Imperial College London

Henry Rzepa

Another mechanistic study we started
in 1972\[cite\]10.1039/P29770000281\[/cite\] is here 40+ years
on subjected to quantum mechanical scrutiny.

[![Indole
diazocoupling](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2015/12/decarbox.svg){.aligncenter
.size-full .wp-image-14967 decoding="async" style="text-align: justify;"
width="440"}](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2015/12/decarbox.svg)

The kinetics are again complex, the mechanism involving protonation^‡^
of the indole carboxylate (by a general acid), followed by the
presumption of a zwitterionic Wheland intermediate that then loses
carbon dioxide in a second step (blue arrows). Kinetically
indistinguishable is a concerted alternative in which both steps are
conflated into a concerted but not necessarily synchronous process (red
arrows). In 1972, this latter mechanistic alternative was never really
considered, iin part because it was not easy to prove or disprove an
asynchronous concerted route by experiment. A brief summary of the
conclusions:

1.  The reaction was found to be catalysed by a general acid.
2.  But a residual rate at low acid concentration was measured,
    corresponding to catalysis by water as an acid (shown in the scheme
    above).
3.  A deuterium isotope effect of \~2.2-2.7 on the apparent protonation
    step was observed when the reaction was conducted in D~2~O rather
    than H~2~O (the disentangled complex kinetics yielded isotope
    effects for two other kinetic parameters as well, also in the range
    2.0-2.6).
4.  The isotope effects were found to be insensitive to various
    substituents on the indole, leading to the final conclusion that
    isotope effects for proton transfer are little influenced by the
    symmetry of the process.

Here, I set out to test some of these forty-year old assumptions; in
particular to see if a model can be constructed that reproduces the
unusually low value of the primary deuterium kinetic isotope effect,
since normally proton transfers to carbon sustain a value closer to 7.

Now for the mechanism. Shown below are eight potential models for the
process.

1.  Model **1** is the most basic, with just a single water molecule
    delivering a proton to the 3-position of the indole and abstracting
    it from the carboxylic acid group.
2.  Models **1a**, **1b** and **1c** add a second water as a passive
    hydrogen bonder.
3.  Model **2** is isomeric to **1a,b,c** but the second water now
    actively participates in the proton relay.
4.  Model **3** replaces the single water molecule with a more acidic
    proton relay molecule, ethanoic acid (red).
5.  Models **4** and **5** augment model **3** with one water molecule
    as well, in two different positions.
6.  Model **6** uses a three-water proton relay with one
    H-bonding water.
7.  Model **7** uses a two-water proton relay with two H-bonding waters.

[![Indole
diazocoupling](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2015/12/decarbox1.svg){.aligncenter
.size-full .wp-image-14967 decoding="async" style="text-align: justify;"
width="440"}](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2015/12/decarbox1.svg)

The results of a B3LYP+D3/Def2-TZVP/SCRF=water calculation are collected
below in the table. The following conclusions can be drawn:

1.  Model **1**, with just a single water molecule acting as proton
    transfer acid/base reveals a concerted route *via* TS. 
2.  Model **1b**, with an extra water acting via a hydrogen bond now
    changes the mechanism to stepwise via  TS1 and  TS2, the latter
    being some 12.6 kcal/mol lower in energy and hence making  TS1 rate
    determining. The kinetic deuterium isotope effect (KIE) on  TS1 of
     7.27 is much larger than is observed.  That for the second step TS2
    is negligible.
3.  Model **2**, isomeric with **1b**, is lower by 4 kcal/mol, largely
    due to a more favourable geometry for linear proton transfer. The
    KIE is getting closer to the observed value as is the free energy
    barrier (measured as ΔG^‡^~298~ 22
    kcal/mol\[cite\]10.1039/P29770000281\[/cite\]).
4.  Model **3** replaces the water proton transfer agent by ethanoic
    acid, with a significant lowering of the barrier. This constitutes a
    prediction for protiodecarboxylation in ethanoic acid solutions.
5.  Models **4** and the isomeric 5 now combines models **2**+**3**, and
    represents one possibility for general acid catalysis in aqueous
    ethanoic acid solutions. The KIE is predicted to rise significantly
    (again, this experiment has not been done).
6.  Model **7** incorporates model 2 (a two-water proton relay) with two
    additional passive water molecules acting *via* hydrogen bonds. The
    barrier is converging to the measured value, and the KIE has now
    dropped below the measured value! As before TS2 is lower (by 6.8
    kcal/mol) than TS1.
7.  Model **6** (below) is isomeric with model **7** and incorporates a
    three-water proton relay with one solvating water,^†^ with a
    predicted KIE higher than model 6.

