Imperial College London

Henry Rzepa

A **scalemic** molecule is the term used by
[Eliel](http://www.uottawa.ca/publications/interscientia/inter.4/eliel/eliel.html){target="_blank"}
to describe any non-racemic chiral compound. Synthetic chemists imply it
when they describe a synthetic product with an observable enantiomeric
excess or **ee** (which can range from close to 0% to almost 100%).
There are two cheminformatics questions of interest to me:

1.  How many non-trivial scalemic molecules have been reported in the
    literature (let's assume their **ee** is significantly greater than
    0%)?
    - The distribution function for the **ee** of these molecules would
      be most interesting!
2.  Of those, how many have the absolute configuration of the
    predominant enantiomer established with high confidence?
    - Or, to put this another way, how many may prove to be
      mis-assigned?

Note the careful qualification in the above questions. Thus by
non-trivial, I mean compounds whose scalemic attributes persist in
solution for a chemically useful duration. That could be taken to mean
configurationally stable chiral molecules, rather than those that might
be conformationally chiral (an example of a trivial scalemic molecule
would be *e.g.* the twist-boat conformation of cyclohexane, which having
D~2~ symmetry is dissymetric, but which would only retain its scalemic
property for a trivially short timescale).

What are boundary values? These are some:

- As I write this, CAS records 61,257,703 chemical substances. Needless
  to say (unless I missed it), the answer to my first question is not to
  be found there.
- Beilstein (Reaxys) records 1,126,995 compounds as having one or more
  reported chiroptical properties (which is the most direct way of
  establishing a molecule is scalemic, although strictly, having say an
  optical rotation of 0° does not necessarily mean the molecule is not
  scalemic). We have no way of knowing how many molecules are scalemic
  for which no chiroptical measurement has been made (but one would hope
  its a small proportion). Perhaps that is a good answer to question
  **1**?
  - of which 1,097,094 relate to optical rotatory power, 17,515 to
    optical rotatory dispersion and 62,248 to electronic circular
    dichroism.
  - it is more difficult to answer how many of these 1,126,995
    substances have a firmly established absolute configuration.
    Measuring a chiroptical property *per se* does NOT in itself
    establish the absolute configuration. Doing so is a fascinating
    exercise in sequential logical argument, and how one does it has
    changed quite a lot over time. And what might I mean with *high
    confidence*? An older assignment (made say \> 40 years ago) might be
    less confident than one established in 2011 (fortunately, we can
    probably trust the absolute configurations of the amino acids!). A
    bit of a can of worms, nevertheless. But it interests me because it
    is a good example of what the **semantic web** is supposed to be all
    about.
- The Cambridge crystallographic database reports 560,307 entries, of
  which 72,340 are in chiral space groups (in which a chiral molecule
  can crystallise) and exhibit no disorder or other errors. We do not
  know how many of these are non-trivial, since all manner of small (and
  low energy) distortions can create a chiral species (in the solid
  state), but which would not persist  for a chemically useful duration
  in solution (*i.e.* it might for example immediately racemize and
  become non-scalemic).
- The [Flack
  parameter](http://dx.doi.org/10.1107/S0108767383001762){target="_blank"}
  has been used since [1983](%2010.1002/chir.20473){target="_blank"} for
  enantiomorph estimation (a value of \~≤ 0.10(10) would be considered
  meaningful). This could in principle provide an answer of known
  confidence to my question **2** above (but would not address the issue
  of non-triviality).
  - The challenge now is to quantify how many compounds have a
    meaningful reported Flack parameter (presumably a sub-set of
    72,340?)

Let me declare one personal interest. Over the last four years or so, we
have been asked to confirm the absolute configuration of around eight
scalemic molecules. After a detailed study, we concluded three were
mis-assigned. Now this in no way implies anything about what the answer
to question **2** above might be! But it does make one think!

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


A
<strong>
 scalemic
</strong>
molecule is the term used by Eliel to describe any non-racemic chiral compound.

Scalemic molecules: a cheminformatics challenge!

This story starts with a calixarene, a molecule (suitably adorned with
substituents) frequently used as a host to entrap a guest and perchance
make the guest do something interesting. Such a calixarene was at the
heart of a [recent story](http://www.ch.ic.ac.uk/rzepa/blog/?p=2828)
where an attempt was made to induce it to capture cyclobutadiene in its
cavity.

