Imperial College London

Henry Rzepa

Clar islands are found not so much in an ocean, but in a type of
molecule known as polycyclic aromatic hydrocarbons (PAH). One member of
this class,
[graphene](http://en.wikipedia.org/wiki/Graphene){target="_blank"}, is
attracting a lot of attention recently as a potential material for use
in computer chips. Clar coined the term in 1972 to explain the
properties of PAHs, and the background is covered in a recent article by
Fowler and co-workers (DOI:
[10.1039/b604769f](http://dx.doi.org/0.1039/b604769f){target="_blank"}).
The concept is illustrated by the following hydrocarbon:

::: {#attachment_1293 .wp-caption .aligncenter style="width: 223px"}
![Clar islands in a polybenzenoid
hydrocarbon](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2009/12/C42H18-diag.jpg "C42H18-diag"){.size-full
.wp-image-1293 loading="lazy" decoding="async"
aria-describedby="caption-attachment-1293" width="213" height="245"}

Clar islands in a polybenzenoid hydrocarbon
:::

The Clar islands are shown in red, and represent in effect the resonance
form of this species which maximises the number of aromatic electronic
sextets possible to achieve via a cyclohexatriene resonance form. It
encapsulates the concept that maximum stabilization is achieved when the
π-electrons in the molecule cluster together (or localize) in cyclic
groups of six (rather than eg other allowed values as predicted by the
4n+2 rule of aromaticity). As a historical note, although Clar
popularized the concept in the 1970s, the (C) representation had in fact
been introduced almost one hundred years earlier, by Henry Armstrong
(DOI: [10.1039/PL8900600095](http://dx.doi.org/10.1039/PL8900600095)).
Many demonstrations that Clar islands are reasonably based in quantum
mechanical reality have been made; a very graphical and convincing one
is that by Fowler and coworkers in the reference noted above, using the
calculated magnetic response property known as π current densities
(although this shows that the six outer islands tend merge into a single
continuous outer periphery).

![Current density maps showing Clar islands (taken from DOI: 10.1039/b604769f](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2009/12/c42-fowler.jpg "c42-fowler"){.size-full .wp-image-1296 loading="lazy" decoding="async" width="240" height="220"}
:   Current density maps showing Clar islands for the molecule above
    (taken from DOI: 10.1039/b604769f)

Previous posts on this blog have mentioned the application of another
computed quantum mechanical property known as ELF, the electron
localization function introduced by Becke and Edgecombe in 1990 (DOI:
[10.1063/1.458517](http://dx.doi.org/10.1063/1.458517) ) and
subsequently adapted for use with DFT-based wavefunctions. ELF is
normally applied to help analyze the bonding in a molecule; the value of
the function is normalized to lie between 1.0 (a simple interpretation
is that this is the value associated with a perfectly localized electron
pair) and 0.0. ELF has no association with magnetic response (the latter
being an excitation phenomenon), but since the Clar islands can also be
considered a localizing property of the π electrons, it is tempting to
ask whether the ELF function can also reveal their characteristics (this
question was first posed in DOI:
[10.1039/b810147g](http://dx.doi.org/10.1039/b810147g)).

::: {#attachment_1302 .wp-caption .aligncenter style="width: 441px"}
![The ELF function, as isosurfaces contoured at various
thresholds](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2009/12/C42H18-small.jpg "C42H18-small"){.size-full
.wp-image-1302 loading="lazy" decoding="async"
aria-describedby="caption-attachment-1302"
onclick="jmolInitialize('../Jmol/');jmolSetAppletColor('black');jmolApplet([450,450],'load wp-content/uploads/2009/12/C42H8-75.jvxl;isosurface \"\" translucent;zoom 5;moveto 4 0 2 0 90 90;');"
width="431" height="478"}

The ELF function, as isosurfaces contoured at various thresholds. Click
for 3D
:::