![Indole
diazocoupling](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2015/12/decarbox-3+1.jpg){.aligncenter
.size-full .wp-image-14967 decoding="async"
onclick="jmolInitialize('../Jmol/','JmolAppletSigned.jar');jmolSetAppletColor('white');jmolApplet([450,450],'load wp-content/uploads/2015/12/decarbox-3+1-858.366540.log;frame 13;vectors on;vectors 4;vectors scale 8.0;color vectors green;vibration 6;');"
style="text-align: justify;" width="400"}

|        |                   |                                                                                                             |                                            |                                             |
|--------|-------------------|-------------------------------------------------------------------------------------------------------------|--------------------------------------------|---------------------------------------------|
| Model  | ΔG^‡^~298~        | dataDOIs                                                                                                    | Mechanism                                  | k^H^/k^D^ \[cite\]10.14469/hpc/179\[/cite\] |
| **1**  | 33.8              | \[cite\]10.14469/ch/191738\[/cite\],\[cite\]10.14469/ch/191728\[/cite\]                                     | TS\[cite\]10.14469/ch/191735\[/cite\]      | 9.88                                        |
| **1a** | 35.6              | \[cite\]10.14469/ch/191737\[/cite\],\[cite\]10.14469/ch/191733\[/cite\]                                     | --                                         | --                                          |
| **1b** | 33.8 (21.2)       | \[cite\]10.14469/ch/191737\[/cite\],\[cite\]10.14469/ch/191732\[/cite\],\[cite\]10.14469/ch/191748\[/cite\] | TS1,TS2\[cite\]10.14469/ch/191741\[/cite\] | 7.27 (1.05)                                 |
| **1c** | 33.9              | \[cite\]10.14469/ch/191737\[/cite\],\[cite\]10.14469/ch/191729\[/cite\]                                     | --                                         | --                                          |
| **2**  | 29.9              | \[cite\]10.14469/ch/191737\[/cite\],\[cite\]10.14469/ch/191731\[/cite\]                                     | TS1,TS2\[cite\]10.14469/ch/191739\[/cite\] | 4.20                                        |
| **3**  | 20.9              | \[cite\]10.14469/ch/191745\[/cite\],\[cite\]10.14469/ch/191743\[/cite\]                                     | TS1,TS2\[cite\]10.14469/ch/191749\[/cite\] | 4.29                                        |
| **4**  | 25.7              | \[cite\]10.14469/ch/191747\[/cite\],\[cite\]10.14469/ch/191734\[/cite\]                                     | TS1,TS2\[cite\]10.14469/ch/191751\[/cite\] | --                                          |
| **5**  | 24.4              | \[cite\]10.14469/ch/191747\[/cite\],\[cite\]10.14469/ch/191742\[/cite\]                                     | TS1,TS2\[cite\]10.14469/ch/191754\[/cite\] | 8.55                                        |
| **6**  | 23.9              | \[cite\]10.14469/ch/191753\[/cite\],\[cite\]10.14469/ch/191755\[/cite\]                                     | TS1,TS2                                    | 5.66                                        |
| **7**  | 24.3 (**8**:17.9) | \[cite\]10.14469/ch/191753\[/cite\],\[cite\]10.14469/ch/191750\[/cite\],\[cite\]10.14469/ch/191752\[/cite\] | TS1,TS2\[cite\]10.14469/ch/191756\[/cite\] | 1.44                                        |

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

These models show that the arrangements of the solvation and
proton-relay components of the mechanism are crucial to understanding
the kinetic isotope effects induced by deuterium. The partition function
ratios responsible for the KIE emerge\[cite\]10.14469/hpc/179\[/cite\]
as a complex function of the structure and so the KIE itself provides a
particularly sensitive probe of these structures. This exploration is
not stochastical in nature;  there are clearly many more variations in
which even more than four water molecules could be used in the model.
One would take the Boltzmann population/weight of each pose and use
these to predict the statistical probability of properties such as the
KIE. Working in the other direction and from the results shown in the
table, a population of \~25% of model **6** and 75% of model **7** would
give a KIE in agreement with experiment. A more complete stochastical
model would no doubt include many more solvation structures.

In 1972, transition state models could only be slowly and painfully
constructed by accumulating kinetic data and making many assumptions.
Quantum computation provides a more systematic and rational way in which
to base the assumptions. What has emerged for this reaction is that the
rate determining protonation of a 3-carboxyindole prior to its
decarboxylation is largely defined by the solvation structures that
accumulate in the transition state;  we are really learning about
solvation here rather than just proton transfer. The two techniques
together, experimental kinetics and quantum chemical modelling, are true
symbiotes in each informing the other.

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

^‡^Here is a crystal structure which shows an O-H hydrogen bond to the
π-face of the indole 5-ring, indicating the indole π-system is basic
enough to hydrogen-bond with an acidic
proton.\[cite\]10.5517/CC10K1M7\[/cite\] ^†^This water molecule has an
additional role, which I will describe in a separate post.

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

#### Acknowledgments

This post has been cross-posted in PDF format at
[Authorea](https://doi.org/10.15200/winn.145337.72491){rel="noopener"
target="_blank"}.

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Another mechanistic study we started in 1972[cite]10.1039/P29770000281[/cite] is here 40+ years on subjected to quantum mechanical scrutiny.

Messaggi di Rogue Scholar

I’ve started so I’ll finish. Mechanism and kinetic isotope effects for protiodecarboxylation of indoles.