Imperial College London

Henry Rzepa

A p[revious
post](http://www.ch.ic.ac.uk/rzepa/blog/?p=1158){target="_blank"} posed
the question; during the transformation of one molecule to another, what
is the maximum number of electron pairs that can simultaneously move
either to or from any one atom-pair bond as part of the reaction? A
rather artificial example (atom-swapping between three nitrosonium
cations) was used to illustrate the concept, in which **three** electron
pairs would **all** move from a triple bond to a region not previously
containing any electrons to form new triple bonds and destroy the old.
Here is a slightly more realistic example of the phenomenon, illustrated
by the (narcisistic) reaction below of a bis(sulfur trifluoride)
carbene. Close relatives of this molecule are actually known, with
either one SF~3~ of the units replaced by a CF~3~ group or a SF~5~
replacing the SF~3~ (DOI:
[10.1021/ja00290a038](http://dx.doi.org/10.1021/ja00290a038){target="_blank"}
).

::: {#attachment_1379 .wp-caption .aligncenter style="width: 355px"}
[![](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2009/12/SF3.jpg "SF"){.size-full
.wp-image-1379 loading="lazy" decoding="async"
aria-describedby="caption-attachment-1379" width="345"
height="44"}](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2009/12/SF3.jpg)

F3SCSF3 and the nature of its S-C bonds
:::

The two C-S bonds in this molecule are not the same (and similarly for
the CF~3~ analogue), one being long (single), the other short (assumed
triple), and the angle subtended at the central carbon is around 150°
(B3LYP/cc-pVTZ calculation, DOI:
[10042/to-3643](http://hdl.handle.net/10042/to-3643)). The transition
state for interconverting one form to the other would presumably
correspond to the concerted movement of **two** pairs of electrons from
one CS region to the other as shown above, not so much a Ménage à trois,
as a Ménage à deux! The transition state itself (DOI:
[10042/to-3644](http://hdl.handle.net/10042/to-3644)) has C~2~ symmetry,
with a calculated free energy barrier of 31 kcal/mol and ν 284*i* cm^-1^
for the bond shifting process.

::: {#attachment_1400 .wp-caption .aligncenter style="width: 312px"}
![Transition state for bond
equalisation](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2009/12/f3scsf3-c2.jpg "f3scsf3-c2"){.size-full
.wp-image-1400 loading="lazy" decoding="async"
aria-describedby="caption-attachment-1400"
onclick="jmolInitialize('../Jmol/');jmolSetAppletColor('black');jmolApplet([450,450],'load wp-content/uploads/2009/12/F3SCSF3-ts.log;frame 25;zoom 5;moveto 4 0 2 0 90 90;vectors on;vectors 4;vectors scale 5.0; color vectors green; vibration 6;animation mode loop;');"
width="302" height="224"}

Transition state for bond equalisation. Click for animation
:::

The molecule above does have a further point of interest; one of the
sulfur atoms (the triply bonded one) is approximately tetrahedral in
coordination, whilst the other has a "T-shape". An inorganic chemist
would describe one sulfur as tetravalent (oxidation state IV), the other
as hexavalent (oxidation state VI) and the equilibrium between them a
dismutation of the two oxidation states. Does this have any reality? The
ELF method has been mentioned a number of times in these posts, and it
is applied here to seek an answer. The ELF basin centroids are shown
below.

::: {#attachment_1302 .wp-caption .aligncenter style="width: 450px"}
![The ELF function, as isosurfaces contoured at various
thresholds](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2009/12/f3scsf3-elf-basin1.jpg "C42H18-small"){.size-full
.wp-image-1302 loading="lazy" decoding="async"
aria-describedby="caption-attachment-1302"
onclick="jmolInitialize('../Jmol/');jmolSetAppletColor('black');jmolApplet([450,450],'load wp-content/uploads/2009/12/F3CSCF3-elf.mol;isosurface \"\" translucent;zoom 5;moveto 4 0 2 0 90 90;');"
width="440" height="318"}

ELF basins for F3SCSF3. Click for 3D
:::

The integrations are as follows: **14** = 2.24 (a single C-S bond),
**30**=1.66 (an incipient carbene forming, as implied above),
**13+15+16** = 4.34 (a reasonably persuasive triple bond, comprising,
unusually, three separated basins). The fluorines **2**, **3** and **6**
all exhibit bonding basins to the S (respectively 2.17, 2.17 and 2.09),
but fluorines **1**,**5** and **4** do not! Sulfur **8** additionally
has a lone pair, **29**=2.31, but sulfur **9** does not. One aspect of
this analysis is the nature of the triple bond between S**9**-C**7**.
Because the three basins are separate, does that mean that the bond
cannot rotate about its axis?

::: {#attachment_1398 .wp-caption .aligncenter style="width: 377px"}
[![](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2009/12/f3scsf3-aim.jpg "AIM Analysis of F3SCSF3"){.size-full
.wp-image-1398 loading="lazy" decoding="async"
aria-describedby="caption-attachment-1398" width="367"
height="246"}](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2009/12/f3scsf3-aim.jpg)

AIM Analysis of F3SCSF3
:::

An alternative AIM analysis is shown above. Now, the CS triple bond is
reduced to a single bond critical point (BCP), labelled **10**. AIM
allows a property known as bond ellipticity to be computed at that BCP.
Typically, single and triple bonds have ellipticities close to zero,
whilst double bonds have a value of around 0.4 to 0.5. That for point
**10** is 0.18, which seems to support the ELF analysis above. Pretty
unsual bonding it would have to be agreed!

::: {#attachment_1409 .wp-caption .aligncenter style="width: 295px"}
[![](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2009/12/f3scsf3-c2-elf.jpg "f3scsf3-c2-elf"){.size-full
.wp-image-1409 loading="lazy" decoding="async"
aria-describedby="caption-attachment-1409" width="285"
height="165"}](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2009/12/f3scsf3-c2-elf.jpg)

ELF centroids for transition state for dismutation.
:::

But what of the original question posed at the start in the diagram; do
**two** pairs of electrons move away together from one triple bond to
form another. A further ELF analysis at the transition state for this
process reveals that in effect the two pairs do different things. One
localizes onto the carbon, to form a proper carbene, the other becomes a
sulfur lone pair. So the valence dismutation involves three pairs of
electrons, not two as shown at the start, with each pair doing its own
thing.

::: {#attachment_1412 .wp-caption .aligncenter style="width: 289px"}
[![](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2009/12/SF11.jpg "F3SCSF3"){.size-full
.wp-image-1412 loading="lazy" decoding="async"
aria-describedby="caption-attachment-1412" width="279"
height="46"}](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2009/12/SF11.jpg)

Six-electron model for valence isomerism in F3SCSF3
:::

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


A previous post posed the question; during the transformation of one molecule to another, what is the maximum number of electron pairs that can simultaneously move either to or from any one atom-pair bond as part of the reaction?

Messaggi di Rogue Scholar

Ménage à deux: Non-classical SC bonds.