Imperial College London

Henry Rzepa

The properties of electrons are studied by both chemists and physicists.
At the boundaries of these two disciplines, sometimes interesting
differences in interpretation emerge. One of the most controversial is
that due to Bader (for a recent review, see DOI:
[10.1021/jp102748b](http://dx.doi.org/10.1021/jp102748b){target="_blank"})
a physicist who brought the mathematical rigor of electronic topology to
bear upon molecules. The title of his review is revealing: "Definition
of Molecular Structure: By Choice or by Appeal to Observation?". He
argues that electron density is observable, and that what chemists call
a bond should be defined by that observable (with the implication that
chemists instead often resort to arbitrary choice). Here I explore one
molecule which could be said to be the focus of the differences between
physics and chemistry; **cis-but-2-ene.**

::: {#attachment_4995 .wp-caption .aligncenter style="width: 356px"}
[![](http://www.ch.imperial.ac.uk/rzepa/blog/wp-content/uploads/2011/10/cis-butene2.jpg "cis-butene"){.size-full
.wp-image-4995 loading="lazy" decoding="async"
aria-describedby="caption-attachment-4995" width="346"
height="137"}](http://www.ch.imperial.ac.uk/rzepa/blog/wp-content/uploads/2011/10/cis-butene2.jpg)

Two possible conformations of cis but-2-ene.
:::

The structure of this system has been determined by electron diffraction
to exhibit a H...H distance of \~2.1Å as in **(a)**,
DOI: [10.3891/acta.chem.scand.24-0043](http://dx.doi.org/10.3891/acta.chem.scand.24-0043).
Why is this of interest? Because a rotational alternative, shown as
**(b)** could result in a significantly longer H...H distance (\~ 2.6Å).
Now bear in mind that the van der Waals radius of hydrogen is estimated
at \~1.2Å, and that two hydrogens will be most strongly attracted by
dispersion forces when separated by \~2.4Å. As they get closer, that
attraction will be counterbalanced by a repulsion, which will eventually
win out. Structure (b) does not benefit from H...H dispersion
attractions, but are the hydrogens in structure (a) too close to do so
as well?

Well, let us adopt Bader's approach, and look at the topology (QTAIM) of
the electronic distribution in [structure
(a)](http://hdl.handle.net/10042/to-8575){target="_blank"}. The features
to concentrate on are the purple dots, which in this analysis have been
named **bond critical points (BCP)**  and the single yellow sphere,
which is a **ring critical point (RCP)**. There are two other types of
critical points, which I will call nuclear attractors (**NACP**) and
cage points (**CCP**). The total occurrences of all these critical
points is determined by a topological theorem (Poincare-Hopf), which
states that **NACP-BCP+RCP-CCP=1**. You can see below that the H...H
region is indeed connected by a bond critical point (none of the other
purple dots are controversial). To a physicist, this is a real feature
of the (observable or in this instance the calculated) electron density.
In effect, it is a topological bond. Unfortunately, chemists like to
think of bonds as entities which result in stability; a bond contributes
to the stability of a molecule (and an anti-bond, should such exist, to
instability). Hence aromaticity (=stability) *vs* anti-aromaticity
(=instability). Chemists, by choice, might prefer not to call the H...H
region a bond because it is probably not contributing to the stability
of the molecule. Of course, the two camps are arguing about different
things; the topology of the electron density ρ(r) vs the energy of the
molecule.

::: {#attachment_4997 .wp-caption .aligncenter style="width: 350px"}
![](http://www.ch.imperial.ac.uk/rzepa/blog/wp-content/uploads/2011/10/cis-butene-aim.jpg "cis-butene-aim"){.size-full
.wp-image-4997 loading="lazy" decoding="async"
aria-describedby="caption-attachment-4997"
onclick="jmolInitialize('../Jmol/');jmolSetAppletColor('yellow');jmolApplet([450,450],'load wp-content/uploads/2011/10/cis-butene-aim.mol;');"
width="340" height="221"}

QTAIM topological analysis of cis but-2-ene. Click for 3D.
:::

Somewhat ignored in this discussion up to this point has been the yellow
dot, the RCP. Firstly, notice how close it is to the H...H BCP.
Secondly, notice from the Poincare-Hopf relationship that if you remove
BOTH of these points, the theorem is still satisfied; a BCP and a RCP
are said to be capable of annihilating each other (much like and
electron and a positron might). So perhaps a chemical picture might
emerge if you choose to consider BOTH points together, rather than just
the BCP?

I have done so below using the NCI (non-covalent interaction) procedure
(which I have [commented on in many other
posts](http://www.ch.imperial.ac.uk/rzepa/blog/?tag=julia-contreras-garcia){target="_blank"}
here). The NCI surface is shown below, embedded within the NCI surface
as purple dots are the BCP and RCP discussed above. Now, the NCI method
cleverly attempts to ascertain whether a region is attractive or
repulsive, and it colour codes the surface accordingly. In the below,
blue is deemed attractive, and red repulsive. We immediately see that
the H...H BCP is embedded in an attractive region, but the adjacent RCP
is embedded in a repulsive region. Whatever attraction the BCP might be
experiencing is negated by the repulsion the RCP has. The two cancel
(annihilate). Taken together, the H...H region is probably repulsive
(ways of quantifying how NCI regions integrate are [being
investigated](http://dx.doi.org/10.1021/jp204278k){target="_blank"} and
will be discussed in a future post). Perhaps this manner of looking at
it satisfies both the physicists and the chemists?

::: {#attachment_4999 .wp-caption .aligncenter style="width: 188px"}
![](http://www.ch.imperial.ac.uk/rzepa/blog/wp-content/uploads/2011/10/cis-butene3.jpg "cis-butene"){.size-full
.wp-image-4999 loading="lazy" decoding="async"
aria-describedby="caption-attachment-4999"
onclick="jmolInitialize('../Jmol/',true);jmolSetAppletColor('white');jmolApplet([600,600],'load wp-content/uploads/2011/10/cis-butene.xyz;isosurface wp-content/uploads/2011/10/cis-butene1.jvxl translucent;');"
width="178" height="221"}

The NCI surface for cis but-2-ene. Click for 3D.
:::

Well, not quite. A chemist would still ask why structure (a) is
preferred over structure (b), if the wider H...H region is not deemed
attractive (I call it a region rather than a bond in a probably futile
attempt to avoid controversy). Actually, the answer might be in how the
two methyl groups each interact with the other part of the molecule, the
alkene, and how that might depend on their orientation with respect to
the alkene. But that analysis is for [another
post](http://www.ch.imperial.ac.uk/rzepa/blog/?p=5040){target="_blank"}!

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


The properties of electrons are studied by both chemists and physicists. At the boundaries of these two disciplines, sometimes interesting differences in interpretation emerge. One of the most controversial is that due to Bader (for a recent review, see DOI: 10.1021/jp102748b) a physicist who brought the mathematical rigor of electronic topology to bear upon molecules.

Messaggi di Rogue Scholar

Are close H…H contacts bonds?