Imperial College London

Henry Rzepa

I have [blogged
before](http://www.ch.imperial.ac.uk/rzepa/blog/?p=6618){target="_blank"}
about the mechanism of this classical oxidation reaction. Here I further
explore computed models, and whether they match the observed kinetic
isotope effects (KIE) obtained using the natural-abundance method
described in the [previous
post](http://www.ch.imperial.ac.uk/rzepa/blog/?p=14070){target="_blank"}.

[![BV](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2015/06/BV1.svg){.aligncenter
.size-full .wp-image-14115 decoding="async"
width="440"}](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2015/06/BV1.svg)

There is much previous study of this rearrangement, and the issue can be
reduced to deciding whether **TS1** or **TS2** is rate-limiting. The
conventional text-book wisdom is that the carbon migration step **TS2**
is the "rds" and it was therefore quite a surprise when Singleton and
Szymanski\[cite\]10.1021/ja992016z\[/cite\] obtained KIE which seemed to
clearly point instead to **TS1** as being rate limiting, inferred from a
large ^13^C effect (\~1.05) at the carbonyl carbon (blue star) and
none at the α-carbon (red star). This result (for this specific reaction
and conditions, which is dichloromethane as solvent) is now routinely
quoted\[cite\]10.1021/jo070956t\[/cite\] when the mechanism is
discussed. This latter article reports\[cite\]10.1021/jo070956t\[/cite\]
calculated energetics for **TS1** and **TS2** (see Table 1 in this
article) and after exploring various models, the conclusion is that
**TS1** and **TS2** are essentially isoenergic. However, no isotope
effects are computed for their models, and so we do not know if **TS1**
or **TS2** agrees better with the reported
values.\[cite\]10.1021/jo070956t\[/cite\] Since I had managed to get
pretty good agreement with experimental KIEs using the
ωB97XD/Def2-TZVPP/SCRF=xylenes model for the Diels-Alder reaction, I
thought I would try the same method to see how it performs for the
Baeyer-Villiger.

It is in fact non-trivial to set up a consistent model. Using arrow
pushing, one can on paper draw three variations for TS1, the formation
of the peroxyhemiacetal tetrahedral intermediate (TI) and also often
called the Criegee intermediate.

[![BV2](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2015/06/BV2.svg){.aligncenter
.size-full .wp-image-14116 decoding="async"
width="400"}](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2015/06/BV2.svg)

1.  **TS1a** is the "text-book" variation, involving the production of a
    zwitterionic intermediate which immediately undergoes a proton
    transfer (PT). The arrows tend not to be used for this last step,
    since the direct transfer would involve a 4-membered ring and a
    highly non-linear geometry at the transferring proton which is
    understood to be "unfavourable". Such zwitterions involve a large
    degree of charge separation and hence a large dipole moment. In a
    non-protic solvent such as dichloromethane, one is very loath to use
    such species in a mechanism, and it's not modelled here either.
2.  Using just cyclohexanone and peracid, it is in fact difficult to
    avoid ionic species. **TS1b** is an attempt which shows the proton
    transfer is done first on the peracid to create a so-called carbonyl
    ylid, and this then reacts with the ketone
3.  If however a proton transfer agent is introduced as **TS1c**, one
    can use this species (shown in red above) to transfer the proton as
    part of a concerted mechanism; this was in fact the expedient used
    in the earlier theoretical study\[cite\]10.1021/jo070956t\[/cite\]
    and this route tends to avoid much if not all of the charge
    separation. The acid comes from the product of the reaction, and
    hence the kinetics may in fact have an induction period when this
    acid builds up. The initial proton transfer reagent may also be
    traces of water present in reagents or solvent. Singleton and
    Szymanski in fact include no supporting information in their article
    and so we do not know what the concentrations used were (assumed for
    the present discussion as 1M) whether everything was rigorously
    dried, or indeed what the kinetic order in \[peracid\] turned out to
    be.

The same problem is faced with **TS2**; how to transfer a proton?
Because we want to compare the relative energies of **TS1** and **TS2**,
we also have to atom-balance the mechanism, and so the additional acid
component introduced into **TS1c** is also retained in two alternative
mechanisms for **TS2** (and for **TS1b**).

[![BV3](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2015/06/BV3.svg){.aligncenter
.size-full .wp-image-14120 decoding="async"
width="250"}](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2015/06/BV3.svg)

1.  **TS2a** uses just the components of the tetrahedral intermediate
    (**TI**), but again in a fashion that requires no charge separation
    during the reaction. The additional acid component (red) plays a
    passive role, hydrogen bonding to the **TI**.
2.  **TS2b** now incorporates the additional acid by expanding the ring
    (green) in an active role.

