Imperial College London

Henry Rzepa

[Previously](http://www.ch.imperial.ac.uk/rzepa/blog/?p=14255){target="_blank"}
on the kinetic isotope effects for the Baeyer-Villiger reaction, I was
discussing whether a realistic computed model could be constructed for
the mechanism. The measured KIE or kinetic isotope effects (along with
the approximate rate of the reaction) were to be our reality check. I
had used ΔΔG energy differences and then HRR (harmonic rate ratios) to
compute\[cite\]10.5281/zenodo.19272\[/cite\] the KIE, and [Dan Singleton
asked](http://www.ch.imperial.ac.uk/rzepa/blog/?p=14070&cpage=1#comment-164910){target="_blank"}
if I had included heavy atom tunnelling corrections in the calculation,
which I had not. His group has shown these are not negligible for
low-barrier reactions such as ring opening of cyclopropyl
carbinyl radical.\[cite\]10.1021/ja1055593\[/cite\] As a prelude to
configuring his suggested programs for computing tunnelling ([GAUSSRATE
and
POLYRATE](http://comp.chem.umn.edu/license/form-user.html){target="_blank"}),
it was important I learnt how to reproduce his KIE
values.\[cite\]10.1021/ja1055593\[/cite\] Hence the title of this post.
Now, read on.

[![cp](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2015/07/cp.svg){.aligncenter
.size-full .wp-image-14329 decoding="async"
width="300"}](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2015/07/cp.svg)

I felt I could contribute to the cause by extending the published
results in two respects:

1.  The reported\[cite\]10.1021/ja1055593\[/cite\] calculations are for
    the model B3LYP/6-31G(d) but the article does not report the
    tolerance to *e.g.* basis set variation (6-31G(d), a modest basis
    set by 2015 standards),
2.  or to the quantum model used (B3LYP, a veritable DFT method).

These two model chemistries can both be tested by "increasing" their
accuracy. The Def2-QZVPP basis set is nearing the CBS, or complete basis
set limit. The coupled-cluster CCSD(T) method is regarded as the gold
standard for single reference calculations. The CASSCF method tests the
response to a multi-reference wave function. Each is applied separately
to ensure only one variable is being changed at a time.

