Imperial College London

Henry Rzepa

I noted in my [WATOC conference
report](http://www.ch.imperial.ac.uk/rzepa/blog/?p=18730) 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\[cite\]10.1021/acs.orglett.7b01621\[/cite\] 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.  
![](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2017/09/dyotropic.jpeg){.aligncenter
.size-large .wp-image-18862 loading="lazy" decoding="async" width="450"
height="592"}

Shown in blue above is the reported outcome, a dyotropic transposition
of a OMs group with a ring CH~2~ 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)\[cite\]10.1021/acs.orglett.7b01621\[/cite\].

1.  The first involved dyotropic-like \[1,2\] transposition of the
    neutral molecule, for which barriers \>39 kcal/mol were
    calculated\[cite\]10.1021/acs.orglett.7b01621\[/cite\]. 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\[cite\]10.1021/acs.orglett.7b01621\[/cite\]). 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\[cite\]10.1021/acs.orglett.7b01621\[/cite\], 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\[cite\]10.1021/acs.orglett.7b01621\[/cite\]. 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](https://doi.org/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-TZVPP**D** basis set level, which allows for a better
      description of negative ions (FAIR data
      DOI: [10.14469/hpc/3095](https://doi.org/10.14469/hpc/3095),[10.14469/hpc/3140](https://doi.org/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](https://doi.org/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.  
    ![](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2017/09/DYO.gif){.aligncenter
    .size-full .wp-image-18871 decoding="async" width="540"}
6.  The energy profile is shown below.   
    [![](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2017/09/E.svg){.aligncenter
    .size-large .wp-image-18873 decoding="async"
    width="450"}](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2017/09/E.svg)
    - 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\[cite\]10.1021/acs.orglett.7b01621\[/cite\] to locate a
      transition state.
    - The region IRC -3 to +2 is where the CH~2~ 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.   
    ![](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2017/09/G.svg){.aligncenter
    .size-large .wp-image-18874 decoding="async" width="450"}
8.  The zone of the ***hidden ion-pair intermediate ***can also be seen
    in this dipole moment plot.  
    [![](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2017/09/DM.svg){.aligncenter
    .size-large .wp-image-18877 decoding="async"
    width="450"}](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2017/09/DM.svg)
9.  This next plot charts the changes in the length of the bond labelled
    **(a)** in the diagram above. As the CH~2~ 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.  
    ![](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2017/09/12.svg){.aligncenter
    .size-large .wp-image-18880 decoding="async" width="450"}
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.  
    [![](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2017/09/2-18.svg){.aligncenter
    .size-large .wp-image-18881 decoding="async"
    width="450"}](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2017/09/2-18.svg)
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)**.[![](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2017/09/3-9.svg){.aligncenter
    .size-large .wp-image-18884 decoding="async"
    width="450"}](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2017/09/3-9.svg)

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\[cite\]10.1021/acs.orglett.7b01621\[/cite\], 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?

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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.

Messaggi di Rogue Scholar

Dyotropic Ring Expansion: more mechanistic reality checks.