rule.  Next for each ring, is the number of antarafacial components odd, or zero.† Finally, does the NICS aromaticity index match with the inference from the first two properties, i.e. 4n+2 + zero a = aromatic, 4n + odd a = aromatic and the corollary of 4n+2 + odd a = anti-aromatic, 4n + zero a = anti-aromatic.

Entry 1:  All three rings correspond to aromatic pericyclic transition states, but with the cycloaddition ring far more aromatic than the electroclisation rings. This is reflected in the bond lengths in the rings. The cycloaddition ring has lengths close to the “aromatic” value of 1.4Å. whereas the electrocyclic rings have highly alternating bond lengths. The calculated lengths correspond to the “cycloaddition” curly arrows in the scheme above and not to the “electrocyclic” arrows. This reaction does not have the characteristics of three simultaneous pericyclic reactions, or to use the parlance of the title of this post, it is not trimerous.

Click image to see 3D model.

Entry 6: This time, the central ring is again strongly aromatic (4n+2 + zero a = aromatic) but the two outer rings are strongly antiaromatic (4n+2 + odd a = anti-aromatic). Again the curly arrows correspond to cycloaddition and not electrocyclisation.

Click image to see 3D model.

Entry 11: As with entry 1, all three rings should again be aromatic (4n+2 + zero a = aromatic;4n + odd a = aromatic).In reality the bond lengths and  aromaticity indicate that this time the curly arrows are those of two concurrent electrocyclic reactions and NOT of one cycloaddition.  But there is a sting in the tail. This symmetrical system is NOT a true transition state. 

Click image to see 3D model.

Entry 10: This is the true transition state corresponding to entry 11, in which completion of one electrocyclic reaction preceeds the other; they are no longer synchronous but asynchronous, with one C-C bond (1.946Å) formed before the other (2.790Å). This pericyclic reaction can indeed be now considered trimerous, albeit with the three individual pericyclic reactions happening at different rates.

Click image to see 3D model

We can see that allowed pericyclic reactions in which three separate modes operate in concert (trimerous) are unlikely to happen. In effect the “aromaticity” tends to localise in one region rather than operate simultaneously in three rings. The collection of examples above also nicely illustrates the operation of the Woodward-Hoffmann rules as recast in terms of transition state aromaticity.

‡The original blog was also data rich, containing the encouragement to Click above to obtain model. It did not however cite the DOI of the repository entry for this data, an omission here rectified. †Or even, but no examples of this in the table.

References

  1. H.S. Rzepa, "The Aromaticity of Pericyclic Reaction Transition States", Journal of Chemical Education, vol. 84, pp. 1535, 2007. https://doi.org/10.1021/ed084p1535

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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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Computationally directed synthesis: 2,3-dimethyl-2-butene + NO(+).

Saturday, September 6th, 2014

In the previous posts, I explored reactions which can be flipped between two potential (stereochemical) outcomes. This triggered a memory from Alex, who pointed out this article from 1999[1] in which the nitrosonium cation as an electrophile can have two outcomes A or B when interacting with the electron-rich 2,3-dimethyl-2-butene. NO NMR evidence clearly pointed to the π-complex A as being formed, and not the cyclic nitrosonium species B (X=Al4–). If you are wondering where you have seen an analogy for the latter, it would be the species formed when bromine reacts with an alkene (≡ Br+, X=Br– or Br3–). The two structures are shown below[1] tetramethyletylene-NO+ Since the topic that sparked this concerned pericyclic reactions, it seemed possible that if it had been formed, species B would immediately undergo a pericyclic electrocyclic reaction to form the rather odd-looking cation C, which might then be trapped by eg X(-) to form the nitrone D. So this post is an exploration of what happens when X-NO (X= CF3COO, trifluoracetate) interacts with 2,3-dimethyl-2-butene, as an illustration of what can be achieved nowadays from about 2 days worth of dry-lab computation as a prelude to e.g. an experiment in the wet-lab (it would take a little more than two days to achieve the latter I suspect). Hence computationally directed synthesis. The model is set up as ωB97XD/6-311G(d,p)/SCRF=chloroform. A transition state is located[2] and the resulting IRC (below) [3] does not quite have the outcome the above scheme would suggest. NOa NOe NOg Neither A nor B is formed; instead it is the tetrahedral species E, which is ~15 kcal/mol endothermic. NOaa I should immediately point out that this is not inconsistent with the formation of A as previously characterised[1]. That is because this experiment was conducted with a non-nucleophilic counter-anion (X=Al4–), whereas in the computational simulation above, we have a nucleophilic anion (X= CF3CO2–). What a difference the inclusion of a counter-ion in the calculation can have! The barrier however (~35 kcal/mol) is a little too high for a facile thermal reaction. In the second of this two-stage reaction, E now ring-opens to form the anticipated D[4] with quite a small barrier of ~6 kcal/mol, but a highly exothermic outcome. I ask this question about it; can this still be described as a pericyclic process? (there is some analogy to the electrocyclic ring opening of a cyclopropyl tosylate). NObNObe So what are the conclusions? Well, because of the rather high initial barrier, the alkene will need activation (by electron donating substituents, perhaps OMe) for the reaction to become more viable. But if it works, it could be an interesting synthesis of nitrones (I have not yet searched to find out if the reaction is actually known).

