Imperial College London

Henry Rzepa

In this follow-up to the previous post, I will try to address the
question **what is the nature of the bonds in penta-coordinate carbon**?

This is a difficult question to answer with any precision, largely
because our concept of a bond derives from trying to define what the
properties of the electrons located in the region between any two
specified atoms are. Such a **local** picture is somewhat at variance
with the idea of electrons being delocalized across the entire molecule.
Two procedures for analyzing the local electronic behaviour which we
have been using recently are AIM (Atoms-in-Molecules) and ELF (the
topology of the Electron localization function). There are many useful
published articles which elaborate these concepts; if you want to read
some of them, start at DOI
[10.1021/ct8001915](http://dx.doi.org/10.1021/ct8001915){target="references"}
and follow the cited articles.

Firstly, the AIM analysis of the system below, where X=cyclopentadienyl
anion and Y=CN.

::: {#attachment_784 .wp-caption .aligncenter style="width: 257px"}
![The Sn2 transition
state](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2009/09/sn2.jpg "sn2"){.size-full
.wp-image-784 loading="lazy" decoding="async"
aria-describedby="caption-attachment-784" width="247" height="185"}

The Sn2 transition state
:::

This is shown below. If you click on the image, you will see a rotatable
version of this diagram. The coloured (red, yellow and green) dots
represent so-called critical points in the curvature of the electron
density function ρ(r). The red dots are known as bond critical points,
or BCPs. These (almost) always are found along the line connecting two
atoms which we tend to refer to as a bond. You will see two that have
been circled in the diagram below, and these appear to show a bond
connecting the central 5-coordinate carbon atom and a carbon of each of
the cyclopentadienyl rings (which themselves are revealed as rings by
the presence of a yellow dot). Indeed, that central carbon atom does
seem to have five red dots radiating out along lines connecting it to
five carbon atoms.

::: {#attachment_813 .wp-caption .aligncenter style="width: 386px"}
![AIM analysis (red = bond critical points, yellow = ring, green =
cage)](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2009/09/cpd-penta-aim.jpg "cpd-penta-aim"){.size-full
.wp-image-813 loading="lazy" decoding="async"
aria-describedby="caption-attachment-813"
onclick="jmolInitialize('../Jmol/');jmolSetAppletColor('yellow');jmolApplet([450,450],'load wp-content/uploads/2009/09/cpd-penta-aim.mol;zoom 120;spin 3;');"
width="376" height="376"}

AIM analysis (red = bond critical points, yellow = ring, green = cage)
:::

So is the case proven for pentavalent carbon? Well, no. Firstly, one has
to inspect the value of ρ(r) at the circled red dot. This has a
(calculated) value of 0.022 au and a calculated bond length of
\~2.7Å. We need to calibrate this against a real system as reported in
DOI:
[10.1021/ja710423d](http://dx.doi.org/10.1021/ja710423d){target="references"}
(below):

::: {#attachment_787 .wp-caption .aligncenter style="width: 205px"}
![Hexa-coordinate
carbon](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2009/09/hexa.jpg "hexa"){.size-full
.wp-image-787 loading="lazy" decoding="async"
aria-describedby="caption-attachment-787"
onclick="jmolInitialize('../Jmol/');jmolSetAppletColor('yellow');jmolApplet([450,450],'load wp-content/uploads/2009/09/GOBLUF.cif;zoom 120;spin 3;');"
width="195" height="172"}

Hexa-coordinate carbon. Click for 3D model
:::

Here, the electron density ρ(r) was actually measured using X-ray
diffraction, and found to be \~0.017 for bond critical points found
connecting the central carbon and each of the four oxygen atoms. The
length of these "bonds" was measured as  \~2.7Å. The agreement with our
frozen transition state is quite striking.

