Imperial College London

Henry Rzepa

Following on from discussing octet expansion in species such as SeMe~6~,
ClMe~3~ and ClMe~5~, I felt impelled to return to SF~6~, often used as
an icon for hypervalence.

With this molecule we have twelve electrons to partition, six from
sulfur and one each from six fluorines (the other six electrons on each
F are presumed to form three sets of lone pairs). Recollect the two ways
of dealing with them:

1.  To place them in pairs firstly into bonding MOs formed from using a
    3s/3p valence atomic orbital basis on the S and a 2s/2p AO basis on
    F and to place any remaining electron pairs into antibonding
    orbitals constructed from the same basis. This would tend to reduce
    individual S-F bond orders.
2.  To place four pairs into bonding MOs and the remaining two pairs
    into MOs constructed using higher or Rydberg valence shells on S.
    This would tend to increase S-F bond orders by forming hyperbonds.

I will start with (delocalized) molecular orbitals (FAIR data
DOI: [10.14469/hpc/3283](https://doi.org/10.14469/hpc/3283)). The HOMO
(highest occupied MO) and the next 16 are in fact various variations of
orbitals which can be regarded as fluorine lone pairs. The first of
interest to us is the A~1g~-symmetric HOMO-17, which certainly looks as
if it is antibonding along the six F-S bonds. But the heavy
delocalization of the MOs makes it really difficult to comment on
bonding/antibonding character.

![](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2017/11/SF6-HIOMO-17-1024x885.jpg){.aligncenter
.size-large .wp-image-19078 loading="lazy" decoding="async" width="450"
height="389"
srcset="https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2017/11/SF6-HIOMO-17-1024x885.jpg 1024w, https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2017/11/SF6-HIOMO-17-300x259.jpg 300w, https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2017/11/SF6-HIOMO-17-768x664.jpg 768w, https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2017/11/SF6-HIOMO-17.jpg 1169w"
sizes="(max-width: 450px) 100vw, 450px"}

So next, the more localized NBO orbitals (FAIR Data
DOI: [10.14469/hpc/3284](https://doi.org/10.14469/hpc/3284)), which
tends to "collect" the wavefunction into localized regions of bonds and
lone pairs. There are twelve equivalent F lone pairs of the following
type:![](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2017/11/SF6-NBO3-823x1024.jpg){.aligncenter
.size-large .wp-image-19079 decoding="async" width="400"
srcset="https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2017/11/SF6-NBO3-823x1024.jpg 823w, https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2017/11/SF6-NBO3-241x300.jpg 241w, https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2017/11/SF6-NBO3-768x955.jpg 768w, https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2017/11/SF6-NBO3.jpg 850w"
sizes="(max-width: 823px) 100vw, 823px"}

Next the remaining six F lone pairs, which are oriented axially along
the S-F bonds. They have distinct S-F anti-bonding
character.![](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2017/11/SF6-NBO2-688x1024.jpg){.aligncenter
.size-large .wp-image-19081 decoding="async" width="400"
srcset="https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2017/11/SF6-NBO2-688x1024.jpg 688w, https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2017/11/SF6-NBO2-202x300.jpg 202w, https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2017/11/SF6-NBO2.jpg 753w"
sizes="(max-width: 688px) 100vw, 688px"}

Finally six S-F bonding pairs ("acorn" orbitals). But note that whilst
they are bonding along one S-F bond, they are mildly antibonding along
the opposing S-F
bond. ![](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2017/11/SF6-NBO1-708x1024.jpg){.aligncenter
.size-large .wp-image-19080 decoding="async" width="400"
srcset="https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2017/11/SF6-NBO1-708x1024.jpg 708w, https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2017/11/SF6-NBO1-208x300.jpg 208w, https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2017/11/SF6-NBO1.jpg 754w"
sizes="(max-width: 708px) 100vw, 708px"}

The Rydberg occupancy is
S:\[core\]3S(0.98)3p(2.13)3d(0.24)4p(0.03)4f(0.01) and
F: \[core\]2S(1.91)2p(5.51)3d(0.01), which gives a total  Rydberg
occupancy of 0.35177e.  Adding up these effects, the NBO analysis tells
us that the individual S-F bond orders are 0.7213. Six times this gives
the Wiberg bond index at sulfur:  4.3276. This is close to the value of
4 expected from utilising an atomic orbital basis of one 2s and three 2p
AOs on sulfur. One can think of this in another way.

1.  Start with a valence shell of twelve electrons to form six
    two-electron S-F bonds. The sulfur would have a bond index of six.
    Then promote either two electrons into fully antibonding orbitals
    (5-1=4) or four into non-bonding orbitals (F lone pairs) or possibly
    intermediate solutions, thus reducing the sulfur bond index by \~two
    bonds to give a bond index of four. Since the antibonding orbitals
    in this case are not fully antibonding, the bond index emerges a bit
    higher at 4.3276, a value also augmented by 0.35177/2 = 0.175885 due
    to Rydberg occupancy.
2.  One might usefully then ask if a bond index for sulfur of ≥ 4 can be
    usefully described as "*hypervalent sulfur*"? As usual in bonding
    theory, we need a reference state for non-hypervalent sulfur. If
    this is taken as two valencies, with a bond index of two, then this
    molecule is definitely hypervalent. If you assume that you can only
    construct the equivalent of four two-electron bonds using just a
    3s^1^/3p^3^ atomic orbital basis, then it is merely mildly
    hypervalent; the four two-electron bonds are then distributed of
    course across six S-F regions, or 0.667 bonds per S-F region. The
    value of 0.7213 actually calculated is exalted by contributions in
    part from Rydberg orbitals. 

What about the octet? 6\*0.7213\*2 = 8.66e, a mildly expanded octet. I
am now going to use the ELF method as an alternative counting procedure.
This is based not on orbitals but on the electron density (a more direct
experimental observable than orbitals). Six disynaptic basins are
located totalling 6.5e. The remainder of the electrons populate the F
lone pairs shown below as four distinct monosynaptic basins per F. This
is an artefact of the resolution of the cube of ELF values and how the
basin centroids are located. These are in fact circular and not point
ELF attractors, forming a circular ELF torus around each fluorine.

![](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2017/11/SF6_bas-945x1024.jpg){.aligncenter
.size-large .wp-image-19085 decoding="async" width="400"
srcset="https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2017/11/SF6_bas-945x1024.jpg 945w, https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2017/11/SF6_bas-277x300.jpg 277w, https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2017/11/SF6_bas-768x832.jpg 768w, https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2017/11/SF6_bas.jpg 960w"
sizes="(max-width: 945px) 100vw, 945px"}

So, ELF suggests that the sulfur "octet" is not exceeded and in this
form of analysis the compound is merely hypercoordinate. In contrast the
orbital-based approach indicates mild hypervalency in which the total
bond index at S modestly exceeds 4. If you regard the normal valency of
sulfur to be two, this is clearly hypervalent. But no substantial
octet-expansion beyond the modest Rydberg type is needed to rationalise
this species and certainly not up to twelve!

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Following on from discussing octet expansion in species such as SeMe

 6

, ClMe

 3

and ClMe

 5

, I felt impelled to return to SF

 6

, often used as an icon for hypervalence.

Messaggi di Rogue Scholar

Hypervalence and octet-expansion in sulfur hexafluoride.