Imperial College London

Henry Rzepa

Consider the four reactions. The first two are taught in introductory
organic chemistry as (a) a [proton
transfer, ]{style="color: #0000ff;"}often abbreviated
[PT,]{style="color: #3366ff;"} from X to B (a base) and (b) a [hydride
transfer]{style="color: #0000ff;"} from X to A (an acid). The third
example is taught as a hydrogen atom transfer or
[HAT]{style="color: #0000ff;"} from X to (in this example) O. Recently
an article has appeared\[cite\]10.1002/anie.201805511\[/cite\] citing an
example of a fourth fundamental type (d), which is given the acronym
[cPCET [which I will expand
later.]{style="color: #000000;"}]{style="color: #3366ff;"} Here I
explore this last type a bit further, in the context that X-H bond
activations are currently a very active area of research.  
[![](https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2018/07/XH-page001.svg){.aligncenter
.size-large .wp-image-19809 decoding="async"
width="450"}](https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2018/07/XH-page001.svg)

To help understand these four types, I have colour-coded the electron
pair constituting the X-H covalent bond in
[red]{style="color: #ff0000;"}.

1.  In mechanism (a), this electron pair stays with X, thus liberating a
    proton which is captured by the base.
2.  The hydride transfer (b) is so-called because in fact this electron
    pair travels together with the proton, hence the term hydride or
    H**[^--^]{style="color: #ff0000;"}**.
3.  Hydrogen atom transfers as in (c) in effect transfer both a proton
    and one electron to another atom (oxygen in the example above),
    leaving behind one electron on X. The electron and the proton are
    said to travel together as a "true" hydrogen atom.
4.  The fourth mechanism (d) is fundamentally different from (c) in that
    whilst the electron and the proton travel in concert (at the same
    time), they do not travel together. In this example the proton
    travels to the oxygen, whilst the electron travels to the iron
    centre, in the process reducing its oxidation state. This mode is
    now called a *concerted proton-coupled electron transfer*, or
    **[cPCET]{style="color: #3366ff;"}** as above.

The tool employed to distinguish between mechanisms (c) and (d) is the
IBO or intrinsic bond orbital localisation
scheme.\[cite\]10.1021/ct400687b\[/cite\] One practical advantage of
such a scheme over better known localisation methods such as NBO
(Natural bond orbitals) is that IBOs can be made to transform smoothly
during the course of a reaction, as followed by say an IRC (Intrinsic
reaction coordinate). NBOs may instead show discontinuous behaviour
along a reaction IRC. Klein and Knizia have located transition states
for examples of both (c) and (d) above and studied the IBOs along such
IRCs. The two IBO reaction transformations are very different, as
illustrated below (used, with permission, from the article itself). For
the HAT type (X=C above), an α-spin IBO morphs from a C-H bond into a
H-O bond, whilst the β-spin counterpart morphs from being located on the
C-H bond into a carbon-centered radical. For the cPCET mode, the α-spin
IBO morphs from C-H to a C-centered radical, but the β-spin region grows
onto an iron d-orbital. It is in fact even more complex than the diagram
above implies, since some reorganisation of the O-Fe region occurs and
the H...:O region is still anti-bonding at the transition state.

![](https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2018/07/024-1024x350.jpg){.aligncenter
.size-large .wp-image-19821 loading="lazy" decoding="async" width="450"
height="154"
srcset="https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2018/07/024-1024x350.jpg 1024w, https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2018/07/024-300x103.jpg 300w, https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2018/07/024-768x262.jpg 768w"
sizes="(max-width: 450px) 100vw, 450px"}

We can see from this that mechanistic reaction analysis is starting to
track the "curly arrows" we conventionally use to represent reactions in
some detail, as well as informing us about the relative detailing timing
of the various curly arrows used. Of course this latter aspect cannot be
easily represented by conventional curly arrows. It seems timely to
revisit the vast corpus of organic and organometallic "curly arrow
pushing" to starting adding such information!

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


A Theoretical Method for Distinguishing X‐H Bond Activation Mechanisms.