::: {#attachment_3395 .wp-caption .aligncenter style="width: 296px"}
[![](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2011/01/calixarene.jpg "calixarene"){.size-full
.wp-image-3395 loading="lazy" decoding="async"
aria-describedby="caption-attachment-3395" width="286" height="285"
srcset="https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2011/01/calixarene.jpg 858w, https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2011/01/calixarene-150x150.jpg 150w, https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2011/01/calixarene-300x298.jpg 300w"
sizes="(max-width: 286px) 100vw, 286px"}](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2011/01/calixarene.jpg)

The basic skeleton of a calixarene
:::

At the base of the calixarene are four hydroxyl groups, arranged in
either a left or right handed manner. The molecule, in other words is
chiral (C~4~ symmetry to be precise). As a chiral molecule, it might
trap left and right-handed guests in a slightly different manner
(forming two possible diastereomeric host-guest complexes).  As it
happens, the guest in the cyclobutadiene story was just such a chiral
molecule. But an essential question to ask is what the barrier to
enantiomerization of such a calixarene might be?  One can envisage
several ways of accomplishing such a conversion.

::: {#attachment_3398 .wp-caption .aligncenter style="width: 408px"}
[![](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2011/01/water-tetramer.jpg "water-tetramer"){.size-full
.wp-image-3398 loading="lazy" decoding="async"
aria-describedby="caption-attachment-3398" width="398" height="362"
srcset="https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2011/01/water-tetramer.jpg 1991w, https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2011/01/water-tetramer-300x273.jpg 300w, https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2011/01/water-tetramer-1024x931.jpg 1024w"
sizes="(max-width: 398px) 100vw, 398px"}](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2011/01/water-tetramer.jpg)

Enantiomerization pathways for a chiral calixarene
:::

All four hydrogens can be moved in a single step, one might move two at
a time in two steps, or one might move one at a time in four steps.
These processes would involve respectively [8, 6 or 4
electrons](http://www.ch.ic.ac.uk/rzepa/blog/?p=3186){target="_blank"}
in each step. There is a fundamental difference between the first
pathway and the last two;  the latter involve  ionic intermediates
(zwitterions) whereas the first is neutral. As such one might imagine
the process would depend on the ability of the solvent to stabilize any
such zwitterion.

Let us start with a gas phase model (ωB97XD/6-311G(d,p)), and a
[transition state](http://hdl.handle.net/10042/to-6366) with one
negative force constant is indeed found with  C~4v~ symmetry. The free
energy barrier ΔG^†^ for the process is 14.0 kcal/mol, which means the
reaction will occur rapidly, even at lower temperatures of  \~200K. A
pack size of 8 seems preferred for this model. This is hardly a surprise
since the formation of ionic intermediates would not be expected. One
might however speculate thus. In the schematic above, n=1 and one might
be tempted to ask if higher values of n (lets say  n=2, a pack size of
10, or n=3, a pack size of 12, etc ) might exhibit similar behaviour. Is
there any limit to the ring/pack size for this type of proton exchange?

::: {#attachment_3401 .wp-caption .aligncenter style="width: 266px"}
![](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2011/01/calixarene-c4v.jpg "calixarene-c4v"){.size-full
.wp-image-3401 loading="lazy" decoding="async"
aria-describedby="caption-attachment-3401"
onclick="jmolInitialize('../Jmol/',true);jmolSetAppletColor('goldenrod');jmolApplet([600,600],'load wp-content/uploads/2011/01/cx-gas-c4v.log;frame 7;set measurementUnits Angstroms;vectors on;vectors 4;vectors scale 5.0; color vectors purple; vibration 15;animation mode loop;connect (atomno=23) (atomno=50) PARTIAL;connect (atomno=50) (atomno=15) PARTIAL;connect (atomno=15) (atomno=52) PARTIAL;connect (atomno=52) (atomno=7) PARTIAL;connect (atomno=23) (atomno=50) PARTIAL;connect (atomno=50) (atomno=15) PARTIAL;connect (atomno=48) (atomno=23) PARTIAL;connect (atomno=31) (atomno=48) PARTIAL;connect (atomno=23) (atomno=50) PARTIAL;connect (atomno=31) (atomno=51) PARTIAL;connect (atomno=51) (atomno=7) PARTIAL;');"
width="256" height="254"
srcset="https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2011/01/calixarene-c4v.jpg 512w, https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2011/01/calixarene-c4v-150x150.jpg 150w, https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2011/01/calixarene-c4v-300x298.jpg 300w"
sizes="(max-width: 256px) 100vw, 256px"}