One can go a little further and inspect the (2nd) derivative of the
electron density at the bond critical point, termed the Laplacian, or
∇^2^ρ, which tells what kind of "bond" one might have. The measured
value of ∇^2^ρ for the system above was \~0.06 au, and the calculated
value for our pentacoordinate system is 0.04 au, which again suggests we
are dealing with a very similar interaction in both systems (one
hypothetical and calculated, the other real and measured). The use of
the term  **interaction** was deliberate.  It is less loaded than the
term  **bond**. Thus the value of ρ(r) for an undisputed C-C single bond
is around 0.28 au, around ten times higher than our putative bonds.
Since we do not really wish to grace a ρ(r) value of 0.022 with the term
*decibond* (or any other fraction of a single bond) perhaps it is best
to call it just an interaction, and leave open the question of how
strong that interaction is! So, despite the  AIM analysis  finding
a *bond critical point*, we shall settle for interpreting that merely as
an interaction, and not a bond!  Well, is an interaction (or come to
that, a decibond) worthy of counting towards a coordination?  Perhaps!

So AIM can provide information about the curvature and density of the
electrons in the region of a bond/interaction. But it does not provide
any information about another simple question which the term bond
implies. How many electrons might be involved? Ever since  G. N. Lewis
coined the term two-electron bond in 1916,  we have become used to
interpreting bonds in terms of simple (often integer) numbers of
electrons.  A carbon-carbon single bond shares two electrons; a double
bond four electrons, and so on. We use this concept all the time in the
technique known  as arrow-pushing, which helps us delineate mechanisms
of reactions. Might it be possible to  identify how **many** electrons
are involved in bonds/interactions of the captured  S~N~2 species above?
Enter the ELF technique. It would not be appropriate to delve into the
theory of this method here; suffice to say that  (approximately), the
 bond-critical-point of the  AIM analysis in this case would map to a
disynaptic basin for ELF. Thus a two-electron single bond will reveal a
disynaptic basin (the centroid of which approximately matches the
position of the  AIM BCP), which can be integrated to approximately two
electrons. Shown below are the centroids of the disynaptic basins
calculated for our S~N~2 species:

::: {#attachment_822 .wp-caption .aligncenter style="width: 347px"}
![ELF basins (purple dots) for the SN2
system](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2009/09/cpd-penta-elf.jpg "cpd-penta-elf"){.size-full
.wp-image-822 loading="lazy" decoding="async"
aria-describedby="caption-attachment-822"
onclick="jmolInitialize('../Jmol/');jmolSetAppletColor('yellow');jmolApplet([450,450],'load wp-content/uploads/2009/09/cpd-penta-elf.mol;zoom 120;spin 3;');"
width="337" height="290"}

ELF basins (purple dots) for the SN2 system. Click for 3D model
:::

The most striking difference with the AIM analysis is that that the
central carbon is surrounded only by **three**, not **five** disynaptic
basins. The BCPs found for the two di-axial interactions have no
counterpart in synaptic basins. Of course, that does not mean that there
are no electrons that can be integrated in that region, just that the
curvature of the density in that region is not sufficiently well defined
to define a bounded volume of space which can be clearly integrated.
Perhaps that condition is what we might mean by a bond!

The three disynaptic basins that do surround the central carbon
integrate to a total of 7.85 electrons, which is close enough to 8 for
us to say that this carbon is **NOT** hypervalent!

So what is our final conclusion? The frozen S~N~2 species is **not**
hypervalent. It could reasonably be said to be coordinated by three
bonds, and two diaxial substituents that interact with the central
carbon weakly. Perhaps rather than penta-coordinate, the central carbon
could be described as **pentacoordinaloid**!

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


In this follow-up to the previous post, I will try to address the question
<strong>
 what is the nature of the bonds in penta-coordinate carbon
</strong>
?    This is a difficult question to answer with any precision, largely because our concept of a bond derives from trying to define what the properties of the electrons located in the region between any two specified atoms are.

Rogue Scholar Beiträge

Capturing penta-coordinate carbon! (Part 2).