|                                                                                                                              |                                                |                                          |                                    |                                             |                                                               |
|------------------------------------------------------------------------------------------------------------------------------|------------------------------------------------|------------------------------------------|------------------------------------|---------------------------------------------|---------------------------------------------------------------|
| Method                                                                                                                       | Expt. KIE\[cite\]10.1021/ja1055593\[/cite\]^‡^ | Pred. KIE (my result)                    | Pred. ΔG~298~^‡^                   | Pred. KIE\[cite\]10.1021/ja1055593\[/cite\] | KIE + Tunnelling correction\[cite\]10.1021/ja1055593\[/cite\] |
| [**B3LYP/6-31G(d)\[cite\]10.14469/ch/191357\[/cite\],\[cite\]10.14469/ch/191358\[/cite\]**]{style="color: #333399;"}         | [**1.079~295~**]{style="color: #333399;"}      | [**1.0582**]{style="color: #333399;"}    | [**8.0**]{style="color: #333399;"} | [**1.058**]{style="color: #333399;"}        | [**1.073**]{style="color: #333399;"}                          |
|                                                                                                                              | [**1.163~173~**]{style="color: #333399;"}      | [**1.1067**]{style="color: #333399;"}    |                                    | [**1.106**]{style="color: #333399;"}        | [**1.169**]{style="color: #333399;"}                          |
| **[B3LYP/Def2-QZVPP\[cite\]10.14469/ch/191353\[/cite\],\[cite\]10.14469/ch/191352\[/cite\]]{style="color: #008000;"}**       | **[1.079~295~]{style="color: #008000;"}**      | **[1.0563]{style="color: #008000;"}**    | [**6.6**]{style="color: #008000;"} | **[1.058]{style="color: #008000;"}**        | **[1.073]{style="color: #008000;"}**                          |
|                                                                                                                              | **[1.163~173~]{style="color: #008000;"}**      | **[1.1031]{style="color: #008000;"}**    |                                    | **[1.106]{style="color: #008000;"}**        | **[1.169]{style="color: #008000;"}**                          |
| **[CASSCF(5,5)/6-31G(d)\[cite\]10.14469/ch/191361\[/cite\],\[cite\]10.14469/ch/191364\[/cite\]]{style="color: #ff0000;"}**   | **[1.079~295~]{style="color: #ff0000;"}**      | **[1.0572]{style="color: #ff0000;"}**    | [**8.2**]{style="color: #ff0000;"} | **[1.058]{style="color: #ff0000;"}**        | **[1.073]{style="color: #ff0000;"}**                          |
|                                                                                                                              | **[1.163~173~]{style="color: #ff0000;"}**      | **[1.1050]{style="color: #ff0000;"}**    |                                    | **[1.106]{style="color: #ff0000;"}**        | **[1.169]{style="color: #ff0000;"}**                          |
| [**CASSCF(5,5)/Def2-TZVPP\[cite\]10.14469/ch/191363\[/cite\],\[cite\]10.14469/ch/191362\[/cite\]**]{style="color: #ff6600;"} | [**1.079~295~**]{style="color: #ff6600;"}      | [**1.0561**]{style="color: #ff6600;"}    | [**7.9**]{style="color: #ff6600;"} | [**1.058**]{style="color: #ff6600;"}        | [**1.073**]{style="color: #ff6600;"}                          |
|                                                                                                                              | [**1.163~173~**]{style="color: #ff6600;"}      | [**1.1028**]{style="color: #ff6600;"}    |                                    | [**1.106**]{style="color: #ff6600;"}        | [**1.169**]{style="color: #ff6600;"}                          |
| **[CCSD(T)/6-31G(d)\[cite\]10.14469/ch/191367\[/cite\],\[cite\]10.14469/ch/191356\[/cite\]]{style="color: #993300;"}**       | **[1.079~295~]{style="color: #993300;"}**      | **[1.0597^†^]{style="color: #993300;"}** | [**9.7**]{style="color: #993300;"} | **[1.058]{style="color: #993300;"}**        | **[1.073]{style="color: #993300;"}**                          |
|                                                                                                                              | **[1.163~173~]{style="color: #993300;"}**      | **[1.1099]{style="color: #993300;"}**    |                                    | **[1.106]{style="color: #993300;"}**        | **[1.169]{style="color: #993300;"}**                          |

†[Actually separate ratios of ^13^C/^12^C(C-4)/^13^C/^12^C(C-3) since
C-3 and C-4 are not equivalent in the reactant species because of the
methylene group pyramidalisation. The KIE calculation input and outputs
are archived.\[cite\]10.5281/zenodo.19949\[/cite\]]{.small}

The[ first two rows of table]{style="color: #000000;"} are my attempt at
an exact replication of the literature. The start point of such a
project would be the supporting information or
SI\[cite\]10.1021/ja1055593\[/cite\] which contains coordinates for the
program GAUSSRATE and defines key structures in the form of a
double-column, page thrown
([broken](http://www.ch.imperial.ac.uk/rzepa/blog/?p=12728){target="_blank"}
might be a better word) PDF file. It was going to be a [bit of a
struggle](http://www.ch.imperial.ac.uk/rzepa/blog/?p=13248){target="_blank"}
to reconstitute this format into the structure required for a Gaussian
calculation, so I simply constructed the models from scratch and
optimised to the ring-opening transition
state\[cite\]10.14469/ch/191358\[/cite\] and
reactant.\[cite\]10.14469/ch/191357\[/cite\] I used a more recent
version of the Gaussian program (G09/D.01 rather than G03/D.02) to do
this, and tightened up some of the criteria to modern cutoff standards.
A continuum solvent model could have been specified  (the solvent used
in the experiments was 1,2-dichlorobenzene) but since no mention was
made of solvent, I assumed a gas phase calculation had originally been
done.  The starting geometry of the reactant deliberately had no
symmetry, but during optimisation it converged to having a plane of
symmetry using the B3LYP/6-31G(d) level of theory (the SI does not note
this symmetry, it is implicit). I then used my
code\[cite\]10.5281/zenodo.19272\[/cite\] to compute the isotope
effects. The KIE program used in the original literature calculation was
not directly mentioned in the supporting information but is presumed to
be Quiver. Dan Singleton has recently sent me these codes, but they
still need to be compiled and tested at my end. I ended up with splendid
agreement for the KIE as you can see above (top two lines). Its
reproducible! Hence the various assumptions I made in achieving
this appear justified.

