Imperial College London

Henry Rzepa

[Previously](https://www.ch.imperial.ac.uk/rzepa/blog/?p=20679){target="_blank"
rel="noopener noreferrer"}, I explored (computationally) the normal
vibrational modes of Co(II)-tetraphenylporphyrin (CoTPP) as a
"flattened" species on copper or gold surfaces for comparison with those
recently imaged\[cite\]10.1038/s41586-019-1059-9\[/cite\]. The initial
intent was to estimate the "flattening" energy. There are six electronic
possibilities for this molecule on a metal surface. Respectively
positively, or negatively charged and a neutral species, each in either
a low or a high-spin electronic state. I reported five of these earlier,
finding each had quite high barriers for "flattening" the molecule. For
the final 6th possibility, the triplet anion, the SCF
(self-consistent-field) had failed to converge, but for which I can now
report converged results.^†^

[![](https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2019/04/flat.svg){.aligncenter
.size-large .wp-image-20781 decoding="async"
width="300"}](https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2019/04/flat.svg)

<table data-border="1">
<colgroup>
<col style="width: 20%" />
<col style="width: 20%" />
<col style="width: 20%" />
<col style="width: 20%" />
<col style="width: 20%" />
</colgroup>
<tbody>
<tr class="header">
<th>charge</th>
<th><p>Spin</p>
<p>Multiplicity</p></th>
<th>ΔG, Twisted Ph,<br />
Hartree</th>
<th>ΔG, “flattened”,<br />
Hartree</th>
<th><p>ΔΔG,</p>
<p>kcal/mol</p></th>
</tr>
&#10;<tr class="odd">
<td rowspan="6">-1</td>
<td rowspan="3">Triplet</td>
<td rowspan="3">-3294.68134 (C<sub>2</sub>)</td>
<td>-3294.64745 (C<sub>2v</sub>)</td>
<td><strong>21.3</strong></td>
</tr>
<tr class="even">
<td>-3294.616684 (C<sub>2v</sub>)</td>
<td>40.6</td>
</tr>
<tr class="odd">
<td>-3294.37012 (D<sub>2h</sub>)</td>
<td>195.3</td>
</tr>
<tr class="even">
<td rowspan="3">Singlet</td>
<td rowspan="3">-3294.67713 (S<sub>4</sub>)</td>
<td>-3294.39418 (D<sub>4h</sub>)</td>
<td>175.6</td>
</tr>
<tr class="odd">
<td>-3294.39321 (D<sub>2h</sub>)</td>
<td>178.2</td>
</tr>
<tr class="even">
<td><span style="color: #ff0000;">-3294.56652
(D<sub>2</sub>)</span></td>
<td><span style="color: #ff0000;">69.4</span></td>
</tr>
<tr class="odd">
<td colspan="5">FAIR data at DOI:<a
href="https://doi.org/10.14469/hpc/5486" target="data"
rel="noopener noreferrer">10.14469/hpc/5486</a> FAIR data version of the
tables in this and previous post at DOI:<a
href="https://doi.org/10.14469/hpc/5561" rel="noopener noreferrer"
target="_blank">10.14469/hpc/5561</a></td>
</tr>
</tbody>
</table>

I am exploring the so-called "flattened" mode, induced by the voltage
applied at the tip of the STM (scanning-tunnelling microscope) probe and
which causes the phenyl rings to rotate as per above. This rotation in
turn causes the hydrogen atom-pair encircled above to approach each
other very closely.^‡^ To avoid these repulsions, the molecule buckles
into one of two modes. The first causes the phenyl rings to stack
*up/down/up/down*. The second involves an all-up stacking, as shown
below. Although these are in fact 4th-order saddle points as isolated
molecules, the STM voltage can inject sufficient energy to convert these
into apparently stable minima on the metal surface.