IRCs using the 6-311G(d,p) basis) for
TS1\[cite\]10.14469/ch/191318\[/cite\] and
TS2\[cite\]10.14469/ch/191317\[/cite\] are interesting in revealing
relative synchronicity of the proton transfers for TS1 but
asynchronicity for TS2 involving a *hidden intermediate*.  
[![BV1a](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2015/06/BV1a.gif){.aligncenter
.size-full .wp-image-14134 decoding="async"
width="440"}](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2015/06/BV1a.gif)

[![BV2a](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2015/06/BV2a.gif){.aligncenter
.size-full .wp-image-14133 decoding="async"
width="440"}](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2015/06/BV2a.gif)

The energy, energy gradient and dipole moment magnitudes for this second
step are particularly fascinating. The dipole moment starts off quite
small (3.1D) at the TI, and is still so at the TS, but almost
immediately afterwards, it shoots up to \~12D as the hidden intermediate
develops (IRC \~4) Two successive proton transfers (IRC \~6, 7) then
reduce the value down again.  
[![BV2E](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2015/06/BV2E.svg){.aligncenter
.size-full .wp-image-14139 decoding="async"
width="440"}](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2015/06/BV2E.svg)  
[![BV2G](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2015/06/BV2G.svg){.aligncenter
.size-full .wp-image-14138 decoding="async"
width="440"}](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2015/06/BV2G.svg)  
[![BV2D](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2015/06/BV2D.svg){.aligncenter
.size-full .wp-image-14137 decoding="async"
width="440"}](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2015/06/BV2D.svg)

A table of results can now be constructed for these various models,
evaluating two different basis sets for the calculation.

<table data-border="1">
<colgroup>
<col style="width: 25%" />
<col style="width: 25%" />
<col style="width: 25%" />
<col style="width: 25%" />
</colgroup>
<tbody>
<tr class="header">
<th>system</th>
<th>ΔΔG<sub>298</sub> (1M)<br />
ωB97XD/6-311G(d,p)/SCRF=DCM, kcal/mol</th>
<th>Dipolemoment,D</th>
<th>ΔG<sub>298</sub> (1M)<br />
ωB97XD/Def2-TZVPP/SCRF=DCM</th>
</tr>
&#10;<tr class="odd">
<th>Reactants</th>
<td>+1.4<sup>a</sup></td>
<td>–</td>
<td>-3.3<sup>a</sup>[cite]10.14469/ch/191322[/cite],[cite]10.14469/ch/191323[/cite],[cite]10.14469/ch/191324[/cite]</td>
</tr>
<tr class="even">
<th>Complexed state</th>
<td>0.0[cite]10.14469/ch/191307[/cite]</td>
<td>5.0</td>
<td>0.0[cite]10.14469/ch/191315[/cite]</td>
</tr>
<tr class="odd">
<th>TS1a</th>
<td>n/a</td>
<td>n/a</td>
<td>n/a</td>
</tr>
<tr class="even">
<th>TS1b</th>
<td>32.9[cite]10.14469/ch/191313[/cite]</td>
<td>8.6</td>
<td>32.2[cite]10.14469/ch/191325[/cite]</td>
</tr>
<tr class="odd">
<th>TS1c</th>
<td>14.9[cite]10.14469/ch/191306[/cite]</td>
<td>3.0</td>
<td>16.1[cite]10.14469/ch/191312[/cite]</td>
</tr>
<tr class="even">
<th>TI</th>
<td>-1.7[cite]10.14469/ch/191311[/cite]</td>
<td>3.1</td>
<td>-0.3[cite]10.14469/ch/191319[/cite]</td>
</tr>
<tr class="odd">
<th>TS2a</th>
<td>22.2[cite]10.14469/ch/191314[/cite]</td>
<td>9.3</td>
<td>25.0[cite]10.14469/ch/191321[/cite]</td>
</tr>
<tr class="even">
<th>TS2b</th>
<td>20.2[cite]10.14469/ch/191306[/cite]</td>
<td>5.4</td>
<td>22.7[cite]10.14469/ch/191320[/cite]</td>
</tr>
<tr class="odd">
<th>Product</th>
<td>-69.8[cite]10.14469/ch/191310[/cite]</td>
<td>5.3</td>
<td>[cite]10.14469/ch/191327[/cite]</td>
</tr>
</tbody>
</table>

[^a^This value is corrected to a standard state of 1M for a termolecular
reaction by 3.78 kcal/mol from the computed free energies at 1 atm as
described previously.\[cite\]10.1021/ol060261z\[/cite\]]{.small}

1.  Firstly, one must note that the *resting state* for the reactants
    depends on the concentration. At 1M at the higher basis set, its the
    separated reactants, but at the lower it is the hydrogen bonded
    complex between them. Increasing the concentration would favour the
    latter.
2.  TS1c is significantly lower in free energy than TS2b, a result
    somewhat at variance with the earlier
    report.\[cite\]10.1021/jo070956t\[/cite\] The functional used in the
    present calculation, the basis set, the dispersion model and the
    solvation model are all improvements on the original work.
3.  Likewise, the energy of TI, the Criegee intermediate emerges
    as similar to the reactants. Coupled with the magnitude of the
    barrier for TS1c this does tend to point to a relatively rapid
    pre-equilibrium and that TS2b determines the rate of reaction.