Returning to the geometry of the cyclopropyl carbinyl radical as having
a plane of symmetry, two of the other methods, CCSD(T)/6-31G(d) and
CASSCF(5,5)/6-31G(d), as well as CASSCF(5,5) at the better Def2-TZVPP
basis all predicted that the methylene radical is twisted by about 20°
with respect to the Cs plane of the ring.

[![cp-asymm](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2015/07/cp-asymm.jpg){.aligncenter
.size-full .wp-image-14338 decoding="async" width="300"
srcset="https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2015/07/cp-asymm.jpg 398w, https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2015/07/cp-asymm-277x300.jpg 277w"
sizes="(max-width: 398px) 100vw, 398px"}](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2015/07/cp-asymm.jpg)

It is useful to check whether this twisting has any impact on the
predicted KIE. The answer is clear (Table). ALL the methods predict
similar KIE to ± 0.003,^†^ which is as about as accurate as can be
measured experimentally at the [1σ level of
confidence](http://www.ch.imperial.ac.uk/rzepa/blog/?p=12705){target="_blank"}.
This is a remarkable result; few other computed molecular properties
turn out to be so insensitive to the quantum procedure used. The next
stage will be to check if the tunnelling corrections required to bring
the calculation into congruence with the measured values are similarly
insensitive.

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

^‡^ The "barrier height" is quoted as 7
kcal/mol\[cite\]10.1021/ja1055593\[/cite\]. This is probably NOT the
activation free energy.

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


Previously on the kinetic isotope effects for the Baeyer-Villiger reaction, I was discussing whether a realistic computed model could be constructed for the mechanism. The measured KIE or kinetic isotope effects (along with the approximate rate of the reaction) were to be our reality check.

Reproducibility in science: calculated kinetic isotope effects for cyclopropyl carbinyl radical.

Stereo-induction is, lets face it, a [subtle
phenomenon](http://www.ch.ic.ac.uk/rzepa/talks/hofmann/){target="_blank"}.
The ratio of two stereoisomers formed in a reaction can be detected very
accurately by experiment, and when converted to a free energy difference
using ΔG = -RT Ln K, this can amount to quite a small value (between 0.5
-- 1.5 kcal/mol). Can modelling reproduce effects originating from such
small energy differences? Well one system that has been argued about now
for several decades is shown below as **1**.

::: {#attachment_2121 .wp-caption .aligncenter style="width: 411px"}
[![](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2010/07/norbornene.jpg "Stereoinduction: syn or anti?"){.size-full
.wp-image-2121 loading="lazy" decoding="async"
aria-describedby="caption-attachment-2121" width="401"
height="148"}](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2010/07/norbornene.jpg)

Norbornene systems
:::

[Way back in
1992](http://dx.doi.org/10.1039/C39920000998){target="_blank"}, we
thought that the explanation for attack by an electrophile on the alkene
from the *syn* face was electrostatic (although it did depend on the
nature of the electropile; thus we concluded that attack by Hg(OH)~2~
was electrostatic, but by BH~3~ was orbital controlled). Recently, a
different explanation has emerged, relating to how the fundamental
normal vibrational modes of the molecule interact with the transition
normal mode for the reaction. A [new example of
this](http://dx.doi.org/10.1038/nchem.577){target="_blank"}, relating to
reaction of the isomeric **2** with a peracid has recently been
discussed on [Steve Bachrach's
blog](http://comporgchem.com/blog/?p=977){target="_blank"}. Here, the
peroxide of the peracid is thought to act as an electrophile (although
one must bear in mind that it does bear two electron lone pairs!). The
conclusion was pretty clear cut; the experimental preference for *syn*
(92%) over the *anti* isomer (8%, ΔΔG = 1.4 kcal/mol) was NOT due to
electrostatic effects, but due to distorsional asymmetry in the
vibrational mode that couples/forms the transition state mode.