The diagram above shows the ELF function computed for the π-electrons of
the molecule above (B3LYP/6-31G(d), as isosurfaces contoured at various
values. At the value of 1.0, no features are discernible, but at 0.95
features which resemble basins associated with each atom centre have
appeared, in the region of the 2p-valence atomic orbital on each carbon
atom we regard as contributing the π-electron to the system. As the ELF
threshold is reduced, these objects start to merge into what are called
valence basins associated with bonds in the molecule. The outer
periphery is the first to start coalescing. By a value of 0.75 (click on
the diagram above to see a 3D model) the basins have merged to form
seven clear-cut rings which happen to coincide exactly with the Clar
islands. This feature persists down to a threshold of 0.55. Below this
value, the seven individual basins merge into a single basin contiguous
across the top (and bottom) surfaces of the molecule. One can also
conceptualize the journey in the other direction. At low ELF values, the
function is continuous, but as the threshold increases, it starts to
bifurcate into separated basins. The first clear-cut bifurcation is
indeed into the Clar islands, and this persists across a relatively wide
range of ELF values, which suggests it is a significant feature. What is
somewhat surprising is the close apparent correspondence of this way of
analysing the electronic properties of the π electrons with their
magnetic response computed via current densities. But association with
aromaticity has previously been made
(DOI: [10.1063/1.1635799](http://dx.doi.org/10.1063/1.1635799){target="_blank"}).
Thus Santos and co-workers have shown that the value of the ELF function
at the point where it bifurcates from a ring into discrete valence or
atomic basins can be related to other metrics of aromaticity. Here, that
value is around 0.75 for the Clar basins, which is also within the range
of values that Santos et al associate with prominent aromaticity
(benzene itself has a value around  0.95).

::: {#attachment_1324 .wp-caption .aligncenter style="width: 195px"}
![A C114
PAH](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2009/12/C114H30.jpg "C114H30"){.size-full
.wp-image-1324 loading="lazy" decoding="async"
aria-describedby="caption-attachment-1324" width="185" height="213"}

A C114 PAH
:::

The ELF function for the 114-carbon unit shown above again reveals
prominent Clar islands, the inner heptet being very similar to the
picture painted using current densities.

::: {#attachment_1325 .wp-caption .aligncenter style="width: 315px"}
![Clar islands in the ELF function for a C114 carbon
PAH](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2009/12/c114-elf.jpg "c114-elf"){.size-full
.wp-image-1325 loading="lazy" decoding="async"
aria-describedby="caption-attachment-1325"
onclick="jmolInitialize('../Jmol/');jmolSetAppletColor('black');jmolApplet([450,450],'load wp-content/uploads/2009/12/C114-68.jvxl;isosurface \"\" translucent;zoom 5;moveto 4 0 2 0 90 90;');"
width="305" height="340"}

Clar islands in the ELF function for a C114 carbon PAH
:::

The final example involves diboranyl isophlorin (DOI:
[10.1002/chem.200700046](http://dx.doi.org/10.1002/chem.200700046){target="_blank"}),
a 20 π-electron antiaromatic system. Such systems are particularly prone
to forming locally aromatic Clar islands as an alternative to global
antiaromaticity (DOI:
[10.1039/b810147g](http://dx.doi.org/10.1039/b810147g)).

::: {#attachment_1334 .wp-caption .aligncenter style="width: 165px"}
![A Diborinyl
system.](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2009/12/diborinyl.jpg "diborinyl"){.size-full
.wp-image-1334 loading="lazy" decoding="async"
aria-describedby="caption-attachment-1334" width="155" height="155"}

A Diboranyl isophlorin.
:::

The ELF function is shown for both the neutral diboranyl system and its
(supposedly more aromatic) dication. Here a mystery forms. No Clar
islands are seen, and instead it is the periphery that bifurcates, at
ELF thresholds of 0.5 for the neutral and 0.7 for the dication. The
latter value clearly is that of an aromatic species, but the former is
somewhat in no-man's land, but certainly less aromatic that the
dication. One for further study I fancy!

::: {#attachment_1337 .wp-caption .aligncenter style="width: 378px"}
![ELF Function for diboranyl molecules (red=neutral, green=dication).
Click for
3D](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2009/12/diboranyl.jpg "diboranyl"){.size-full
.wp-image-1337 loading="lazy" decoding="async"
aria-describedby="caption-attachment-1337"
onclick="jmolInitialize('../Jmol/');jmolSetAppletColor('black');jmolApplet([450,450],'load wp-content/uploads/2009/12/diboranyl-50.jvxl;isosurface \"\" translucent;zoom 5;moveto 4 0 2 0 90 90;');"
width="368" height="204"}

ELF Function for diboranyl molecules (red=neutral, green=dication).
Click for 3D
:::

Does the ELF function have any possible advantage over the use of
current density methods for analysing aromaticity? Well, the latter is
normally applied to flat systems with planes of symmetry defining the
π-system, and with respect to which an applied magnetic field is
oriented. How to orient this magnetic field is not so obvious for
prominently non-planar or helical molecules. Since the ELF function does
not depend on the orientation of an applied magnetic field, it may be a
useful adjunct for studying the properties of π-electrons in non-planar
systems.

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


Clar islands are found not so much in an ocean, but in a type of molecule known as polycyclic aromatic hydrocarbons (PAH). One member of this class, graphene, is attracting a lot of attention recently as a potential material for use in computer chips.

Messaggi di Rogue Scholar

Clar islands in a π Cloud