References

  1. G.I. Borodkin, I.R. Elanov, A.M. Genaev, M.M. Shakirov, and V.G. Shubin, "Interaction in olefin–NO+ complexes: structure and dynamics of the NO+–2,3-dimethyl-2-butene complex", Mendeleev Communications, vol. 9, pp. 83-84, 1999. https://doi.org/10.1070/mc1999v009n02abeh000995
  2. H.S. Rzepa, "C8H12F3NO3", 2014. https://doi.org/10.14469/ch/24979
  3. H.S. Rzepa, "Gaussian Job Archive for C8H12F3NO3", 2014. https://doi.org/10.6084/m9.figshare.1162797
  4. H.S. Rzepa, "Gaussian Job Archive for C8H12F3NO3", 2014. https://doi.org/10.6084/m9.figshare.1162676

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Posted in pericyclic, reaction mechanism | 2 Comments »

Full circle. Stereoisomeric transition states for [1,4] pericyclic shifts.

Monday, August 18th, 2014

This post, the fifth in the series, comes full circle. I started off by speculating how to invert the stereochemical outcome of an electrocyclic reaction by inverting a bond polarity. This led to finding transition states for BOTH outcomes with suitable substitution, and then seeking other examples. Migration in homotropylium cation was one such, with the “allowed/retention” transition state proving a (little) lower in activation energy than the “forbidden/inversion” path. Here, I show that with two electrons less, the stereochemical route indeed inverts.mob-inva First, a [1,4] alkyl shift with inversion at the migrating carbon (ωB97XD/6-311G(d,p)/SCRF=chloroform); as a four-electron process, this is the “allowed” route.[1] mob-inva The “forbidden” route corresponds to retention of configuration at the migrating carbon.[2] mob-retb The barriers for each process can be seen below from the IRCs. That for inversion is ~4.5 kcal/mol lower than retention. This nicely transposes the values for the six-electron homologue shown in the previous post. mob-invmob-ret There is one more nugget of insight that can be extracted. The start/end-point for the six-electron process (homotropylium cation) was, as the name implies, homoaromatic. Now, with a four-electron system we also have an inverse. Nominally, we should now end with homo-antiaromaticity (but see [3]). But antiaromaticity is avoided whenever possible, and so the homoaromatic bond observed in homotropylium is not formed. It resolutely remains a σ-bond (1.48Å) thus sequestering two electrons, and the remaining two electrons simply form a delocalised allyl cation. With the six-electron homotropylium, reactant/product were stabilised by that additional (homo)aromaticity, thus inducing a relatively high barrier. With the four-electron system here, no such reactant/product stabilisation occurs, and hence the reaction barriers are now significantly lower. A rather neat pedagogic example.

References

  1. H.S. Rzepa, "Gaussian Job Archive for C8H11(1+)", 2014. https://doi.org/10.6084/m9.figshare.1142175
  2. H.S. Rzepa, "Gaussian Job Archive for C8H11(1+)", 2014. https://doi.org/10.6084/m9.figshare.1142174
  3. C.S.M. Allan, and H.S. Rzepa, "Chiral Aromaticities. A Topological Exploration of Möbius Homoaromaticity", Journal of Chemical Theory and Computation, vol. 4, pp. 1841-1848, 2008. https://doi.org/10.1021/ct8001915

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An unusual [1,6] shift in homotropylium cation exhibiting zones of aromaticity.

Tuesday, August 12th, 2014

One thing leads to another. Thus in the previous post, I described a thermal pericyclic reaction that appears to exhibit two transition states resulting in two different stereochemical outcomes. I noted that another such reaction appeared to be a [1,6] carousel migration in homotropylium cation,[1] where transition states for both retention and inversion of the configuration of the migrating group (respectively formally allowed and forbidden) were reported (scheme below). Here I explore this system further. homotropylium Firstly, the pathway leading to inversion.[2] The reaction path (ωB97XD/6-311G(d,p)/SCRF=chloroform) has got a very odd (table-top mountain) shape, whereby the region of the transition state (IRC = 0.0) is very flat, and the region close to reactant and (identical) product is very steep. The gradient norm shows this best, with sharp spikes at IRC ± 4.2. Something clearly is happening here to cause this behaviour. Before moving on to analyze this, I want you first to observe the methyl groups below. Note how one of them rotates at the start of the process, and the other at the end. I have elsewhere called this behaviour the methyl flag, and it is due to stereoelectronic re-alignments of the C-H groups accompanying the changes in the conjugated array. htropa htrop htropG The homotropylium cation is said to be homoaromatic, indicating that cyclic conjugation can be maintained across a ring in which the σ framework is interrupted at one point. A NICS probe placed at the ring critical point of this molecule reveals a chemical shift of -11.3 ppm[3], very similar to eg that obtained for benzene itself. The three highest doubly occupied NBOs (below) show two normal π-type orbitals and one rather different one that spans the homo-bond (the MOs, before you ask, are a bit of a mess, with lots of mixed contributions from other parts of the σ framework).