It is a sign of the times that one travels to a conference
well-connected. By which I mean email is on a constant drip-feed, with
venue organisers ensuring each delegate receives their WiFi password
even before their room key. So whilst I was at a conference [espousing
the benefits of open
science](http://www.ch.imperial.ac.uk/rzepa/blog/?p=18318), a
nice example of open collaboration was initiated as a result of a
received email.^‡^

Steven
Kirk [![](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2017/05/orcid_16x16.gif){loading="lazy"
decoding="async" width="16"
height="16"}](https://orcid.org/0000-0002-0462-6962){target="_blank"
rel="noopener noreferrer"} contacted me with the following query: *Do
you know of any open-access database of calculated IRCs with coverage of
as broad a range of classes of chemical reactions as possible*? I
recollected that about six years ago, I was exploring the use of iTunesU
as a system for delivering course content in a rich-media format. I
produced animations for about 115 reactions (many of which as it happens
were taken from this blog, but quite a number were also unique to that
project) and placed them into iTunesU, and now sending
the URL <https://itunes.apple.com/gb/course/id562191342> to Steven.

I should at this point explain something of the structure of such an
iTunesU course.

1. An essential feature is the course icon, seen below on the left.
 Since the course is hosted by Imperial College, it had to be an
 officially approved icon. I am sure you can believe me if I tell you
 that this took a month or so to obtain, with a fair bit of
 persistence required!
2. I also had to get approval to place the iTunes app on all the
 teaching computers so that students could open the course. Believe
 me again when I tell you that I had to persuade the Apple lawyers in
 Cupertino to release a special license for this app to persuade our
 administrators here to install it on the Windows teaching clusters.
 Another few months had passed by. 
 ![](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2017/05/096-1024x619.jpg){.aligncenter
 .size-large .wp-image-18335 decoding="async" width="550"
 srcset="https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2017/05/096-1024x619.jpg 1024w, https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2017/05/096-300x181.jpg 300w, https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2017/05/096-768x464.jpg 768w, https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2017/05/096.jpg 2048w"
 sizes="(max-width: 1024px) 100vw, 1024px"}
3. When creating an entry (using
 *e.g. *<https://itunesu.itunes.apple.com/coursemanager/> ) one has
 to specify values for various descriptors, also often called
 metadata. Thus any one entry has fields for **name** and
 **description**, with the **popularity** added by Apple. Only a few
 words are visible in the description field, which can be expanded in
 iTunes using the *i*
 button.![](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2017/05/097-1024x89.jpg){.aligncenter
 .size-large .wp-image-18336 loading="lazy" decoding="async"
 width="450" height="39"
 srcset="https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2017/05/097-1024x89.jpg 1024w, https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2017/05/097-300x26.jpg 300w, https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2017/05/097-768x66.jpg 768w, https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2017/05/097.jpg 1456w"
 sizes="(max-width: 450px) 100vw, 450px"}
4. Steven meanwhile had replied asking if the original data that was
 used to generate the IRC might be available. Specifically his second
 question was "*So the DOIs are only stamped into the animation's
 bitmaps, or are they also somewhere in the metadata?*". That
 little *i* button is not easy to spot, and there is no indication,
 in the event, of what information it might actually contain.
5. Here it is expanded. The contents are unstructured text, into which
 I have placed the required
 DOI.![](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2017/05/098.jpg){.aligncenter
 .size-full .wp-image-18337 decoding="async" width="540"
 srcset="https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2017/05/098.jpg 718w, https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2017/05/098-300x236.jpg 300w"
 sizes="(max-width: 718px) 100vw, 718px"}
6. The lesson here is that I had fortunately had the foresight to
 include a link to the IRC data in anticipation of just such a
 question from someone in the future. But black mark to Apple here;
 the text cannot be selected and copied into a clipboard! It is
 fairly unFAIR data, since it can only be inter-operated (the I of
 FAIR) by a human re-typing it by hand. And the human has also to
 recognise the pattern of a DOI; a machine could not obtain this
 information easily. Moreover Steven is a Linux user; he does not
 readily have access to the iTunes app on this operating system!
7. Also, there were 115 such entries, and now the prospect was rearing
 that each would have to be hand processed. Moreover, because the
 text was unstructured, there was no guarantee that I would have
 adopted the same pattern for all 115 entries.
8. Fortunately Steven was on the ball. I quote again: *it turns out
 iTunes isn't needed at all. A service I found on the web
 <http://picklemonkey.net/feedflipper-home/> takes an ITunes URL and
 converts it to an RSS feed. Opening this feed in Firefox and RSSOwl
 respectively let me save the feed as XML and HTML (both attached).*
9. This is currently where we stand (Steven's first email was two days
 ago), but it's not finished yet. Depending on how assiduous I was
 five years ago, some DOIs to the data may be acquired from the list.
 Sometimes I simply wrote e.g. *See
 http://www.ch.imperial.ac.uk/rzepa/blog/?p=6816* knowing that the
 links to the data were there instead. I can already see that some
 descriptions have neither a DOI nor a link to the blog. More
 detective work will be needed, unfortunately.

