One thread that runs through this blog is that of hypervalency. It was therefore nice to come across a recent review of the concept[cite]10.1039/c5sc02076j[/cite] which revisits the topic, and where a helpful summary is given of the evolving meanings over time of the term hypervalent.

Imperial College London

Henry Rzepa

One thread that [runs through this
blog](http://www.ch.imperial.ac.uk/rzepa/blog/?cat=7) is that of
***hypervalency***. It was therefore nice to come across a recent review
of the concept\[cite\]10.1039/c5sc02076j\[/cite\] which revisits the
topic, and where a helpful summary is given of the evolving meanings
over time of the term hypervalent. The key phrase "*it soon became clear
that the two principles of the 2-centre-2-electron bond and the octet
rule were sometimes in conflict*" succinctly summarises the issue. Two
molecules that are discussed in this review caught my eye, CLi~6~ and
SeMe~6~. The former is stated as "*anomalous in terms of the Lewis
model*", but as I have shown in [an earlier
post](http://www.ch.imperial.ac.uk/rzepa/blog/?p=10801), the carbon is
in fact not anomalous in a Lewis sense because of a large degree of
Li-Li bonding. When this is taken into account, the Lewis model of the
carbon becomes more "normal". Here I take a look at the other cited
molecule, SeMe~6~.

I should start by summarising what I think are two fundamental ways in
which electrons can be added to the valence shell of a main group
element.

- If an s/p basis only is used for the (main group) valence shell, then
  once eight electrons have populated the four bonding molecular
  orbitals constructed from this basis, additional electrons can then go
  into the four antibonding orbitals. This simple concept is often
  taught as an explanation for why the bond orders across the range N≡N,
  O=O, F-F and Ne...Ne decrease regularly (in fact one could also add CC
  to the left of this series, which is thought to have a weak quadruple
  bond). The Lewis octet is maintained throughout.
- The second fundamental possibility is to expand the valence shell
  basis set to s/p/d or s/s/p/p (the second s or p-shell is the Rydberg
  level, *i.e.* 3s for carbon) or even s/s/p/p/d. That would be a true
  Lewis octet expansion, which depends on identifying significant
  Rydberg occupancy. This latter is in fact very rare, and few examples
  have been conclusively identified. One such as been [discussed on this
  blog ](http://www.ch.imperial.ac.uk/rzepa/blog/?p=15823) and more
  examples were presented at the [Aachen bond
  Slam](http://dipc.ehu.es/bondslam/index.php/Hypervalence) in
  September 2017. Unlike the first mechanism (which reduces bond
  orders), this one actually increases bond orders and any bonds where
  the atomic orbital contributions have a significant Rydberg component
  can be considered as "***Hyperbonds***".

One can then address the issue of hypervalency (and any octet expansion)
by analysing the basis set contributions of the orbitals. These orbitals
can be either canonical molecular orbitals or localised (NBO) orbitals.
If a single determinant wavefunction is appropriate, then the orbitals
would be doubly occupied (for closed shell species). If the molecule has
multi-reference character, then of course fractional electron occupancy
of these orbitals may be required (as would *e.g.* be the case for
ozone, O~3~, another molecule asserted in the review as
hypervalent\[cite\]10.1039/c5sc02076j\[/cite\]).

There are other ways of analysing the wavefunction. The one discussed at
length in the review\[cite\]10.1039/c5sc02076j\[/cite\] is from an
atomic charge map, but also mentioned is an ELF partitioning. This
derives not from an orbital population but from the distribution of a
function (ELF) calculated from the electron density itself. It was this
latter method that was cited for SeMe~6~. The ELF method partitions
electrons into so-called basins, which can be monosynaptic (lone pairs
and ionic bonds), disynaptic (covalent bonds) and more rarely
trisynaptic (3-centre bonds). Using this analysis, six disynaptic
octahedrally-arranged ELF basins were located for  SeMe~6 ~ ("*in which
the Se--C bonds are relatively non-polar, can have electron populations
exceeding 8 at the central atom"*\[cite\]10.1039/c5sc02076j\[/cite\])
and for which the total integration cames to 11.34e (FAIR Data DOI for
this calculation can be see
at [10.14469/hpc/3219](https://doi.org/10.14469/hpc/3219)).

![](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2017/11/165-1024x1008.jpg){.aligncenter
.size-large .wp-image-18979 loading="lazy" decoding="async" width="450"
height="443"
srcset="https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2017/11/165-1024x1008.jpg 1024w, https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2017/11/165-300x295.jpg 300w, https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2017/11/165-768x756.jpg 768w, https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2017/11/165.jpg 1040w"
sizes="(max-width: 450px) 100vw, 450px"}The key phrase is "non-polar",
since the Lewis concept relates to shared electron pair or covalent
hypervalency. It was this aspect that I focused on seven years back in
looking at whether [e.g.
IF~7~](http://www.ch.imperial.ac.uk/rzepa/blog/?p=2687) was hypervalent
(along with I(CN)~7~). These were too ionic to reveal disynaptic
covalent ELF basins. So in an effort to reduce the polarity, I tried
II~7~ and At.At~7~, on the grounds that these homonuclear molecules
might be less polar. The seven I-I or At-At ELF disynaptic basins
integrated to totals of 6.55 and 6.47e respectively; there was no
evidence of "octet expansion" for either central halogen. Instead of
course, the six electrons in the octet-excess needed to create seven I-I
bonds actually populate I-I antibonding orbitals, as per method 1 above.
Accordingly the I-I bond orders reduce from 1.0 to *e.g.* 0.47 for the
axial substituents and 0.37 for the five equatorial groups.