HONBO (two) HONBO-2

Click for 3D

Click for 3D

Click for 3D

Click for 3D

At the transition state for the [1,6] migration, the same NICS probe registers a value of +2.6 ppm[4], now firmly in the non-aromatic zone. So this reaction is characterised by two zones, ring-aromatic ones at the start and the end of the process, and a higher energy non-aromatic one in the middle of the reaction pathway as ~enclosed by the region of IRC ± 4.2. The homo-bond in the aromatic zone starts with a length of 1.74Å, reduces to 1.53Å at the transition state and ends up as a normal aromatic bond of length 1.41Å. Meanwhile, the relocated homo-bond changes in the opposite sense, starting as a normal aromatic length of 1.41Å, becoming 1.53Å at the transition state and ending as a homo-length of 1.74Å. Presumably, virtually full strength homoaromaticity can be sustained for a homo-bond of 1.74Å, but as that bond mutates to a σ-bond of 1.53Å, the cyclic conjugation falls off the edge of the cliff, to be restored only at the end. Pericyclic reactions are themselves said to sustain aromatic transition states,[5] and so a simplistic way of looking at this is that the “aromaticity” relocates (or morphs) from the reactant to the transition state, and then back again during the course of the migration. A reaction path from which one can indeed learn a lot.

Now to the pathway in which the migrating group retains configuration. This is no longer a single step concerted reaction,[6] since at the half-way point we no longer have a transition state but a shallow intermediate (~IRC +2, [7]). It (formally at least) becomes a two-step non-concerted process, and the overall barrier is ~5 kcal/mol lower than for the inversion path. The aromaticity changes in a similar manner to before (i.e. IRC ~-5).htrop-ra

Htrop-retHtrop-retG

So this emerges as not quite the example I thought it was, but nonetheless unusual with the “forbidden” pathway being concerted and the “allowed” pathway being non-concerted. Molecular dynamics on these two systems would indeed be interesting to see what proportion of the trajectories go via each pathway.

References

  1. A.M. Genaev, G.E. Sal’nikov, and V.G. Shubin, "Energy barriers to carousel rearrangements of carbocations: Quantum-chemical calculations vs. experiment", Russian Journal of Organic Chemistry, vol. 43, pp. 1134-1138, 2007. https://doi.org/10.1134/s1070428007080076
  2. H.S. Rzepa, "Gaussian Job Archive for C10H13(1+)", 2014. https://doi.org/10.6084/m9.figshare.1134556
  3. H.S. Rzepa, "Gaussian Job Archive for C10H13(1+)", 2014. https://doi.org/10.6084/m9.figshare.1135694
  4. H.S. Rzepa, "Gaussian Job Archive for C10H13(1+)", 2014. https://doi.org/10.6084/m9.figshare.1135695
  5. H.S. Rzepa, "The Aromaticity of Pericyclic Reaction Transition States", Journal of Chemical Education, vol. 84, pp. 1535, 2007. https://doi.org/10.1021/ed084p1535
  6. H.S. Rzepa, "Gaussian Job Archive for C10H13(1+)", 2014. https://doi.org/10.6084/m9.figshare.1135668
  7. H.S. Rzepa, "Gaussian Job Archive for C10H13(1+)", 2014. https://doi.org/10.6084/m9.figshare.1134559

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Posted in pericyclic, reaction mechanism | 5 Comments »

Using a polar bond to flip: on the knife-edge!