Transition state for enantiomerization of a calixarene in the gas phase.
Click for 3D.
:::

What about in solution? Well, let us apply the mildest of solvents,
benzene as a so-called continuum field. This has a very low dielectric
(2.3) and you might imagine it would have hardly any effect. Well click
on the below. The C~4v~ geometry now has three
[computed](http://hdl.handle.net/10042/to-6367){target="_blank"}
negative force constants; the two additional ones are shown below (they
are degenerate with a wavenumber of 101i cm^-1^).

<table data-border="0">
<colgroup>
<col style="width: 50%" />
<col style="width: 50%" />
</colgroup>
<tbody>
<tr class="odd">
<td><div id="attachment_3417" class="wp-caption aligncenter"
style="width: 210px">
<img
src="http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2011/01/calixarene-cs.jpg"
title="calixarene-cs" class="size-full wp-image-3417" loading="lazy"
decoding="async" aria-describedby="caption-attachment-3417"
onclick="jmolInitialize(&#39;../Jmol/&#39;,true);jmolSetAppletColor(&#39;goldenrod&#39;);jmolApplet([600,600],&#39;load wp-content/uploads/2011/01/cx-ben-c4v.log;frame 8;set measurementUnits Angstroms;vectors on;vectors 4;vectors scale 5.0; color vectors purple; vibration 15;animation mode loop;connect (atomno=23) (atomno=50) PARTIAL;connect (atomno=50) (atomno=15) PARTIAL;connect (atomno=15) (atomno=52) PARTIAL;connect (atomno=52) (atomno=7) PARTIAL;connect (atomno=23) (atomno=50) PARTIAL;connect (atomno=50) (atomno=15) PARTIAL;connect (atomno=48) (atomno=23) PARTIAL;connect (atomno=31) (atomno=48) PARTIAL;connect (atomno=23) (atomno=50) PARTIAL;connect (atomno=31) (atomno=51) PARTIAL;connect (atomno=51) (atomno=7) PARTIAL;&#39;);"
srcset="https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2011/01/calixarene-cs.jpg 562w, https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2011/01/calixarene-cs-150x150.jpg 150w, https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2011/01/calixarene-cs-300x300.jpg 300w"
sizes="(max-width: 200px) 100vw, 200px" width="200" height="200" />
<p>C4v symmetric geometry for calixarene in benzene solvent, with three
negative force constants. Click for animation of E mode.</p>
</div></td>
<td><div id="attachment_3418" class="wp-caption aligncenter"
style="width: 210px">
<img
src="http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2011/01/calixarene-cs1.jpg"
title="calixarene-cs1" class="size-full wp-image-3418" loading="lazy"
decoding="async" aria-describedby="caption-attachment-3418"
onclick="jmolInitialize(&#39;../Jmol/&#39;,true);jmolSetAppletColor(&#39;goldenrod&#39;);jmolApplet([600,600],&#39;load wp-content/uploads/2011/01/cx-ben-c4v.log;frame 9;set measurementUnits Angstroms;vectors on;vectors 4;vectors scale 5.0; color vectors purple; vibration 15;animation mode loop;connect (atomno=23) (atomno=50) PARTIAL;connect (atomno=50) (atomno=15) PARTIAL;connect (atomno=15) (atomno=52) PARTIAL;connect (atomno=52) (atomno=7) PARTIAL;connect (atomno=23) (atomno=50) PARTIAL;connect (atomno=50) (atomno=15) PARTIAL;connect (atomno=48) (atomno=23) PARTIAL;connect (atomno=31) (atomno=48) PARTIAL;connect (atomno=23) (atomno=50) PARTIAL;connect (atomno=31) (atomno=51) PARTIAL;connect (atomno=51) (atomno=7) PARTIAL;&#39;);"
srcset="https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2011/01/calixarene-cs1.jpg 562w, https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2011/01/calixarene-cs1-150x150.jpg 150w, https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2011/01/calixarene-cs1-300x300.jpg 300w"
sizes="(max-width: 200px) 100vw, 200px" width="200" height="200" />
<p>C4v geometry for calixarene in benzene. Click for animation of second
E mode.</p>
</div></td>
</tr>
</tbody>
</table>