::: {#attachment_20787 .wp-caption .aligncenter style="width: 410px"}
![](https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2019/04/all-up-1024x335.jpg){.size-large
.wp-image-20787 decoding="async"
aria-describedby="caption-attachment-20787"
onclick="jmolApplet([450,450],'load wp-content/uploads/2019/04/triplet-anion-alt-394.log;frame 44;spin 3;vectors on;vectors 4;vectors scale 8.0;color vectors green;vibration 6;','c1');"
width="400"
srcset="https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2019/04/all-up-1024x335.jpg 1024w, https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2019/04/all-up-300x98.jpg 300w, https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2019/04/all-up-768x251.jpg 768w, https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2019/04/all-up.jpg 1921w"
sizes="(max-width: 1024px) 100vw, 1024px"}

All syn mode, Triplet anion
:::

The *up/down/up/down* "flattened" form (below) shows a much more modest
planarisation energy than all the other charged/neutral states reported
in the [previous
post](https://www.ch.imperial.ac.uk/rzepa/blog/?p=20679){target="_blank"
rel="noopener noreferrer"}, whereas the *all-up* isomer (which on the
face of it looks a far easier proposition to come into close contact
with a metal surface) is far higher in free energy.

The caption to Figure 3 in the original
article\[cite\]10.1038/s41586-019-1059-9\[/cite\] does not explicitly
mention the nature of the metal surface on which the vibrations were
recorded, but we do get "*The intensity in the upper right corner of the
320-cm^−1^ map is from a neighbouring Cu--CO stretch"* which suggests it
is in fact a copper surface. Coupled with the other observation that *in
"contrast to gold, the Kondo resonance of cobalt disappears on Cu(100),
suggesting that it acquires nearly a full electron from the metal (see
Extended Data Fig. 2)*," the model below of a triplet-state anion on the
Cu surface seems the most appropriate.

::: {#attachment_20798 .wp-caption .aligncenter style="width: 410px"}
![](https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2019/04/udud.jpg){.size-full
.wp-image-20798 decoding="async"
aria-describedby="caption-attachment-20798"
onclick="jmolApplet([450,450],'load wp-content/uploads/2019/04/triplet-anion-284.log;frame 46;spin 3;vectors on;vectors 4;vectors scale 8.0;color vectors orange;vibration 6;','c2');"
width="400"
srcset="https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2019/04/udud.jpg 1015w, https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2019/04/udud-300x288.jpg 300w, https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2019/04/udud-768x737.jpg 768w"
sizes="(max-width: 1015px) 100vw, 1015px"}

Syn/anti mode, Triplet anion with C2v symmetry
:::

There is one final remark made in the article worth repeating here:
"*This suggests that the vibronic functions are complex-valued in this
state, as expected for Jahn--Teller active degenerate orbitals of the
planar porphyrin.^26^*" Orbital degeneracy can only occur if the
molecule has *e.g.* D~4h~ point group symmetry, whereas the triplet
anion stationary-point shown in the figure above has only C~2v~ symmetry
for which no orbital degeneracies (E) are expected. Enforcing D~4h~
symmetry on Co(II) tetraphenylporphyrin results in eight pairs of H...H
contacts of 1.34Å,^‡^ which is an impossibly short distance (the
shortest known is \~1.5Å). Moreover this geometry has an equally
impossible free energy 176 kcal/mol above the relaxed free molecule.
Visually from Figure 3, the H...H contact distance looks even shorter
(below, circled in red)! A D~2h~ form (with no E-type orbitals) can also
be located.

