Imperial College London

Henry Rzepa

So ingrained is the habit to think of a bond as a simple straight line
connecting two atoms, that we rarely ask ourselves if they are bent, and
if so, by how much (and indeed, does it matter?). Well Hursthouse,
Malik, and Sales, as long ago as 1978, asked just such a question about
the unlikeliest of bonds, a quadruple Cr-Cr bond, found in the compound
*[di-μ-trimethylsilylmethyl-bis-\[(tri-methylphosphine)
(trimethylsilylmethyI)chromium(II)](https://www.ccdc.cam.ac.uk/structures/Search?Ccdcid=1214468&DatabaseToSearch=Published){rel="noopener"
target="_blank"}*(DOI:
[10.1039/dt9780001314](https://doi.org/10.1039/dt9780001314){target="_blank"
rel="noopener"}\[cite\]10.1039/dt9780001314\[/cite\]). They arrived at
this conclusion by looking very carefully at how the overlaps with
the Cr d-orbitals might be achieved.

::: {#attachment_1548 .wp-caption .aligncenter style="width: 270px"}
![](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2010/01/Cr-Cr.jpg "Cr-Cr"){.size-full
.wp-image-1548 loading="lazy" decoding="async"
aria-describedby="caption-attachment-1548"
onclick="jmolApplet([450,450],'load wp-content/uploads/2010/01/MSIPCR10.cif;zoom 120; set antialiasDisplay ON;','c1');"
width="260" height="212"}

A system with a bent Cr-Cr quadruple bond. Click for 3D
:::

One would indeed instinctively think that whilst the relatively weak
single bond (about which rotation is easily possible) might be bendable,
it seems less intuitive to imagine that something as apparently strong
as a quadruple bond could be so. What might the measurable consequences
be? Well, Girolami et al 16 years later (DOI:
1[0.1021/om00017a023](http://dx.doi.org/10.1021/om00017a023){target="_blank"
rel="noopener"}\[cite\]10.1021/om00017a023\[/cite\]) pointed out that
such compounds exhibit restricted rotation about the Cr-CH~2~ bonds in
the system, with quite significant barriers. This, it was felt, was due
to an agostic CH...Cr interaction,  which might in turn have induced
bending of the Cr-Cr bond itself. There the story sort of peters out;
no-one else has discussed bent quadruple bonds, or indeed exactly how
bent they actually are.

Well, another 16 years has passed, and now we have a rather better set
of tools with which to answer such questions, yes you guessed (if you
have read my earlier posts), AIM and ELF. Lets start with AIM, shown
below (B3LYP/6-311G(d) calculation, for a somewhat reduced model
compared to the real system).

::: {#attachment_1570 .wp-caption .aligncenter style="width: 353px"}
![](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2010/01/Cr-Cr-aim2.jpg "Cr-Cr-aim"){.size-full
.wp-image-1570 loading="lazy" decoding="async"
aria-describedby="caption-attachment-1570"
onclick="jmolApplet([450,450],'load wp-content/uploads/2010/01/cr-aim.mol;zoom 120; set antialiasDisplay ON;','c3');"
width="343" height="360"}

AIM analysis. Click for 3D
:::

The bond critical point labelled **1** is the Cr-Cr interaction. It has
a ρ(r) of 0.142, really very modest for a purportedly quadruple bond.
The ∇^2^ρ(r) is +0.39, which is the wrong sign for a simple covalent
bond, and indeed matches the criteria for the (homonuclear) charge shift
category popularized by Shaik and Hibberty. Point **2** is the
Cr-CH~2~(si) bond (of calculated length 2.157Å), ρ(r) 0.078 and with an
ellipticity ε of 0.34. This latter value compares to *e.g.* a value of
0.0 expected for a single (rotatable) bond and \~0.4 for a double bond,
and seems to match very well with the observation of restricted rotation
about this bond. So far, so good! Surprising however is the absence of
any BCP in the region marked with a **?**, given that the Cr-C length in
this region is 2.257Å (only slightly longer than than that for point
**2** and surely a good candidate for some sort of Cr-C bond!). There is
no sign of any **bending** of the Cr-Cr bond in this type of analysis
(*i.e.* point **1** lies along the Cr-Cr axis), or indeed of any
evidence for α CH...Cr agostic bonding.

Time then for **ELF** (below). Well, in one regard, a similar picture to
the earlier AIM is obtained. Points **1** and **2** sort of match, and
again, no point is found in the region marked with a **?**. However,
there the similarities end.

::: {#attachment_1557 .wp-caption .aligncenter style="width: 327px"}
![none](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2010/01/Cr-Cr-elf.jpg "Cr-Cr elf"){.size-full
.wp-image-1557 loading="lazy" decoding="async"
aria-describedby="caption-attachment-1557"
onclick="jmolApplet([450,450],'load wp-content/uploads/2010/01/cr-elf.mol;zoom 120; set antialiasDisplay ON;','c2');"
width="317" height="320"}

ELF basin centroids for Cr-Cr system. Click for 3D
:::

Thus, point **1** (the apparent quadruple bond) integrates to only
**1.04** electrons! But wait for it, it lies well off the straight line
connecting the two chromium atoms. Wow! So the bond really is bent! And,
because it is contains only 1.04 electrons, that might explain why it
can bend so easily! Well, if the Cr-Cr bond does not contain the
electrons, where have they gone? The mystery is solved when point **2**
is inspected (there are of course two of them, the molecule having C~2~
symmetry). These each correspond to 1.92 electrons. The ELF analysis
furthermore tells us that point **2** is actually trisynaptic, covering
both chromium atoms and the carbon. We have found 4.88 electrons
associated with the Cr-Cr bond after all (and this is not bad, since one
rarely finds the full quota directly in such regions using ELF). To
indicate this, point **2** above is actually shown connected to three
atoms.

So to summarise, our Cr-Cr quadruple bond in the ELF analysis occupies
three different synaptic basins, arranged in a triangle around the C-Cr
axis (as shown below), and with the straight line between the Cr-Cr not
entertaining any basin. That certainly is bent!

::: {#attachment_1561 .wp-caption .aligncenter style="width: 269px"}
[![](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2010/01/Cr-Cr-elf1.jpg "Cr-Cr-elf1"){.size-full
.wp-image-1561 loading="lazy" decoding="async"
aria-describedby="caption-attachment-1561" width="259"
height="261"}](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2010/01/Cr-Cr-elf1.jpg)

View showing the three synaptic basins comprising the Cr-Cr bond
:::

ELF of course gives only one interpretation of the bonding; there are
others. But this interpretation certainly seems to give an interesting
and unusual insight into this remarkable (and largely ignored)
phenomenon.

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

This blog has DOI: https://doi.org/10.14469/hpc/12424

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

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


So ingrained is the habit to think of a bond as a simple straight line connecting two atoms, that we rarely ask ourselves if they are bent, and if so, by how much (and indeed, does it matter?). Well Hursthouse, Malik, and Sales, as long ago as 1978, asked just such a question about the unlikeliest of bonds, a quadruple Cr-Cr bond, found in the compound
<em>
 di-μ-trimethylsilylmethyl-bis-[(tri-methylphosphine)
</em>

Messaggi di Rogue Scholar

Blisteringly bent (quadruple) bonds