How might the situation described above been avoided? Well, Apple in
iTunesU only provided in effect one metadata field, and this was an
unstructured one. Anything went in that field. Had they provided (or had
the course creator been able to configure it themselves) there might
have been another field entitled say "**data source**". This could
moreover been made a mandatory field and a structured one. Thus it might
have only accepted known types of persistent identifier, such as a DOI.
Further, the system could have checked that the DOI was actually
resolvable. Before you ask, I did log a "bug" with Apple asking this be
done, but nothing ever was. With such a tool to hand, I might have
achieved data sources for all the 115 entries. The resulting XML (as
generated above) could have been used to automate the retrieval of all
115 datasets describing this course. 

At this stage then, Steven can follow-up his interest in building a
reaction IRC library and analysing it. I will do all I can to encourage
Steven not to make the mistakes I did and to ensure that any further
data that is required to augment the library does not suffer the
problems above. On the other hand, I console myself that in two days,
much of the data for the course I created five years ago was
salvageable; I wonder how many other iTunesU courses there are for which
that can be said!

I will let (with some blushing) the final word be Steven's: *You are one
of the few chemists who has both pioneered and built the principles of
'open chemistry' into their actual scientific work. I visit your blog
occasionally knowing that there is a very high probability I could
download and tinker with the results of real calculations.*

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

^‡^Might I assure all the speakers that I concentrated totally on their
talks rather than incoming emails!

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

It is a sign of the times that one travels to a conference well-connected. By which I mean email is on a constant drip-feed, with venue organisers ensuring each delegate receives their WiFi password even before their room key.

Conference report: an example of collaborative open science (reaction IRCs).

The BBC TV quiz series **Mastermind** was first broadcast in the UK in
1972, the same time I was starting to investigate the mechanism of
diazocoupling to substituted indoles as part of my Ph.D. researches. The
BBC program became known for the catch phrase *[I\'ve started so I\'ll
finish](https://en.wikipedia.org/wiki/Mastermind);* here I will try to
follow this precept with the project I started then. [![Indole
diazocoupling](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2015/12/indole-4.svg){.aligncenter
.size-full .wp-image-14967 decoding="async"
width="440"}](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2015/12/indole-4.svg)
In 1972, one measured the rates of chemical reactions to gain insights
into the transition state kinetic model. To obtain more data, we used
isotopes such as ^2^H or ^3^H, together with substituents such as
R-t-butyl to modify the potential energy surfaces of the reactions by
inducing *steric
effects*.\[cite\]10.1039/P29750001209\[/cite\],\[cite\]10.5281/zenodo.18777\[/cite\]
We found that the kinetics for this reaction were actually complex^‡^
(in part because of pH dependence) involving a Wheland intermediate (the
formation of which is shown with red curly arrows above) followed by the
collapse of this intermediate to the diazo-coupled product (blue
arrows). Coupling to 2-methyl indole (R=X=H, R\'=Me), 2-t-butyl indole
(R=H, R\'=t-butyl) and 4-methyl-2-t-butyl indole (R=Me, R\'=t-butyl)
revealed that the kinetic isotope effects induced by replacing H by D or
T were \"*not apparent*\" (*i.e.* close to 1), the inference being that
the rate constant k~1~ for those systems was slower than k~2~;
the~ ~formation of the Wheland intermediate was *rate determining* (the
rds) for the reaction. But with 2-methyl-4,6-di-t-butyl indole
(R=t-butyl, R\'=Me) this changed and a deuterium isotope effect of \~7
was observed. The rate determining proton removal from the Wheland
intermediate k~2~ was now slower than k~1~. With 2,4,6-tri-t-butyl
indole, we ended by noting that the reaction become almost too slow to
observe and furthermore was accompanied by loss of a t-butyl cation as
well as a proton. At this point we attempted to infer some transition
state models consistent with these observations. Note that we had
relatively little data with which to derive our 3D models (one needs to
define a geometry using 3N-6 variables, along with its relative energy
and force constants). The text and diagram of our attempt is shown
below.
![TS1](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2015/12/Indole-ts-model.jpg){.aligncenter
.size-full .wp-image-14967 decoding="async" width="400"} The main points
of this argument were;