<table data-border="0">
<colgroup>
<col style="width: 50%" />
<col style="width: 50%" />
</colgroup>
<tbody>
<tr class="odd">
<td><div id="attachment_20816" class="wp-caption aligncenter"
style="width: 235px">
<img
src="https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2019/04/d4h.jpg"
class="size-large wp-image-20816" decoding="async"
aria-describedby="caption-attachment-20816"
onclick="jmolApplet([250,400],&#39;load wp-content/uploads/2019/04/anion-singlet-d4h-370.log;frame 56;spin 3;vectors on;vectors 4;vectors scale 8.0;color vectors green;vibration 6;&#39;,&#39;c3&#39;);"
width="225" />
<p><strong>Singlet, Calculated with D<sub>4h</sub> symmetry. Click for
vibrations.</strong></p>
</div></td>
<td><div id="attachment_20828" class="wp-caption aligncenter"
style="width: 235px">
<img
src="https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2019/04/d2h-singlet-1024x1022.jpg"
class="size-large wp-image-20828" decoding="async"
aria-describedby="caption-attachment-20828"
onclick="jmolApplet([250,400],&#39;load wp-content/uploads/2019/04/anion-singlet-d2h.log;frame 55;spin 3;vectors on;vectors 4;vectors scale 8.0;color vectors green;vibration 6;&#39;,&#39;c4&#39;);"
srcset="https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2019/04/d2h-singlet-1024x1022.jpg 1024w, https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2019/04/d2h-singlet-150x150.jpg 150w, https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2019/04/d2h-singlet-300x300.jpg 300w, https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2019/04/d2h-singlet-768x766.jpg 768w, https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2019/04/d2h-singlet-144x144.jpg 144w, https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2019/04/d2h-singlet.jpg 1255w"
sizes="(max-width: 1024px) 100vw, 1024px" width="225" />
<p><strong>Singlet, Calculated with D<sub>2h</sub> symmetry. Click for
vibrations.</strong></p>
</div></td>
</tr>
<tr class="even">
<td colspan="2"><div id="attachment_20808"
class="wp-caption aligncenter" style="width: 310px">
<img
src="https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2019/04/D4h-article.jpg"
class="size-full wp-image-20808" decoding="async"
aria-describedby="caption-attachment-20808" width="300" />
<p><strong>Taken from Figure 3 (Ref 1).</strong></p>
</div></td>
</tr>
</tbody>
</table>

These totally flat species are calculated to be at 13 or 12th-order
saddle points, with the eight most negative force constants having
vectors which correspond to up/down avoidance motions of the proximate
hydrogen pairs encircled above and the remaining being buckling modes of
the entire ring.

So to the mystery, being the nature of the "flattened" CoTPP on the
copper metal surface, as represented in Figure 3 of the
article.\[cite\]10.1038/s41586-019-1059-9\[/cite\] Is it truly flat, as
implied by the article? If so, the energy of such a species would be
beyond the limits of what is normally considered feasible. Moreover, it
would represent a species with truly mind-blowing short H...H contacts.
Or could it be a saddle-shaped geometry, where the phenyl rings are not
lying flat in contact with the metal but interacting *via* the phenyl
para-hydrogens? That geometry has not only a much more reasonable energy
above the unflattened free molecule, but also acceptable H...H contacts
(\~2.0.Å) However, would such a shape correspond to the visualised
vibrational modes also shown in Figure 3? I have a feeling that there
must be more to this story.

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

^†^These convergence problems were solved by improving the basis set
*via* adding "diffuse" functions, as in (u)ωB97XD/6-311+G(d,p).
Convergence to the lowest energy electronic state (^3^B~2~) is achieved
using a Huckel initial guess rather than the default Harries, which
gives the higher energy ^3^A~2~. ^‡^If the crystal structure for these
species is flattened without geometry optimisation, the H-H distance is
around 0.8Å ^♥^This blog has a DOI:
[10.14469/hpc/5559](https://doi.org/10.14469/hpc/5559).

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


Previously, I explored (computationally) the normal vibrational modes of Co(II)-tetraphenylporphyrin (CoTPP) as a “flattened” species on copper or gold surfaces for comparison with those recently imaged[cite]10.1038/s41586-019-1059-9[/cite]. The initial intent was to estimate the “flattening” energy. There are six electronic possibilities for this molecule on a metal surface.

Imaging normal vibrational modes of a single molecule of CoTPP: a mystery about the nature of the imaged species.

