Imperial College London

Henry Rzepa

The phenomenon of *bond stretch isomerism*, two isomers of a compound
differing predominantly in just one bond length, is one of those
chemical concepts that wax and
occasionally wane.\[cite\]10.1016/S1631-0748(02)01380-2\[/cite\] Here I
explore such isomerism for the elements Ge, Sn and Pb.

In [one earlier
post](http://www.ch.imperial.ac.uk/rzepa/blog/?p=14043){target="_blank"
rel="noopener"}, I noted a form of bond stretch isomerism that can arise
from a Jahn-Teller distortion ending in two different geometries in
which one or more pairs of bonds swap short/long lengths. Examples
include substituted
cyclo-octatetraenes\[cite\]10.1039/P29920001951\[/cite\] and octahedral
d^9^-Cu(II) complexes.\[cite\]10.1021/ja905399x\[/cite\] A more
interesting seminal possibility was implied by [G. N.
Lewis](http://www.rsc.org/events/detail/21281/the-atom-and-the-molecule-a-symposium-celebrating-gilbert-n-lewis){target="_blank"
rel="noopener"} a century ago when discussing the arrangement of
electrons in a (carbon-carbon) triple
bond.\[cite\]10.1021/ja02261a002\[/cite\]

![lewis1](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2016/02/lewis1-1-1024x421.jpg){.aligncenter
.size-large .wp-image-15802 loading="lazy" decoding="async" height="185"
width="450"
srcset="https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2016/02/lewis1-1-1024x421.jpg 1024w, https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2016/02/lewis1-1-300x123.jpg 300w, https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2016/02/lewis1-1-768x316.jpg 768w"
sizes="(max-width: 450px) 100vw, 450px"}  
[\*]{style="color:#FF0000;"}It took \~50 years to prove this assertion
wrong.\[cite\]10.1021/ic50025a016\[/cite\]

[In a
commentary](http://www.ch.imperial.ac.uk/rzepa/blog/?p=14037){target="_blank"
rel="noopener"}, I reported the results of a search of the crystal
structure database for the geometries associated with RX≡XR systems (X=
C, Si, Ge, Sn, Pb). Here I focus the
search\[cite\]10.14469/hpc/249\[/cite\] specifically for X=Sn,Ge; this
version of bond stretch isomerism also allows angles to change (=
rehybridisation at atoms) in order to provide a mechanism for a barrier
separating the two forms.

![](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2016/02/Sn-Sn.jpg "Cr"){.aligncenter
.size-full .wp-image-15761 decoding="async" width="400"}

For X=Sn, note the presence of up to three clusters, although the
relatively low number of hits makes the statistics less certain.

1.  The hotspot cluster centered around angles of 125° and a Sn-Sn
    distance of \~2.6Å.
2.  Another with angles of \<100° and Sn-Sn distances of \~3.3Å.
3.  A third with angles of \<100° and Sn-Sn distances of 2.8Å, which may
    or may not be a genuine unique form of bonding.

This pattern was commented on in 2010
by Power\[cite\]10.1039/C0SC00240B\[/cite\], whose group
synthesized most of the examples in the hits above.^‡^ A plot of
compounds with Ge-Ge bonds reveals both similarity with (two, possibly
three clusters) and difference from (the clusters are closely spaced in
terms of the Ge-Ge bond length, but separated in terms of angle) Sn.^†^

![GeGe](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2016/02/GeGe.jpg){.aligncenter
.size-full .wp-image-15761 decoding="async" width="400"
srcset="https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2016/02/GeGe.jpg 653w, https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2016/02/GeGe-300x223.jpg 300w"
sizes="(max-width: 653px) 100vw, 653px"}

Time for some computations (which at least will remove random errors in
the geometry). I selected the only known example of an
RPb-PbR compound\[cite\]10.1021/ja993346m\[/cite\] as a seed and put it
through a B3LYP+D3/Def2-TZVPP calculation (with 172 atoms and 2920 basis
functions, this is a relatively large calculation!), which reproduces
the known structure pretty well (table).

[![QIMQUY](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2016/02/QIMQUY.svg){.aligncenter
.size-large .wp-image-15675 decoding="async"
width="300"}](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2016/02/QIMQUY.svg){rel="attachment wp-att-15675"}

So what about another bond stretch isomers? The Pb=Pb variation is
indeed a stable minimum around 28.0 kcal/mol above the known structure,
which seems to put this form out of experimental reach (with this
ligand/aryl group at least). With Sn for the same aryl ligand, the
energy difference is smaller (\~15.8 kcal/mol for this ligand; Powers
reports other systems where the energy difference may be only \~5
kcal/mol). Judging by the distribution of the 13 hits recovered from the
CSD search, both bond stretch isomers may be accessible
experimentally. The calculations show that the GeGe bond isomers are
much closer in energy than SnSn (for this ligand). For all three metals
however, the calculated difference in the metal-metal length for the two
isomers is \~0.45 -- 0.52Å. This strongly suggests that whereas the SnSn
plot above is demonstrating bond length isomerism, the GeGe plot may not
be; at least not of the same type that the calculations here are
revealing (*via* the Wiberg bond orders).

