Imperial College London

Henry Rzepa

Science is about making connections. And these can often be made between
the most unlikely concepts. Thus in the posts I have made about
**pentavalent carbon**, one can identify a series of conceptual
connections. The first, by Matthias Bickelhaupt and co, resulted in the
suggestion of a possible **frozen S~N~2 transition state**. They used
astatine, and this enabled a connection to be made between another good
nucleophile/nucleofuge, cyclopentadienyl anion. This too seems to lead
to a frozen Sn2 transition state. The cyclopentadienyl theme then asks
whether this anion can coordinate a much simpler unit, a C^2+^ dication
(rather than Bickelhaupt's suggestion of a (NC)~3~C^+^ cation/radical)
and indeed that complex is also frozen, again with 5-coordinate carbon,
and this time with five equal C-C bonds. So here, the perhaps inevitable
progression of ideas moves on to examining the properties of this
complex, the outcome being a quite counter-intuitive suggestion which
moves us into new territory.

The journey starts with the previous observation that the HOMO of the
carbyliumylidene cation, shown in the previous post, has prominent
electron density along the five-fold symmetry axis of the molecule;

::: {#attachment_855 .wp-caption .aligncenter style="width: 190px"}
![The HOMO
orbital](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2009/09/C5-homo1.jpg "C5-homo"){.size-full
.wp-image-855 loading="lazy" decoding="async"
aria-describedby="caption-attachment-855"
onclick="jmolInitialize('../Jmol/');jmolSetAppletColor('white');jmolApplet([450,450],'load wp-content/uploads/2009/09/C5-40.jvxl;isosurface \"\" translucent;zoom 120;spin 3;');"
width="180" height="221"}

The HOMO orbital. Click for 3D
:::

This suggests that the apical 5-coordinate carbon might actually be
**basic**, and hence coordinate a proton to form a di-cation (below). So
adding a proton results in the following stable (in the sense of having
all positive force constants) structure, with apical C-C bond lengths of
1.7Å (compared to 1.8Å for the unprotonated system) and the bouncing
castle/trampoline mode of 875 cm^-1^ (DOI:
[10.14469/ch/2410](https://doi.org/10.14469/ch/2410)) is likewise
increased (for the pentamethyl derivative of the structure shown below).
The apical C-H stretch has the highest value of all the CHs in the
molecule, 3208 cm^-1^. The calculated proton affinity of the parent
compound is 134.2 kcal/mol. To put this into context, we can compare
this value with a range of first and second proton affinities reported
for carbon bases by Frenking\[cite\]10.1002/cphc.200800208\[/cite\]. The
highest second proton affinity there reported (ie protonation of an
already positive system) is around 106 kcal/mol, which is a good deal
less than that found here! So we might conclude that our value must be a
candidate for highest second proton affinity ever proposed for a carbon
base.

::: {#attachment_879 .wp-caption .aligncenter style="width: 252px"}
![Hexa-coordinate
Carbon?](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2009/10/C52+.jpg "C52+"){.size-full
.wp-image-879 loading="lazy" decoding="async"
aria-describedby="caption-attachment-879"
onclick="jmolInitialize('../Jmol/');jmolSetAppletColor('white');jmolApplet([450,450],'load wp-content/uploads/2009/10/c5-CH.cml; frame 1; zoom 100;connect (atomno=6) (atomno=4) PARTIAL;connect (atomno=6) (atomno=3) PARTIAL;connect (atomno=6) (atomno=2) PARTIAL;connect (atomno=6) (atomno=1) PARTIAL;connect (atomno=6) (atomno=5) PARTIAL;connect (atomno=4) (atomno=3) aromatic;connect (atomno=4) (atomno=5) aromatic;connect (atomno=1) (atomno=5) aromatic;connect (atomno=1) (atomno=2) aromatic;connect (atomno=2) (atomno=3) aromatic;measure 6 5;');"
width="242" height="107"}

Hexa-coordinate Carbon?
:::

The value of ρ(r) for the AIM bond critical point located for each of
the five apical C-C bonds is 0.156 au, again up from the value for the
unprotonated species. As before, the Cp ring itself shows no ring
critical point. An ELF analysis (below) shows five disynaptic basins in
the C-C bond region, with the basin integrating to 0.75 electrons each.
Together with the electrons in the apical C-H bond, 6.09 electrons are
associated with basins surrounding this carbon atom. Both the AIM and
the ELF concur in describing this carbon as not only hexa-coordinated,
but hexavalent (although the bonds are not the conventional two-electron
type, but perhaps more akin to a six-centre-four-electron interaction).

::: {#attachment_911 .wp-caption .aligncenter style="width: 370px"}
![ELF
Basins](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2009/10/C5-elf2.jpg "C5-elf"){.size-full
.wp-image-911 loading="lazy" decoding="async"
aria-describedby="caption-attachment-911"
onclick="jmolInitialize('../Jmol/');jmolSetAppletColor('white');jmolApplet([450,450],'load wp-content/uploads/2009/10/C5-CH-elf.mol; frame 1; zoom 100;spin 3;');"
width="360" height="350"}

ELF Basins. Click for 3D
:::

So I suggest that simple protonation of a highly basic cation has
resulted in a six-coordinate carbon atom, which exhibits six strong
bonds coordinated around it. I suppose it is inevitable again that one
ends this post with the question whether this species too might one day
be made.

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


Science is about making connections. And these can often be made between the most unlikely concepts. Thus in the posts I have made about
<strong>
 pentavalent carbon
</strong>
, one can identify a series of conceptual connections.

Messaggi di Rogue Scholar

It’s Hexa-coordinate carbon Spock – but not as we know it!