On February 6th I was alerted to this intriguing
article\[cite\]10.1038/nchem.2716\[/cite\] by a phone call, made 55
minutes before the article embargo was due to be released.
[Gizmodo](http://gizmodo.com/){target="_blank"} wanted to know if I
could provide an (almost)^†^ [instant^‡^
quote](http://gizmodo.com/a-wild-new-helium-compound-could-rewrite-chemistry-text-1792042165).
After a few days, this report of a stable compound of helium and sodium
still seems impressive to me and I now impart a few more thoughts here.

The discovery originates from 17 authors based in 17 different
institutions, an impressive illustration of global science and
cooperation. I illustrate with this diagram, to be found not in the main
article body but in its supporting information and for which the caption
reads:

![](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2017/02/101-1024x658.jpg){.aligncenter
.size-large .wp-image-17415 loading="lazy" decoding="async" width="450"
height="289"
srcset="https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2017/02/101-1024x658.jpg 1024w, https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2017/02/101-300x193.jpg 300w, https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2017/02/101-768x493.jpg 768w, https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2017/02/101.jpg 1656w"
sizes="(max-width: 450px) 100vw, 450px"}  
*Computed charge density (eÅ^-3^) of Na~2~He at 300 GPa, plotted in the
\[110\] plane of the conventional cell. The color bar gives the scale.*

The nuclei carry of course the greatest charge density, but the density
labelled "2e" is not nuclear-centered. This is typical of species known
as electrides, where positive cations are associated with just electrons
acting as the counter-anion and about which there was an [extensive
debate](http://www.ch.imperial.ac.uk/rzepa/blog/?p=14272) earlier on
this blog. There is much discussion in the
article\[cite\]10.1038/nchem.2716\[/cite\] about the essential role of
the He atoms in bringing about the formation of such an electride, an
effect that is summarised in a second diagram also found in the
supporting information:

![](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2017/02/102.jpg){.aligncenter
.size-full .wp-image-17416 decoding="async" width="450"
srcset="https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2017/02/102.jpg 813w, https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2017/02/102-300x235.jpg 300w, https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2017/02/102-768x603.jpg 768w"
sizes="(max-width: 813px) 100vw, 813px"}

I found myself thinking that it would be great to have the first diagram
represented as a movie, evolving as the pressure is increased from say
ambient to 300 GPa, and presumably showing the "2e" feature (which means
diamagnetic electrons) forming as the pressure increases. Would their
evolution be abrupt (a step change) or gradual as the pressure increases
and the interatomic distances all decrease? As I understand it, this
chemical phenomenon is due not so much to the usual coulombic
attraction between positive nuclei and negative charge density from the
electronic wavefunction leading to *e.g.* covalent bonds, but to
electron repulsions induced by decreasing nuclear separations resulting
in electride-like ionisation and hence electron localisation into the
"interstitial cavities" of the lattice. Without pressure, you would just
have sodium and helium atoms!

The urge to obtain this intriguing electronic wavefunction for myself
now appeared (wavefunctions are rarely if ever included in supporting
information). To do this you must have atom coordinates available, But
such data was not to be found in the supporting information. It was
eventually tracked down (by a crystallographer; thanks Andrew!) to the
caption in Figure 2.

![](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2017/02/100-1024x105.jpg){.aligncenter
.size-large .wp-image-17418 loading="lazy" decoding="async" width="450"
height="46"
srcset="https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2017/02/100-1024x105.jpg 1024w, https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2017/02/100-300x31.jpg 300w, https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2017/02/100-768x79.jpg 768w"
sizes="(max-width: 450px) 100vw, 450px"}

However, you probably do need to be a crystallographer to convert this
data into a set of coordinates. This was done and is here deposited as a
CIF file for you to play with if you wish
(DOI:[10.14469/hpc/2154](https://doi.org/10.14469/hpc/2154))\[cite\]10.14469/hpc/2154\[/cite\]. I
have reduced the packing of the unit cell obtained from this CIF file
(198 atoms) to just 60 and you can enjoy them by clicking on the diagram
below. I should point out that if one uses a program that can recognise
the periodic lattice such as **Crystal** (used in the article discussed
here), there is no need to make such reductions, but in this instance I
wanted to use a program such as **Gaussian** in discrete (non-periodic)
mode, for which the calculation (B3LYP/Def2-SVPD) has
DOI: [10.14469/hpc/2156](https://doi.org/10.14469/hpc/2156)\[cite\]10.14469/hpc/2156\[/cite\]
and where you can also find a wavefunction file to play with if you
wish.