![](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2017/11/I8-elf.jpg){.aligncenter
.size-full .wp-image-18980 decoding="async" width="350"
srcset="https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2017/11/I8-elf.jpg 551w, https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2017/11/I8-elf-292x300.jpg 292w"
sizes="(max-width: 551px) 100vw, 551px"}

One interesting property of the centroid of the ELF basins is that you
can infer the polarity of the bond from its position along the bond
axis. For II~7~,~ ~the centroids are displaced towards the central
iodine, indicating it is more electronegative, and away from the
terminal iodine, indicating it is the electropositive partner. I mention
this since the ELF basins for SeMe~6~ show the centroids to be strongly
displaced **towards** the carbon and away from the Se (0.38/0.62),
indicating that this molecule is in fact polar and NOT non-polar as was
asserted. 

To follow-up this latter observation, I did an NBO analysis of the
wavefunction for SeMe~6~ (FAIR Data
DOI: [10.14469/hpc/3220](https://doi.org/10.14469/hpc/3220)). This
reveals the following properties.

- Se populations: \[core\]4S( 1.30)4p( 3.04)4d( 0.06)5p( 0.01) of which
  Rydberg = 0.06516, natural charge on Se, 1.60224
- C populations:  \[core\]2S( 1.20)2p( 3.65)3S( 0.01)3p( 0.01) of which
  Rydberg = 0.01838, natural charge on C -0.86670
- H populations:  1S( 0.80)
- Total Rydberg population: 0.20556
- Wiberg Se-C bond orders:  0.6689
- Wiberg bond indices:  Se 4.0431, C 3.8252,  H 0.9621

So according to this orbital-based analysis, SeMe~6~ is in effect a
partially ionic compound with no evidence of significant Rydberg
occupancies and hence no evidence of any octet expansion at Se. Thus we
see two different interpretations emerging, depending on the analytical
method used:

1.  SeMe~6 ~is a polar molecule with no hypervalent attributes as judged
    using orbital analysis.
2.  As a polar molecule, it has six methyl carbanion-like substituents
    in which the carbon "lone pairs" all point towards the Se,
    manifesting as disynaptic ELF basins and indicating a total
    valence-basin octet-expanded population of 11.34e at Se. Even though
    this octet expansion originates mostly from the carbon atomic
    orbitals, the disynaptic nature of these valence basins means that
    the Se could indeed be defined as hypervalent.

Well, SeMe~6~ has turned out to be rather less clear-cut than
implied* by* the assertion *"in which the Se--C bonds are
relatively non-polar".* There are however possible modifications
to SeMe~6~ that might yet make it less polar. These may be the subject
of a follow-up post.

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


One thread that runs through this blog is that of

 
 hypervalency
 

. It was therefore nice to come across a recent review of the concept[cite]10.1039/c5sc02076j[/cite] which revisits the topic, and where a helpful summary is given of the evolving meanings over time of the term hypervalent.

Hypervalence revisited. The odd case of hexamethyl selenium.

This is a spin-off from the table [I constructed
here](http://www.ch.imperial.ac.uk/rzepa/blog/?p=17633#comment-227278){target="_blank"}
for further chemical examples of the classical/non-classical norbornyl
cation conundrum. One possible entry would include the transition state
for inversion of methane *via* a square planar geometry as compared with
*e.g.* NiH~4~ for which the square planar motif is its minimum. So is
square planar methane a true transition state for inversion (of
configuration) of carbon?

The history of this topic is nicely told as far back as
1993\[cite\]10.1021/ja00069a056\[/cite\], when square planar methane was
shown to be a 4th-order saddle point (*i.e.* four negative force
constants) and not the first order one required of a transition state. A
true transition state was located,^‡^ and here I show it as part of an
animated IRC (intrinsic reaction coordinate). Go to
DOI: [10.14469/hpc/2288](https://doi.org/10.14469/hpc/2288) for the
calculation outputs.

![](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2017/03/ch4a.gif){.aligncenter
.size-full .wp-image-17705 decoding="async" width="450"}

To convince yourself that the configuration really does invert, focus on
the CIP rule. With atom 1 pointing behind, atoms 2 → 3  → 4 rotate in a
clockwise direction. Now focus on the final point at the end of the IRC,
when 2 → 3  → 4 rotate anti-clockwise. The configuration has inverted!
The barrier as can be seen below is \~118 kcal/mol. At this value the
half-life for the process would be far longer than the age of the
universe.

[![](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2017/03/ch4-3_tot_ener.svg){.aligncenter
.size-large .wp-image-17706 decoding="async"
width="450"}](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2017/03/ch4-3_tot_ener.svg)

The process can be described as an interesting variation
on pseudorotation, for which the classic example is of course PF~5~.^†^
Alternatively it can be thought of as the partial extrusion of H~2~ to
give carbene, followed by re-addition of the H~2~ to reform methane.
Partial because the extrusion is never fully achieved.

I have to say I did not expect anything quite so interesting to be
associated with methane;  one can learn from the simplest of molecules!

------------------------------------------------------------------------

^‡^ It was not entirely trivial to recover appropriate coordinates for
recomputing this TS from the article. But it is in fact an easy one to
find from scratch. Hopefully with the files at
[10.14469/hpc/2288](https://doi.org/10.14469/hpc/2288) to help, this
will not be an issue here.

^†^There are many kinds of pseudo-rotations. For others see
here.\[cite\]10.1021/ic0519988\[/cite\] and
\[cite\]10.1021/ic062473y\[/cite\]

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


This is a spin-off from the table I constructed here for further chemical examples of the classical/non-classical norbornyl cation conundrum. One possible entry would include the transition state for inversion of methane

 via

a square planar geometry as compared with

 e.g.

NiH

 4

for which the square planar motif is its minimum.

Messaggi di Rogue Scholar

Hypervalence revisited. The odd case of hexamethyl selenium.

How does methane invert (its configuration)?