Imperial College London

Henry Rzepa

Previously, I explored the [Graham reaction to form a
diazirine](https://www.ch.imperial.ac.uk/rzepa/blog/?p=20464). The
second phase of the reaction involved an Sn2′ displacement of N-Cl
forming C-Cl. Here I ask how facile the simpler displacement of C-Cl by
another chlorine might be and whether the mechanism is Sn2 or the
alternative
Sn1.[![](https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2019/03/diazirine3.svg){.aligncenter
.size-medium .wp-image-20566 decoding="async"
width="400"}](https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2019/03/diazirine3.svg)
The reason for posing this question is that as an Sn1 reaction, simply
ionizing off the chlorine to form a diazacyclopropenium cation might be
a very easy process. Why? Because the resulting cation is analogous to
the cyclopropenium cation, famously proposed by Breslow as the first
example of a 4n+2 aromatic ring for which the value of n is zero and not
1 as for benzene.\[cite\]10.1021/ja01576a067\[/cite\] Another example of
a famous "Sn1" reaction is the solvolysis of t-butyl chloride to form
the very stable tertiary carbocation and chloride anion (except in fact
that it is not an Sn1 reaction but an [Sn2
one](https://www.ch.imperial.ac.uk/rzepa/blog/?p=5228)!)

Here is the located transition state for the above, using Na^+^.6H~2~O
as the counter-ion to the chloride. The calculated free energy of this
transition state is 3.2 kcal/mol lower than the previous Sn2′ version
(FAIR data collection,
[10.14469/hpc/5045](https://data.hpc.imperial.ac.uk/resolve/?doi=5045&access=)),
with an overall barrier to reaction of 26.5 kcal/mol. This compares to
\~24.5 kcal/mol obtained by Breslow for solvolysis of the cyclopropenyl
tosylate. Given the relatively simple solvation model I used in the
calculation (only six waters to solvate all the ions, and a continuum
solvent field for water), the agreement is not too bad.

![](https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2019/03/sn2.gif){.aligncenter
.size-medium .wp-image-20563 decoding="async"
onclick="jmolApplet([450,450],'load wp-content/uploads/2019/04/sn2.log;frame 137;vectors on;vectors 4;vectors scale 8.0;color vectors green;vibration 6;spin 3;','c1');"
width="540"}

The animation above is of a normal vibrational mode known as the
transition mode (click on the image above to get a 3D rotatable animated
model). The calculated vectors for this mode (its energy being an
eigenvalue of the force constant matrix) are regularly used to
"characterise" a transition state. I will digress with a quick bit of
history here, starting in 1972 when another famous article
appeared.\[cite\]10.1021/ja00763a011\[/cite\] The key aspect of this
study was the derivation of the first derivatives of the energy of a
molecule with respect to the (3N) geometrical coordinates of the atoms,
using a relatively simply quantum mechanical method (MINDO/2) to obtain
that energy. Analytical first derivatives of the MINDO/2 Hamiltonian
were then used to both locate the transition state for a simple reaction
and then to evaluate the second derivatives (the force constant matrix)
using a finite difference method. That force constant matrix, when
diagonalized, reveals one negative root (eigenvalue) which is
characteristic of a transition state. The vectors reveal how the atoms
displace along the vibration, and should of course approximate to the
path to either reactant or product.

Since that time, it has been a more or less mandatory requirement for
any study reporting transition state models to characterise them using
the vectors of the negative eigenvalue. The eigenvalue invariably
expressed as a wavenumber. Because this comes from the square root of
the mass-weighted negative force constant, it is often called the
imaginary mode. Thus in this example, 115*i* cm^-1^, the *i* indicating
it is an imaginary number. The vectors are derived from quadratic force
constants, which is a parabolic potential surface for the molecule.
Since most potential surfaces are not quadratic, it is recognized as an
approximation, but nonetheless good enough to serve to characterise the
transition state as the one connecting the assumed reactant and product.
Thousands of published studies in the literature have used this
approach.

So now to the animation above. If you look closely you will see that it
is a **nitrogen** and not a carbon that is oscillating between two
chlorines (here it is the lighter atoms that move most). The vectors
confirm that, with a large one at N and only a small one at C. So it is
Sn2 displacement at nitrogen that we have located? 

Not so fast. This is a reminder that we have to explore a larger region
of the potential energy surface, beyond the quadratic region of the
transition state from which the vectors above are derived. This is done
using an IRC (intrinsic reaction coordinate). Here it is, and you see
something remarkable.

[![](https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2019/04/SN2.gif){.aligncenter
.size-full .wp-image-20623 decoding="async"
width="450"}](https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2019/04/SN2.gif)

The Cl...N...Cl motions seen above in the transition state mode change
very strongly in regions away from the transition state. On one side of
the transition state, it forms a Cl...C bond, on the other side a
Cl...N.

[![](https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2019/04/tot_ener.svg){.aligncenter
.size-medium .wp-image-20620 decoding="async"
width="450"}](https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2019/04/tot_ener.svg)

It is also reasonable to ask why the paths either side of the transition
state are not the same? That may be because with only six explicit water
molecules, three of which solvate the sodium ion, there are not enough
to solvate equally the chloride anions either side of the transition
state. As a result one chlorine does not behave in quite the same way as
the other. The addition of an extra water molecule or two may well
change the resulting reaction coordinate significantly.

The overall message is that there are two ways to characterise a
computed reaction path. One involves looking at the motions of all the
atoms just in the narrow region of the transition state. Most reported
literature studies do only this. When the full path is explored with an
IRC, a different picture can emerge, as here. The Cl...N...Cl Sn2 mode
is replaced by a Cl...C/N...Cl mode. This example however is probably
rare, with most reactions the transition state vibration and the IRC do
actually agree!

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


Previously, I explored the Graham reaction to form a diazirine. The second phase of the reaction involved an Sn2′ displacement of N-Cl forming C-Cl. Here I ask how facile the simpler displacement of C-Cl by another chlorine might be and whether the mechanism is Sn2 or the alternative Sn1.

Messaggi di Rogue Scholar

Smoke and mirrors. All is not what it seems with this Sn2 reaction!