Imperial College London

Henry Rzepa

In an earlier [post](http://www.ch.ic.ac.uk/rzepa/blog/?p=63) I wrote
about the iconic S~N~1 solvolysis reaction, and presented a model for
the transition state involving 13 water molecules. Here, I follow this
up with an improved molecule containing 16 water molecules, and how the
barrier for this model compares with experiment. This latter is nicely
summarized in the following article: [Solvolysis of t-butyl chloride in
water-rich methanol + water
mixtures](http://dx.doi.org/10.1039/F19736901195){target="references"},
which (for pure water) cites the following activation parameters  

- ΔH^†^~283~ = 23.0 kcal/mol
- ΔG^†^~283~ = 19.7 kcal/mol
- ΔS^†^~283~ = +11.1 cal/mol/K

But first, a word about how this new transtion state has been obtained.
The DFT treatment used is quite standard (B3LYP/6-31G(d) ), and one can
indeed locate a transition state using just this approach (this is how
the previous model was obtained). One has to work very hard to orient
the starting guess for the geometry so that as many hydrogen bonds
between the waters themselves, and to the substrate, are created. The
previous model took quite a few guesses and attempts! The solvent in
such a model is simulated by the explicit water molecules themselves. Of
course, the quality of the *solvent* then depends on how many water
molecules are used. A proper solvent field using explicit water
molecules is thought to require 100s of water molecules! But a
reasonable approximation/compromise may well be 13.

So how can the model be improved? Well, in many ways, some of which
include treating the dynamics of the system. But I will stick just to
two.

1.  Firstly, we assume that the water molecules are used to form a
    **bridge** between the incoming nucleophile (another water) and the
    leaving group (the chloride). In the previous model, two such
    bridges were constructed using the 13 water molecules. But in fact,
    there is still space between two of the methyl groups to construct a
    third bridge. This takes the total solvent molecules to 16.
2.  Solvent can also be modelled as a *continuum*, in which a cavity
    which the substrate occupies is surrounded by a field generated by
    the continuum solvent. The problem with these cavity approaches in
    the past has been that it is not easy to optimize the geometry of
    the molecule contained within the cavity. Because the cavity was
    constructed by tesselation, the first derivatives of the energy of
    the molecule within the cavity were not regular, and as a result,
    geometry optimization (and particularly transition state
    optimization) would frequently meander and fail to converge. Darrin
    York and Martin Karplus came to the rescue (some time ago, it has to
    be said, DOI:
    [10.1021/jp992097l](http://dx.doi.org/10.1021/jp992097l){target="references"})
    by formulating a smoothed out solvation cavity where the first (and
    second derivatives) are stable and well behaved. This new algorithm
    has now been implemented in Gaussian09, and it now allows really
    easy transition state location within a solvent cavity

The result of this optimization is shown below (and can be seen in
original form at the following DOI:
[10042/to-2894](http://hdl.handle.net/10042/to-2894){target="references"}).

::: {#attachment_1138 .wp-caption .aligncenter style="width: 264px"}
![Transition state for Sn1 solvolysis of tert-butyl
chloride](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2009/11/sn1.jpg "Transition state for  Sn1 solvolysis of  tert-butyl chloride"){.size-full
.wp-image-1138 loading="lazy" decoding="async"
aria-describedby="caption-attachment-1138"
onclick="jmolInitialize('../Jmol/');jmolSetAppletColor('cyan');jmolApplet([450,450],'load wp-content/uploads/2009/11/sn1-16-74.xyz; frame 1; zoom 100; connect (atomno=15) (atomno=1) PARTIAL;connect (atomno=1) (atomno=14) PARTIAL;vectors  on;vectors 4;vectors scale 5.0; color vectors black; vibration 20;animation mode loop;measure  17 24;measure 21 26;measure 22 18;measure 15 43;measure 44 30;measure 31 27;');"
width="254" height="301"}

Transition state for Sn1 solvolysis of tert-butyl chloride. Click for
animation.
:::

The model has not changed that much compared to before. The reaction
(imaginary) mode still clearly shows formation of the C-O bond and
cleavage of the C-Cl bond. Also as before, there is a lot of motion of
the methyl groups, as the forming cation induces stereo-electronic
alignment with the adjacent C-H bonds (and which explains the large
secondary deuterium isotope effects measured for this reaction,
k~H~/k~D~ (298) = 2.39, see DOI:
[10.1021/ja01080a004](http://dx.doi.org/10.1021/ja01080a004){target="references"}).
The hydrogen bonding pattern is also retained (despite the surrounding
solvent field!). But what of the predicted activation parameters

- ΔH^†^~298~ = 17.4 kcal/mol
- ΔG^†^~298~ = 18.7 kcal/mol
- ΔS^†^~298~ = -4.4 cal/mol/K

The overall free energy is in great agreement with experiment! But the
entropy is the wrong sign!! The calculation is predicting that the
transition state is more rigid than the reactant. One can see how this
might happen, since the greater ionic character produces very much
stronger hydrogen bonds, which strengthen the three solvent bridges. It
may be simply that the rigid-rotor-harmonic-oscillator approximation
breaks down horribly for the entropy in this calculation. But it is
encouraging that the activation barrier is reproducing experiment, which
suggests the model cannot be completely wrong!

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


In an earlier post I wrote about the iconic S
<sub>
 N
</sub>
1 solvolysis reaction, and presented a model for the transition state involving 13 water molecules. Here, I follow this up with an improved molecule containing 16 water molecules, and how the barrier for this model compares with experiment.

Messaggi di Rogue Scholar

The SN1 Reaction- revisited