I could not resist revisiting this system. As in 1992, a molecular
electrostatic potential was calculated for **2**. The method used was
wB97XD/aug-cc-pvdz, and if you want the archive of this calculation to
evaluate it yourself, [see
here](http://hdl.handle.net/10042/to-4996){target="_blank"}).

::: {#attachment_2122 .wp-caption .aligncenter style="width: 273px"}
![](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2010/07/norbornene-0.031.jpg "Electrostatic potential"){.size-full
.wp-image-2122 loading="lazy" decoding="async"
aria-describedby="caption-attachment-2122"
onclick="jmolInitialize('../Jmol/');jmolSetAppletColor('white');jmolApplet([450,450],'load wp-content/uploads/2010/07/norbornene_0.029.jvxl;isosurface \"\" translucent;zoom 60;spin 3;');"
width="263" height="263"}

MEP for 2. Click on diagram for 3D.
:::

A very clear electrostatic bias for *syn* attack emerges (orange =
attractive to a proton=electrophile). This electrostatic picture is not
directly related to any distortional asymmetry, although of course both
could arise from the same electronic factors. They may indeed be
different manifestations of the same underlying nature of the
wavefunction. But I would claim here that to make the clear statement
that electrostatic effects are **NOT** responsible for the
discrimination in this reaction is perhaps too simplistic (electrostatic
potentials were not reported in the original article). The control
experiment is **3**, which is known to be far less selective. The
calculated electrostatic potential likewise shows much less
discrimination.

::: {#attachment_2136 .wp-caption .aligncenter style="width: 231px"}
![](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2010/07/norbornene4-0.029.jpg "The norbornene with a four-membered ring"){.size-full
.wp-image-2136 loading="lazy" decoding="async"
aria-describedby="caption-attachment-2136"
onclick="jmolInitialize('../Jmol/');jmolSetAppletColor('white');jmolApplet([450,450],'load wp-content/uploads/2010/07/norbornene4_0.029.jvxl;isosurface \"\" translucent;zoom 60;spin 3;');"
width="221" height="239"}

The norbornene with a four-membered ring
:::

Is there another take on **2**? Well, how about an NBO (natural bond
order) analysis? The interaction energy between the filled C1-C2 orbital
and the antibonding C15-C16 π\* bond is 3.24. This could be regarded as
pushing electrons into the anti-periplanar *syn* face of the alkene. The
corresponding C2-C9/C15-C16 interaction resulting in an
*anti*-preference is less at 2.55 kcal/mol. This effect arises because
the C1-C2 bond (localised as an NBO) is a better donor (E=-17.8eV) than
C2-C9 (E=-18.1eV). Because C2 is common to both, it must be the
difference between C1 and C9 (i.e. the hybridization of each). Perhaps
it's an orbital effect after all?

::: {#attachment_2124 .wp-caption .aligncenter style="width: 304px"}
[![](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2010/07/norbornene-0.029.jpg "Norbornene electrostatic potential"){.size-full
.wp-image-2124 loading="lazy" decoding="async"
aria-describedby="caption-attachment-2124" width="294"
height="294"}](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2010/07/norbornene-0.029.jpg)

Norbornene electrostatic potential
:::

I would conclude by saying that it can be ferociously difficult to
identify the fundamental origins of stereo-induction. But I leave the
argument in the hands of the reader now. What do you think?

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


Stereo-induction is, lets face it, a subtle phenomenon. The ratio of two stereoisomers formed in a reaction can be detected very accurately by experiment, and when converted to a free energy difference using ΔG = -RT Ln K, this can amount to quite a small value (between 0.5 – 1.5 kcal/mol). Can modelling reproduce effects originating from such small energy differences?

Messaggi di Rogue Scholar

Reproducibility in science: calculated kinetic isotope effects for cyclopropyl carbinyl radical.

The mysteries of stereoinduction.