|        |                 |                                                   |                                                 |                   |                                     |
|--------|-----------------|---------------------------------------------------|-------------------------------------------------|-------------------|-------------------------------------|
| System | Relative energy | XX distance                                       | RXX angle                                       | Wiberg bond order | DataDOI                             |
| Pb=Pb  | +28.0           | 2.767                                             | 118.7                                           | 1.666             | \[cite\]10.14469/ch/191856\[/cite\] |
| Pb-Pb  | 0.0             | 3.215 (3.188)^\[cite\]10.1021/ja993346m\[/cite\]^ | 93.7 (94.3)^\[cite\]10.1021/ja993346m\[/cite\]^ | 0.889             | \[cite\]10.14469/ch/191873\[/cite\] |
| Sn=Sn  | +15.8           | 2.640                                             | 123.1                                           | 1.911             | \[cite\]10.14469/ch/191884\[/cite\] |
| Sn-Sn  | 0.0             | 3.126                                             | 95.5                                            | 0.892             | \[cite\]10.14469/ch/191881\[/cite\] |
| Ge=Ge  | +0.5            | 2.263                                             | 125.2                                           | 2.138             | \[cite\]10.14469/ch/191882\[/cite\] |
| Ge-Ge  | 0.0             | 2.777                                             | 99.7                                            | 0.866             | \[cite\]10.14469/ch/191883\[/cite\] |

No doubt the particular bond length form is being facilitated by the
nature of the ligand and the steric interactions therein imparted, both
repulsive AND attractive. These interactions can be visualised *via* NCI
(non-covalent-interaction) plots (click on the image to obtain a
rotatable 3D model). First Pb-Pb followed by Pb=Pb. Note how in both
cases, the PbPb region is enclosed in regions of weak attractive
dispersion interactions, which however avoid the \"hemidirected\" inert
Pb lone pairs.\[cite\]10.1039/C4DT01406E\[/cite\]

![Pb-Pb](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2016/02/pb-pb-nci.jpg){.aligncenter
.size-large .wp-image-15675 decoding="async"
onclick="jmolInitialize('../Jmol/','JmolAppletSigned.jar');jmolSetAppletColor('white');jmolApplet([450,450],'load wp-content/uploads/2016/02/Pb-Pb_den.cub.xyz;isosurface colour red blue wp-content/uploads/2016/02/Pb-Pb_den.cub.jvxl opaque;');"
width="400"}
![Pb=Pb](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2016/02/pb=pb-nci.jpg){.aligncenter
.size-large .wp-image-15675 decoding="async"
onclick="jmolInitialize('../Jmol/','JmolAppletSigned.jar');jmolSetAppletColor('white');jmolApplet([450,450],'load wp-content/uploads/2016/02/Pb=Pb_den.cub.xyz;isosurface colour red blue wp-content/uploads/2016/02/Pb=Pb_den.cub.jvxl opaque;');"
width="400"}

So in the end we have something of a mystery. There is evidence from
crystal structures that at least two bond-stretch isomers of RSnSnR
compounds can form, but the calculations indicate that the Sn=Sn form is
significantly higher in energy (although not impossibly so for thermal
accessibility). Conversely, the Ge=Ge equivalent is very similar in
energy to a Ge-Ge form with a significantly longer bond length, but
there seems no crystallographic evidence for such a big difference in
bond lengths. Perhaps the answer lies with the ligands?

It seems particularly appropriate on the centenary of G. N. Lewis\'
famous paper in which he clearly notes the possibility of three isomeric
forms for the *triple bond*, to pay tribute to the impact his
suggestions continue to make to chemistry.

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

^‡^The individual entries can be inspected via the following
dois: \[cite\]10.5517/CCYYS5T\[/cite\],\[cite\]10.5517/CC6942P\[/cite\],\[cite\]10.5517/CCTWKLT\[/cite\],\[cite\]10.5517/CCTWKMV\[/cite\],\[cite\]10.5517/CCTWKPX\[/cite\],\[cite\]10.5517/CCTWKQY\[/cite\],\[cite\]10.5517/CCTWKRZ\[/cite\],\[cite\]10.5517/CCTWKT1\[/cite\],\[cite\]10.5517/CCNYK04\[/cite\],\[cite\]10.5517/CC7FYSC\[/cite\]

^†^You can view individual entries via the following DOIs:
\[cite\]10.5517/CC13R2MK\[/cite\],\[cite\]10.5517/CCT4VVM\[/cite\],\[cite\]10.5517/CC136VY3\[/cite\],\[cite\]10.5517/CC9ZXBH\[/cite\],\[cite\]10.5517/CC61ZRY\[/cite\],\[cite\]10.5517/CCTWKS0\[/cite\],\[cite\]10.5517/CCTWKNW\[/cite\],\[cite\]10.5517/CCTWKKS\[/cite\],\[cite\]10.5517/CCYYS4S\[/cite\],\[cite\]10.5517/CCYYS3R\[/cite\]

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

#### Acknowledgments

This post has been cross-posted in PDF format at
[Authorea](https://doi.org/10.15200/winn.145586.67442){rel="noopener"
target="_blank"}.

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


The phenomenon of
<em>
 bond stretch isomerism
</em>
, two isomers of a compound differing predominantly in just one bond length, is one of those chemical concepts that wax and occasionally wane.[cite]10.1016/S1631-0748(02)01380-2[/cite] Here I explore such isomerism for the elements Ge, Sn and Pb.     	In one earlier post, I noted a form of bond stretch isomerism that can arise from a Jahn-Teller distortion ending in two different

Rogue Scholar Beiträge

Bond stretch isomerism. Did this idea first surface 100 years ago?