::: {#attachment_17423 .wp-caption .aligncenter style="width: 310px"}
![](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2017/02/103.jpg){.aligncenter
.size-full .wp-image-17423 decoding="async"
aria-describedby="caption-attachment-17423"
onclick="jmolInitialize('../Jmol/','JmolAppletSigned.jar');jmolSetAppletColor('white');jmolApplet([450,450],'load wp-content/uploads/2017/02/60.mol;spin 3;');"
width="300"
srcset="https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2017/02/103.jpg 744w, https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2017/02/103-297x300.jpg 297w"
sizes="(max-width: 744px) 100vw, 744px"}

Click for 3D model
:::

An ELF analysis for this non-periodic wavefunction looks as below. The
ELF basins labelled "2e" located in the centre of the cube show an
integrated electron population of \~1.9e and correspond to the localised
electron pairs noted in the article above.

::: {#attachment_17448 .wp-caption .aligncenter style="width: 360px"}
![](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2017/02/104.jpg){.aligncenter
.size-full .wp-image-17448 decoding="async"
aria-describedby="caption-attachment-17448"
onclick="jmolInitialize('../Jmol/','JmolAppletSigned.jar');jmolSetAppletColor('white');jmolApplet([450,450],'load wp-content/uploads/2017/02/Na2He_bas.mol;spin 3;');"
width="350"}

Click for 3D
:::

The basins on the boundaries of this non-periodic unit show reduced
integrations (red arrows below, 0.08 -- 1.7e) and are artefacts of the
non-periodic approximation introduced.

![](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2017/02/105-1024x1019.jpg){.aligncenter
.size-large .wp-image-17453 loading="lazy" decoding="async" width="450"
height="448"
srcset="https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2017/02/105-1024x1019.jpg 1024w, https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2017/02/105-150x150.jpg 150w, https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2017/02/105-300x298.jpg 300w, https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2017/02/105-768x764.jpg 768w, https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2017/02/105-144x144.jpg 144w, https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2017/02/105.jpg 1576w"
sizes="(max-width: 450px) 100vw, 450px"}

The ionization into an electride is brought about by the close proximity
of the atoms as induced by high pressure. Releasing the pressure would
allow the ionized electrons to re-attach themselves to the valence shell
of the sodium atoms, thus destroying the unique properties of the
system. It is certainly true that this system challenges our normal
concepts of what a molecule is. The presence of He is essential and yet
its electrons are hardly involved in the re-organised wavefunction. I
cannot wait for more examples to be discovered!

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

^†^To meet the 55 minute deadline, I was given about 15 minutes thinking
time!

^‡^Instant responses on social media now seem a *sine qua non* of the
political world, so why not the scientific
one[😛](https://yapapp.net/emojis-irony)!

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


On February 6th I was alerted to this intriguing article[cite]10.1038/nchem.2716[/cite] by a phone call, made 55 minutes before the article embargo was due to be released. Gizmodo wanted to know if I could provide an (almost)
<sup>
 †
</sup>
instant
<sup>
 ‡
</sup>
quote. After a few days, this report of a stable compound of helium and sodium still seems impressive to me and I now impart a few more thoughts here.

Messaggi di Rogue Scholar

Imaging normal vibrational modes of a single molecule of CoTPP: a mystery about the nature of the imaged species.

Na2He: a stable compound of helium and sodium at high pressure.