1. That the Wheland complex is asymmetric, with the diazonium ion
 adopting a pseudo-axial line of attack.
2. In contrast, the leaving proton lies closer to the plane of the
 indole ring
3. The abstracting base experiences \"*steric hindrance*\" if R
 = t-butyl but not if R\' = t-butyl.

I was eager to find out how one might test these models by quantum
computation and my next stop in 1974 was to Austin Texas, where Michael
Dewar\'s  group was soon to [break the
record](http://www.ch.imperial.ac.uk/rzepa/blog/?p=5290) for computing
the geometry of a molecule with 49 atoms (similar in size to the
reactions shown above) using the then very new semi-empirical MINDO/3
valence-shell quantum theory. The theory still needed much improvement
in a great many aspects and the last forty years has brought us features
such as density functional theories, far more accurate all-electron
basis sets, superior geometry optimisation methods for transition
states, code parallelisation, solvation treatments and increasing
recognition that a particular form of electron correlation associated
with dispersion energies needed specific attention. These methods would
not have become applicable to molecules of this size had the computers
themselves not become perhaps 10 million times faster during this
period, with a commensurate increase in the digital memories required
and decrease in cost. Time then to apply a B3LYP+D3/Def2-TZVP/SCRF=water
quantum model to the problem. Four species were computed for each set of
substituents; the reactant, a transition state for C...N bond formation
(TS1), a Wheland intermediate and a transition state for C-H bond
cleavage (TS2). The relative free energies of the last three with
respect to the first are shown in the table below. An IRC for R=R\'=H
(below) was used to show that a *bona-fide*^†^ Wheland intermediate is
indeed formed.\[cite\]10.14469/ch/191707\[/cite\]

| |
|--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|
| IRC animation for TS1, R=R\'=H |
| ![TS1 IRC](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2015/12/indole1.gif){.aligncenter .size-full .wp-image-14967 decoding="async" onclick="jmolInitialize('../Jmol/','JmolAppletSigned.jar');jmolSetAppletColor('white');jmolApplet([450,450],'load wp-content/uploads/2015/12/indole-ts1.log;frame 13;');" width="400"} |
| IRC for TS2, R=R\'=H |
| ![TS2](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2015/12/indole-ts2a.gif){.aligncenter .size-full .wp-image-14967 decoding="async" onclick="jmolInitialize('../Jmol/','JmolAppletSigned.jar');jmolSetAppletColor('white');jmolApplet([450,450],'load wp-content/uploads/2015/12/indole-ts2.log;frame 87;');" width="350"} |

The relative free energies (kcal/mol) are shown in the table below and
the following conclusions can be drawn from this computed model:

