Imperial College London

Henry Rzepa

Curly arrow pushing is one of the essential tools of a mechanistic
chemist. Many a published article will speculate about the arrow pushing
in a mechanism, although it is becoming increasingly common for these
speculations to be backed up by quantitative quantum mechanical and
dynamical calculations. These have the potential of exposing the
underlying choreography of the electronic dance (the order in which the
steps take place). The basic grammar of describing that choreography
tends to be the full-headed **curly arrow** for closed shell systems and
its half-barbed equivalent for open shell systems. An effectively
unstated and hence implicit rule for closed shell systems is that only
one curly arrow is used per breaking or forming bond, i.e. electrons
move around bonds in pairs. So consider the following reaction (inspired
by a posting on  [Steve Bachrach's
blog](http://comporgchem.com/blog/?p=487#comments){target="references"})

![Oxygen-nitrogen exchange between three nitrosonium
cations](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2009/11/no-exchange.jpg "Oxygen-nitrogen exchange between three nitrosonium cations"){.aligncenter
.size-full .wp-image-1159 loading="lazy" decoding="async" width="522"
height="152"}

This is very much a hypothetical mechanism, or a thought-experiment if
you will. Three nitrosonium cations decide to get together to swap their
partners. Each diatomic molecule swaps e.g. one oxygen for another
during this exchange reaction (it could easily be studied experimentally
of course using isotopic substitution). Three sets of three curly arrows
have been used, shown in different colours above.  One set of these
arrows at least has plenty of analogy in the real world; representing a
~π~2~s~+~π~2~s~+~π~2~s~ cycloaddition reaction. The other two sets
represents rotation of the  in-plane π-set and the in-plane σ-set. What
about the choreography? Can all three sets move at the same time? If so,
they would provide an exception to the rule above; three bonds would
concurrently change their order from 3 to 0; the other three the reverse
of 0 to 3.

What does quantum mechanics say about this? Well, a well defined,
synchronous concerted transition state can indeed be found
(B3LYP/6-31G(d), DOI:
 [10042/to-2905](http://hdl.handle.net/10042/to-2905){target="references"}) It
has one imaginary frequency (click on the above diagram to view the
animation) which does indeed perform the bond transposition function
required! It has the form of the so-called Kekule mode (deriving from a
mode found in benzene which involves shortening of the lengths of three
bonds, and lengthening of the other three, much in the manner of the
resonance named after  Kekule; see e.g. DOI:
[10.1039/B911817A](http://dx.doi.org/10.1039/B911817A){target="references"}
for more details). Of course, describing it as a change in the bond
orders 3 → 0/0 → 3 is simplistic; the bond order in the nitrosonium
cation itself is almost certainly somewhat less than three.  But
clearly, the implicit rule that  mechanistic arrow pushing should not
involve more than one arrow departing from or arriving at any one bond
can be broken. I will leave it to the reader of this blog to see what
happens when you try to rearrange the choreography of the above
reaction. Try pushing first one set of three arrows, then another and a
final third. What do you get? (the why of the dance is almost certainly
due to electrostatic repulsions between the three nitrosonium cations).

::: {.wp_orcid_field}
[https://orcid.org/0000-0002-8635-8390](https://orcid.org/0000-0002-8635-8390){target="_blank"
rel="author"}
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Curly arrow pushing is one of the essential tools of a mechanistic chemist. Many a published article will speculate about the arrow pushing in a mechanism, although it is becoming increasingly common for these speculations to be backed up by quantitative quantum mechanical and dynamical calculations.

Messaggi di Rogue Scholar

Mechanistic Ménage à trois