Sunday, August 10th, 2014

In my first post on the topic, I discussed how inverting the polarity of the C-X bond from X=O to X=Be (scheme below) could flip the stereochemical course of the electrocyclic pericyclic reaction of a divinyl system. This was followed up by exploring what happens at the half way stage, i.e. X=CH2, the answer being that one gets an antarafacial pathway as with X=O. Here I fill in another gap, X=BH to see if a metaphorical microscope can be used to view the actual region of the “flip” to a suprafacial mode.divinylketon This time, uniquely, it proved possible to locate TWO transition states for this process, one suprafacial[1] and one antarafacial[2], this latter being 10.5 kcal/mol lower in ΔG† (ωB97XD/6-311G(d,p)/SCRF=dichloromethane). It is quite rare to be able to find BOTH stereochemical outcomes of a thermal pericyclic reaction.‡

First, the antarafacial IRC (X=BH)[3]. There are several interesting features. Note at IRC = -8, the divinyl compound appears as a Hidden Intermediate (HI), having formed from a compound where the HB=C substituent has ring opened from a cyclobutene-like precursor (initial electrocyclic). If you watch the animation, you can see the antarafacial bond forming from the bottom face of the vinyl group on the left to the top face of the vinyl group in the HI on the right (antarafacial=conrotation). Because the entire process is concerted (no real intermediates participate), we have here an unusual pericyclic cascade where one electrocyclic reaction is immediately followed by another quite different one.BH-antaraa BH-antara BH-antaraG Now for the suprafacial IRC[4]. It is pretty similar to the previous path, but again if you inspect very carefully you will see that it is the TOP face of the vinyl group on the left forming the bond to the TOP face of the vinyl group on the right (suprafacial/disrotation). BH-supraaBH-supraBH-supraG You might ask if the molecules used here are realistic, i.e. could they form the basis of real reactions to be conducted in a laboratory? Well, the C=B-C fragment has 9 hits in the CCDC crystal database (none for C=B-H). One example is cited here.[5]. So, yes, possibly a realistic system, except the barriers do look too high. Perhaps suitable substituents might help? But even if this could not be carried out in a test-tube, it does teach one about pericyclic reactions and how one might manipulate them.

‡One such is the [1,6] sigmatropic shift in homotropylium cation involving migration of a Me2C+ group, where the “allowed” process in which the migrating group retains its configuration has a barrier of 17.7 kcal/mol and the “forbidden” route where the migrating group inverts its configuration with a barrier of 38.6 kcal/mol (thanks to Alex Genaev; I will strive to make the coordinates available via the repository shortly).

References

  1. H.S. Rzepa, "Gaussian Job Archive for C5H7B", 2014. https://doi.org/10.6084/m9.figshare.1133933
  2. H.S. Rzepa, "Gaussian Job Archive for C5H7B", 2014. https://doi.org/10.6084/m9.figshare.1133934
  3. H.S. Rzepa, "Gaussian Job Archive for C5H7B", 2014. https://doi.org/10.6084/m9.figshare.1133936
  4. H.S. Rzepa, "Gaussian Job Archive for C5H7B", 2014. https://doi.org/10.6084/m9.figshare.1134015
  5. M. Menzel, H.J. Winkler, T. Ablelom, D. Steiner, S. Fau, G. Frenking, W. Massa, and A. Berndt, "Diborylcarbenes as Reactive Intermediates in Double 1,2‐Rearrangements with Low Activation Enthalpies", Angewandte Chemie International Edition in English, vol. 34, pp. 1340-1343, 1995. https://doi.org/10.1002/anie.199513401

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Using a polar bond to flip: a follow up project.

Wednesday, August 6th, 2014

In my earlier post on the topic, I discussed how inverting the polarity of the C-X bond from X=O to X=Be could flip the stereochemical course of the electrocyclic pericyclic reaction of a divinyl system. An obvious question would be: what happens at the half way stage, ie X=CH2? Well, here is the answer. divinylketon CH2 The reaction occurs in two stages (ωB97XD/6-311G(d,p)/SCRF=dichloromethane)[1] but overall is a concerted, albeit asynchronous, reaction. The initial stage is a conrotatory ring closure (as observed with X=O but opposite to X=Be), and reaching what we will call a HI (hidden intermediate). This HI clearly has zwitterionic character, and manifests its presence most obviously at IRC = -3.5 below. CH2CH2G The polarity of this HI is revealed by the dipole moment (6D) and molecular electrostatic potentials, below. The dipole vector goes from -ve to +ve, and the MEP clearly reveals the polarity below. cd7 C2-MEP This ionic HI however is not stable, and in the second stage of the reaction collapses to the neutral bicyclic hydrocarbon shown below. Overall, it amounts to a  2+2 cycloaddition, but with a very unusual pathway in which one C-C bond is very much formed before the other (which is how the reaction escapes the clutches of the Woodward-Hoffmann forbidden-ness). cd8 Why is all this worth this follow-up? Well, one can now start to “design” the reaction. All three carbon atoms with formal charges can be stabilised or destabilised with appropriate substituents. It should not be too difficult to stabilise out the HI into just an I(intermediate), or indeed to remove it from the profile. Nice perhaps for a group of students, who can partition up the substituents amongst themselves and discover if they have the desired effect. And would any of this tinkering change the stereochemical outcome?

References

  1. H.S. Rzepa, "Gaussian Job Archive for C6H8", 2014. https://doi.org/10.6084/m9.figshare.1128205

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