## Kinetic isotope effects for our models

Having constructed models, we can now subject them to testing against
the measured kinetic isotope effects.\[cite\]10.1021/ja992016z\[/cite\]

[![bv4](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2015/06/bv4.svg){.aligncenter
.size-full .wp-image-14149 decoding="async"
width="350"}](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2015/06/bv4.svg)

1.  The measured values are shown above. The first set (a) are what are
    described as ***intermolecular*** isotope effects and result from
    measuring changes in the isotopic abundance obtained by recovering
    unreacted starting material after a large proportion of the reaction
    has gone to completion. This was interpreted as indicating **TS1**
    was rate limiting. Using instead the uncomplexed cyclohexanone has
    only a small effect (C1: 1.023 complexed, 1.021 uncomplexed).
2.  The values in parentheses were obtained using the **TS1c** model
    above and are relative to the complexed reactant involving hydrogen
    bonds between the cyclohexanone, the peracid and the acid catalyst.
    The agreement can only be described as partial.
    -  The predicted ^13^C isotope effect at C1 is about half of the
      measured value. The previous [calibration of the method being
      used](http://www.ch.imperial.ac.uk/rzepa/blog/?p=14070){target="_blank"}
      had resulted in agreement within experimental error for the Diels
      Alder reaction, and so this large disagreement is unexpected.
    - The ^2^H KIE at C2 is within experimental error.
    - The  ^2^H KIE at C3 is badly out. Here, it is the experimental
      result that seems wrong, since there is no reason to expect any
      KIE at this position especially since the ^13^C at the same
      position is 1.00 for both measured and calculated values.
3.  So we might infer an inconclusive result. I can only speculate on
    the computed model here, and invoke in effect the variation
    principle. If the model is wrong, we would expect a more correct
    model to have a lower rather than higher energy relative to
    reactants. The free energy of activation however is already low,
    corresponding to a very fast room temperature reaction; too fast
    indeed to easily recover any unreacted starting material if that
    were to be rate limiting!
4.  Set (b) corresponds to what is described as an ***intramolecular***
    KIE as defined by **TS2**, since it is measured from isotopic ratio
    changes in the product rather than reactant as the reaction
    progresses.
    - The value in (...) is relative to the complexed reactants and the
      value in \[...\] is relative to **TI**.
    - The predicted ^13^C isotope effect at C2m (the migrating carbon)
      agrees within experimental error with the measured value if the
      **TI** is used as the reference. This nicely shows how isotope
      effects for what may not be a rate limiting step can be measured
      by this technique.
    - The predicted ^13^C isotope effect at C1 (which is not reported in
      the original article) relative to **TI** is significant, and it
      would be nice to confirm the computed model by a measurement at
      this position.
    - The other KIE also agree reasonably with experiment when **TI** is
      specified as the reactant for this step.

So is there support from the calculations for the formation of the
semi-peroxyacetal being rate limiting, as claimed by Singleton and
Szymanski\[cite\]10.1021/ja992016z\[/cite\]? There is no doubt that the
KIE obtained from measuring the product is different from measuring the
reactant, but the lack of agreement for two of the measured values for
**TS1** is a concern. Perhaps one might conclude that this is an
experiment well worth repeating. Of the two computed models, **TS1** and
**TS2**, the variation principle would again lead us to suspecting that
the one with higher energy can only be decreased by improvement, whereas
improvement of the one with the lower energy cannot also increase its
relative energy. So if a new model for the carbon migration step can be
found, its activation free energy must be lower than that already
identified. But the excellent agreement between **TS2b** shown in (b)
suggests that this model is already pretty good! Lowering its energy by
\>7kcal/mol to make **TS1** rate limiting would probably require quite a
different model.

What I think is more certain is the value of subjecting the measured KIE
to computed models, in the knowledge that if the model is indeed
realistic a good agreement should be expected. And it is a shame that
the natural abundance KIE method cannot be applied to oxygen isotope
effects, which would surely settle the issue.^‡^ And I should end by
reminding that there is evidence that the mechanism may be quite
sensitive to variation of solvent, ketone, peracid, pH, etc, and so
these conclusions only apply to this specific reaction in
 dichloromethane.

------------------------------------------------------------------------

^‡^ For TI \> TS2, the ^18^O KIE is predicted as 1.048 (peroxy oxygen)
and 1.032 (acyl oxygen). For Reactant \> TS1, the values are
respectively 0.998 and 1.003.

------------------------------------------------------------------------

::: {.wp_orcid_field}
[https://orcid.org/0000-0002-8635-8390](https://orcid.org/0000-0002-8635-8390){target="_blank"
rel="author"}
:::


I have blogged before about the mechanism of this classical oxidation reaction. Here I further explore computed models, and whether they match the observed kinetic isotope effects (KIE) obtained using the natural-abundance method described in the previous post. There is much previous study of this rearrangement, and the issue can be reduced to deciding whether
<strong>
 TS1
</strong>
or
<strong>
 TS2
</strong>
is rate-limiting.

Publicaciones de Rogue Scholar

Natural abundance kinetic isotope effects: mechanism of the Baeyer-Villiger reaction.