Imperial College London

Henry Rzepa

A
[comment](http://www.ch.imperial.ac.uk/rzepa/blog/?p=10733&cpage=1#comment-54661){target="_blank"}
made on the previous post on the topic of hexa-coordinate carbon cited
an article entitled "*Observation of hypervalent CLi~6~ by
Knudsen-effusion mass spectrometry*"\[cite\]10.1038/355432a0\[/cite\] by
Kudo as a amongst the earliest of evidence that such species can exist
(in the gas phase). It was a spectacular vindication of the earlier
theoretical
prediction\[cite\]10.1021/ja00379a051\[/cite\],\[cite\]10.1021/ja00356a045\[/cite\]
that such 6-coordinate species are stable with respect to dissociation
to CLi~4~ and Li~2~.

The terminology describes these lithium carbides as
effectively **hypervalent**; Kudo in the abstract of his 1992 article
uses the more explicit phrase "*carbon can expand its octet of electrons
to form this relatively stable molecule*". We are taught early on in
chemistry that the carbon octet is due to double occupation of four
molecular orbitals formed using linear combinations derived from the
relatively low energy 2s/2p carbon atomic orbital basis. Octet expansion
on carbon must therefore involve to some degree the next atomic shell
(3s/3p), which is normally regarded as too high in energy to be capable
of significant population for carbon. But use of the 3s/3p shell seems
at first sight inevitable. If one constructs an octahedral complex
CLi~6~ surely ten electrons must be involved in bonding, four from the
carbon and six from the equivalent lithiums? The 3s/3p carbon population
must therefore be \~2 electrons, and we can truly describe a molecule
where carbon has of necessity expanded its octet of electrons to ten as
hypervalent. Or can we?

How does a quantitative (ωB97XD/6-311++G(d) )
calculation\[cite\]http://hdl.handle.net/10042/24790\[/cite\] reveal
this effective hypervalency? 

1.  [The octahedral geometry is indeed a stable minimum, with the lowest
    vibrational wavenumber being 194
    cm^-1^.]{style="line-height: 13px;"}
2.  It also checks out as clearly a closed shell species, stable to open
    shell perturbations.
3.  An NBO analysis reveals the Rydberg population (those 3s/3p atomic
    orbitals) to be only 0.09 electrons.
4.  It partitions the electrons into 13.97 for the 1s cores of the seven
    atoms, 7.67 "valence-Lewis" (i.e. shared covalent) and a mysterious
    2.27 (valence, non-Lewis).

We now have a problem. One of the standard methods for partitioning
electrons has isolated two of our ten electrons and placed them, with
small partial occupancy, into unshared "lone pairs", located as it
happens on the lithium atoms (shown below for one of these partial lone
"pairs"). The carbon is NOT hypervalent, and it has NOT expanded its
octet.

::: {#attachment_10805 .wp-caption .aligncenter style="width: 192px"}
![Click for
3D](http://www.ch.imperial.ac.uk/rzepa/blog/wp-content/uploads/2013/07/CLi6-Lp.jpg){.wp-image-10805
loading="lazy" decoding="async"
aria-describedby="caption-attachment-10805"
onclick="jmolInitialize('../Jmol/','JmolAppletSigned.jar');jmolSetAppletColor('white');jmolApplet([450,450],'load wp-content/uploads/2013/07/CLi6_mo13.cub.xyz;zoom 60;isosurface color green yellow wp-content/uploads/2013/07/CLi6_mo13.cub.jvxl translucent;');"
width="182" height="144"}

Click for 3D
:::

So I tried another procedure, deliberately chosen to be rather different
from the orbital-based NBO formalism. This is analysis of the ELF, or
electron localisation function, and represents an attempt to derive the
result based on a function related to the electron density. The red
spheres shown below are the centroids of the **twelve** ELF basins
located:

::: {#attachment_10804 .wp-caption .aligncenter style="width: 331px"}
![Click for
3D](http://www.ch.imperial.ac.uk/rzepa/blog/wp-content/uploads/2013/07/CLi6.jpg){.wp-image-10804
loading="lazy" decoding="async"
aria-describedby="caption-attachment-10804"
onclick="jmolInitialize('../Jmol/','JmolAppletSigned.jar');jmolSetAppletColor('white');jmolApplet([450,450],'load wp-content/uploads/2013/07/CLi6.mol2;');"
width="321" height="283"}

Click for 3D
:::

Each of these (equivalent) basins has an electron population of \~0.81,
making \~9.7 electrons in total. Each lithium sits on a square
arrangement of four of these basins, and so has access to \~3.2 valence
electrons. How do we interpret the situation for carbon however? Does
its valence shell contain an expanded 9.7 electrons? Well, not
necessarily. You can see that each of the basins has a three-centre
relationship between the one carbon and TWO lithiums. These electrons
contribute not just to C-Li bonding, but also to Li...Li bonding. So
these 9.7 electrons contribute in part to bonding that does NOT involve
the carbon. We can see this in the (Wiberg) bond orders, 0.254 for the
C-Li interaction, and 0.116 for adjacent Li...Li interactions (such an
explanation was also
[suggested](http://www.ch.imperial.ac.uk/rzepa/blog/?p=2687 "Hypervalency:  Third time lucky?")
for why II~7~ has no expanded octet at the central iodine). In fact, the
origins of this effect were first clearly identified in the theoretical
analysis of 1983\[cite\]10.1021/ja00356a045\[/cite\]: "*the extra
electrons beyond the usual octet are involved with metal-metal bonding
rather than with interactions of the metals with the central atoms*".

It is nice to see that despite the passage of 30 years, and despite the
introduction of many new ways of analysing the wavefunctions and hence
the bonding of molecules, the essential original
interpretation\[cite\]10.1021/ja00356a045\[/cite\] remains robustly
correct! 

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


A comment made on the previous post on the topic of hexa-coordinate carbon cited an article entitled “
<em>
 Observation of hypervalent CLi
 <sub>
  6
 </sub>
 by Knudsen-effusion mass spectrometry
</em>
”[cite]10.1038/355432a0[/cite] by Kudo as a amongst the earliest of evidence that such species can exist (in the gas phase). It was a spectacular vindication of the earlier theoretical

Messaggi di Rogue Scholar

Is CLi6 hypervalent?