Each of these additional two negative force constants shows a
displacement heading towards the zwitterion shown in the scheme below.
As one increases the polarity of the solvent, so the force constant
becomes more negative. Thus for
[dichloromethane](http://hdl.handle.net/10042/to-6368){target="_blank"},
it is now 322i cm^-1^ and with
[water](http://hdl.handle.net/10042/to-6363){target="_blank"} it is 376i
cm^-1^

So now the question is what happens when either of the two additional
negative force constants is followed downhill? Will it form a true
zwitterion (which would have C~s~ symmetry), in which case it would be
(two) 6 electron processes to enantiomerize the calixarene instead of
one 8 electron one.

::: {#attachment_3428 .wp-caption .aligncenter style="width: 310px"}
![](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2011/01/calixarene-cs3.jpg "calixarene-cs3"){.size-full
.wp-image-3428 loading="lazy" decoding="async"
aria-describedby="caption-attachment-3428"
onclick="jmolInitialize('../Jmol/',true);jmolSetAppletColor('goldenrod');jmolApplet([600,600],'load wp-content/uploads/2011/01/cx-benzene-cs.log;frame 10;set measurementUnits Angstroms;vectors on;vectors 4;vectors scale 5.0; color vectors purple; vibration 15;animation mode loop;connect (atomno=23) (atomno=50) PARTIAL;connect (atomno=50) (atomno=15) PARTIAL;connect (atomno=15) (atomno=52) PARTIAL;connect (atomno=52) (atomno=7) PARTIAL;connect (atomno=23) (atomno=50) PARTIAL;connect (atomno=50) (atomno=15) PARTIAL;connect (atomno=48) (atomno=23) PARTIAL;connect (atomno=31) (atomno=48) PARTIAL;connect (atomno=23) (atomno=50) PARTIAL;connect (atomno=31) (atomno=51) PARTIAL;connect (atomno=51) (atomno=7) PARTIAL;');"
width="300" height="300"
srcset="https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2011/01/calixarene-cs3.jpg 562w, https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2011/01/calixarene-cs3-150x150.jpg 150w, https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2011/01/calixarene-cs3-300x300.jpg 300w"
sizes="(max-width: 300px) 100vw, 300px"}

True transition state for proton exchange in solution phase calixarene
:::

In fact this geometry of C~s~ symmetry, which does resemble the
zwitterion shown in the scheme above, is **NOT** a minimum but a true
transition state itself (the free energy barrier hardly changed from the
value for the gas phase). So the answer seems to be that a calixarene
enantiomerizes *via* *transition state* not of C~4v~ but of C~s~
symmetry, and which resembles a zwitterion but is not actually one. The
*8-pack*of electrons was tempted to take a short rest-break on their way
to shifting the four protons, but in the end did it in a single journey!
So we have an unusual zwitterionic but nevertheless concerted transition
state for the process.

Still unresolved is whether such cyclic transfer of four protons between
four oxygen atoms continues to be concerted for larger rings, or whether
the system is finally tempted to break up the transfer by resting with
one or more discrete intermediates along the way. I finally note that in
the calixarene
[reported](http://dx.doi.org/10.1126/science.1188002){target="_blank"}
which catalysed the thoughts above, the four oxygens are capped with a
guanidinium cation sitting just above them, and this too may have an
interesting effect on the proton transfer process.

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


This story starts with a calixarene, a molecule (suitably adorned with substituents) frequently used as a host to entrap a guest and perchance make the guest do something interesting. Such a calixarene was at the heart of a recent story where an attempt was made to induce it to capture cyclobutadiene in its cavity.

Rogue Scholar Beiträge

Scalemic molecules: a cheminformatics challenge!

Do electrons prefer to move in packs of 4, 6 or 8 during proton exchange in a calixarene?