1. For R=R\'=H, ΔG~298~^‡^ for TS1 is ***higher*** than TS2 ([✔ with
 expt]{style="background-color:#00FF00;"})
2. With R=t-butyl,R\'=Me, ΔG~298~^‡^ of TS1 is 3.1 kcal/mol ***lower***
 than with R=R\'=H. This indicates that t-butyl and methyl groups
 actually ***activate*** electrophilic addition by stabiisation of
 the induced positive charge, and have ***no steric effect*** upon
 the first step ([✔ with our
 conclusions]{style="background-color:#00FF00;"}).
3. For R= t-butyl,R\'=Me, ΔG~298~^‡^ of TS1 is ***lower*** than TS2 ([✔
 with expt]{style="background-color:#00FF00;"}).
4. With R=R\'= t-butyl, ΔG~298~^‡^ of TS2 is 4.9 kcal/mol higher than
 with R=R\'=H and is 3.1 kcal/mol higher with
 R=t-butyl,R\'=Me, indicating the steric effect acts on this stage.
5. The angle of approach of the diazonium electrophile is \~123-118°
 for R=R\'=H and R=R\'=t-butyl, about 30° away from a
 strict pseudo-axial \"reactant-like\" approach as implied in our
 sketch above ([❌ with diagram
 above]{style="background-color:#FFA500;"})
6. The angle of proton abstraction with the plane of the indole ring is
 107° for R=R\'=H and 100.3° for R=R\'=t-butyl, the hydrogen being
 closer to pseudo-axial than equatorial, relative to the plane of the
 indole ring  ([❌ with diagram
 above]{style="background-color:#FFA500;"}).
7. The position along the reaction path for proton abstraction is much
 later with R=R\'=t-butyl (r~C-H~ \~1.42Å) than R=R\'=H (r~C-H~
 \~1.27Å),  ([❌ with the statement
 above]{style="background-color:#FFA500;"}: a *reactant-like
 transition state even for the proton expulsion step*).
8. The cross-over between TS1/TS2 as the rds is in the region of the
 substituents R=Me,R\'=t-butyl (\~[✔ with
 expt]{style="background-color:#00FF00;"}).
9. The steric interaction occurs not so much between the incoming base
 and the t-butyl groups, but because of enforced proximity between
 the t-butyl group and the diazo group induced during the proton
 removal stage.
10. The steric effect induced by R=t-butyl is greater than when
  R\'=t-butyl.
11. The Wheland intermediate is in a relatively shallow minimum.

<table data-border="1">
<colgroup>
<col style="width: 12%" />
<col style="width: 12%" />
<col style="width: 12%" />
<col style="width: 12%" />
<col style="width: 12%" />
<col style="width: 12%" />
<col style="width: 12%" />
<col style="width: 12%" />
</colgroup>
<tbody>
<tr class="header">
<th>R, R'</th>
<th>TS1, 
ΔG298‡  k1</th>
<th>∠ N1-C3-N2</th>
<th>Int 
ΔG298 </th>
<th>TS2, 
ΔG298‡  k2</th>
<th>∠ N1-C3-H</th>
<th>ΔΔG‡ 
(TS2-TS1)</th>
<th>kH/kD 
(calc) 
[cite]10.5281/zenodo.19272[/cite],[cite]10.14469/hpc/176[/cite]</th>
</tr>
&#10;<tr class="odd">
<td>R=R'=H</td>
<td>21.4[cite]10.14469/ch/191705[/cite],[cite]10.14469/ch/191698[/cite]</td>
<td>122.9</td>
<td>19.6[cite]10.14469/ch/191713[/cite]</td>
<td>18.6[cite]10.14469/ch/191712[/cite]</td>
<td>107.0</td>
<td>-1.8</td>
<td>0.925 (TS1)</td>
</tr>
<tr class="even">
<td>R=Me,R'=t-butyl</td>
<td>16.9[cite]10.14469/ch/191723[/cite],[cite]10.14469/ch/191719[/cite]</td>
<td>121.8</td>
<td>15.2[cite]10.14469/ch/191721[/cite]</td>
<td>18.4[cite]10.14469/ch/191720[/cite]</td>
<td>101.8</td>
<td>+1.5</td>
<td>0.900 (TS1) 
6.4 (TS2)</td>
</tr>
<tr class="odd">
<td>R=t-butyl,R'=Me</td>
<td>18.3[cite]10.14469/ch/191722[/cite],[cite]10.14469/ch/191717[/cite]</td>
<td>115.2</td>
<td>16.0[cite]10.14469/ch/191726[/cite]</td>
<td>21.7[cite]10.14469/ch/191714[/cite]</td>
<td>100.9</td>
<td>+3.4</td>
<td>6.8 (TS2)</td>
</tr>
<tr class="even">
<td>R=R'=t-butyl</td>
<td>17.8[cite]10.14469/ch/191715[/cite],[cite]10.14469/ch/191706[/cite]</td>
<td>117.6</td>
<td>17.8[cite]10.14469/ch/191709[/cite]</td>
<td>23.5[cite]10.14469/ch/191718[/cite]</td>
<td>100.4</td>
<td>+5.2</td>
<td>6.9 (TS2)</td>
</tr>
</tbody>
</table>

