Imperial College London

Henry Rzepa

The [discussion appended to the
post](http://www.ch.imperial.ac.uk/rzepa/blog/?p=7234&cpage=1#comment-10033){target="_blank"
rel="noopener"} on curly arrows is continued here. Recollect the curly
arrow diagram (in modern style) derived from Robinson's original
suggestion:

![](http://www.ch.imperial.ac.uk/rzepa/blog/wp-content/uploads/2012/07/robinson11.svg "robinson1"){.aligncenter
.size-full .wp-image-7269 decoding="async"}

The pertinent point is that the angle subtended at the nitrogen atom
evolves from being bent (\~115°) on the left, to linear (180°) on the
right. The nitrogen hybridisation changes from trigonal (sp^2^) to
digonal (sp). Because of this, the scheme must represent a reaction
rather than a resonance. What kind of species is the molecule on the
right? A ωB97XD/6-311G(d,p) solution of the wave equation indicates it
is a ***transition state***. The normal mode indicates that the nitrogen
atom is moving out of the plane of the ring, evolving the C=N double
bond back into having a nitrogen lone pair, and apparently on the way to
a most interesting non-planar valence-bond isomer of nitrosobenzene. You
might have noticed a nitro group has appeared in the 4-position. I did
this to try to stabilize the negative charge in this position shown on
the right above to prevent it from being a transition state; this
subterfuge failed!

::: {#attachment_7270 .wp-caption .aligncenter style="width: 268px"}
![](http://www.ch.imperial.ac.uk/rzepa/blog/wp-content/uploads/2012/07/nitroso-C2v.jpg "nitroso-C2v"){.wp-image-7270
loading="lazy" decoding="async"
aria-describedby="caption-attachment-7270" width="258" height="157"}

The linear form is a transition state. Click for 3D
:::

What about an [IRC](http://hdl.handle.net/10042/20247){target="_blank"
rel="noopener"} (intrinsic reaction coordinate)? It starts off downhill
from the transition state at IRC = 0.0. To quote Monty Python, and [now
for something completely
different](http://en.wikipedia.org/wiki/And_Now_for_Something_Completely_Different){target="_blank"
rel="noopener"}. At IRC 2.65, something does indeed happen, a most
unusual feature in potential energy surfaces; a ***bifurcation point***.

![](http://www.ch.imperial.ac.uk/rzepa/blog/wp-content/uploads/2012/07/NO-rot.svg "NO-rot"){.aligncenter
.size-full .wp-image-7275 decoding="async"}

![](http://www.ch.imperial.ac.uk/rzepa/blog/wp-content/uploads/2012/07/NO-rotg.svg "NO-rotg"){.aligncenter
.size-full .wp-image-7276 decoding="async"}

I am going to have to explain this. Normally, a transition state (a
saddle point of order 1) connects two minima. But a bifurcation means
that one transition state leads directly downhill (without any
intervening minima) to another transition state. When the lower energy
transition state is reached, the potential bifurcates, since it now has
two (equal) directions for it to continue its downhill descent. Our IRC
at this point has to somehow chose which of these two to take. In fact
the choice is made randomly. To be precise, small so-called round-off
errors in computing the derivatives of the path favour by a tiny tiny
margin one of the pathways over the other, and so off it heads. As you
can see below, this second pathway involves an (anticlockwise) rotation
of the nitroso group (it could also have chosen clockwise).

![](http://www.ch.imperial.ac.uk/rzepa/blog/wp-content/uploads/2012/07/NO-rot1.gif "NO-rot"){.aligncenter
.size-full .wp-image-7305 loading="lazy" decoding="async" width="321"
height="331"}

That rotation can now be represented by the following.

![](http://www.ch.imperial.ac.uk/rzepa/blog/wp-content/uploads/2012/07/robinson2.svg "robinson2"){.aligncenter
.size-full .wp-image-7273 decoding="async"}

I continue to be surprised at where we have arrived at from Robinson's
original curly arrows; bifurcated potential energy surfaces. Well, that
introductory student tutorial to curly arrow pushing is going to have to
cover a lot of ground! 

\[qrcode content="Robinson" size="200″ alt="QRCode" class="CLASS_NAME"
align="right"\]

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


The discussion appended to the post on curly arrows is continued here. Recollect the curly arrow diagram (in modern style) derived from Robinson’s original suggestion:      The pertinent point is that the angle subtended at the nitrogen atom evolves from being bent (~115°) on the left, to linear (180°) on the right.

Publicaciones de Rogue Scholar

The first ever curly arrows. And now for something completely different.