### Possible errors in the model: {#possible-errors-in-the-model}

1. I have not included any explicit solvent water in which hydrogen
 bonds to the base (the chloride anion) might moderate its
 properties.
2. The ion-pair reactant complex between the phenyl diazonium chloride
 and the indole has many possible orientations, and these have not
 been optimised.
3. The free energies are subject to the usual errors due to the
 rigid-rotor approximations and other artefacts of partition
 functions.
4. Other DFT functionals have not been explored, nor have better basis
 sets.
5. [This current
 study](http://www.ch.imperial.ac.uk/rzepa/blog/?p=12056){target="_blank"
 rel="noopener"} is confined to formation of the *cis*-diazo product.

But even such a model seems to reproduce much of what we learnt about
diazocoupling to 2,4-substituted indoles. The calculations you see above
took about a week to set up and complete; the original experimental work
took (in real-time) \~150 weeks (interleaved with two other mechanistic
studies). Also efficient implementation of the quantum theories,
together with the computer resources to evaluate the molecular energies
and geometries, was almost entirely lacking in 1972 and this has
probably only become a realistic project in the last five years or so.
So that 43 year wait to finish what I started seems not unreasonable.
Nowadays of course, combining experimental kinetic measurements with
computational models very often goes hand in hand. It is also worth
speculating about the wealth of mechanistic data garnered during the
heyday of physical organic chemistry during  the period \~1940-1980. The
experiments were not then informed by feedback from computational
modelling. However, it seems unlikely that very many of these
mechanistic studies will ever be retrospectively augmented with computed
models; the funding for the resources to do so is unlikely to ever be
seen as a priority.

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

^‡^A little more complex than the scheme above, since the reaction also
exhibits dependency on acid concentration. Nowadays, there are a number
of computer programs available for analysing such complex kinetics, but
in 1972 I had to write my own non-linear least squares
fitting analysis of the steady state equation to the measured
rates\[cite\]10.5281/zenodo.18777\[/cite\] This replaced the use of
graph paper to analyse (of necessity much simpler) rate equations. I
note that mentions of non-linear least squares methods in kinetic
analyses start around 1986\[cite\]10.1021/j100281a038\[/cite\] Even
by 1992, the topic was considered novel enough to warrant a
publication\[cite\]10.1002/aic.690380419\[/cite\]

^†^The related diazo coupling to activated aryls such as phenol or
aniline shows a mechanistic cross-over between an entirely synchronous
path in which no Wheland intermediate is involved (e.g.
phenol)\[cite\]10.14469/ch/191700\[/cite\] to one where the intermediate
does form (*e.g.* aniline).\[cite\]10.14469/ch/191699\[/cite\] Diazo
coupling to *e.g.* benzofuran rather than indole by the way is also
stepwise, but *via* a very shallow Wheland
intermediate\[cite\]10.14469/ch/191730\[/cite\] and with a higher
barrier than indole, making it a very slow reaction.

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#### Acknowledgments

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The BBC TV quiz series

 Mastermind

was first broadcast in the UK in 1972, the same time I was starting to investigate the mechanism of diazocoupling to substituted indoles as part of my Ph.D. researches. The BBC program became known for the catch phrase

 I've started so I'll finish;

here I will try to follow this precept with the project I started then.

Messaggi di Rogue Scholar

A Theoretical Method for Distinguishing X‐H Bond Activation Mechanisms.

Conference report: an example of collaborative open science (reaction IRCs).

I’ve started so I’ll finish. The mechanism of diazo coupling to indoles – forty (three) years on!