Imperial College London

Henry Rzepa

The previous post contained an exploration of the anomeric effect as it
occurs at an atom centre X for which the effect is manifest in crystal
structures. Here I quantify the effect, by selecting the test molecule
**MeO-X-OMe**, where **X** is of two types:

1.  A two-coordinate atom across the series B-O and Al-S, and carrying
    the appropriate molecular charge such that X carries two lone pairs
    of electrons (thus the charge is 0 for O, but -3 for B).
2.  A four-coordinate atom across the series B-O and Al-S, with X-H
    bonds replacing the lone pairs on this centre in the previous
    example, and again with appropriate molecule charges (*e.g.* +2 for
     SH~2~).

The donor in the anomeric interaction always originates on the oxygen of
the MeO group attached to X. The acceptor is always the X-O σ\* empty
orbital. The results (table below, ωB97XD/Def2-TZVPP calculation, NBO
E(2) in kcal/mol) confirm that as X gets more electronegative, the
X-O σ\* empty orbital becomes a better acceptor, and so the NBO E(2)
interaction energy which quantifies the anomeric interaction gets
larger. Eventually (with X=OH~2~) the donation of electrons into the
X-O σ\* empty orbital becomes so effective that the X-O bond (in this
case O-O) dissociates fully and the NBO perturbation cannot be computed.
Also for reference, a "normal" anomeric interaction (such as is found in
*e.g.* sugars) is around 18 kcal/mol. Anything larger than this could be
considered especially strong, and anything less than \~10 kcal/mol would
be regarded as weak. 

|                                       |        |       |             |
|---------------------------------------|--------|-------|-------------|
| X\[cite\]10.14469/hpc/1221\[/cite\]\* |        |       |             |
| BH~2~                                 | CH~2~  | NH~2~ | OH~2~       |
| 12.5                                  | 17.7   | 18.5  | dissociates |
| AlH~2~                                | SiH~2~ | PH~2~ | SH~2~       |
| 6.9                                   | 12.9   | 21.9  | 31.3        |
| B                                     | C      | N     | O           |
| 8.3                                   | 11.7   | 12.9  | 14.2        |
| Al                                    | Si     | P     | S           |
| 4.8                                   | 6.6    | 11.2  | 18.2        |

For the entry X=S, the E(2) term is actually larger than for the oxygen.
I should note that the Me group itself is not passive in this process.
The C-H bonds can also act as significant electron donors, but here I am
not going to analyse this additional complexity.

This table reveals that there is nothing special about carbon as an
anomeric centre, and here also the normal intimate association with the
term anomeric and heterocyclohexanes such as found in sugars.

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

\* Here I introduce a refinement to my normal process of citing the data
produced for any specific calculation. Rather than including 16
individual citations for each cell in the table, I have gathered all
these calculations into a collection and cite here only the DOI of that
collection. When resolved, the individual members of that collection can
then be inspected for the actual data.

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rel="author"}
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The previous post contained an exploration of the anomeric effect as it occurs at an atom centre X for which the effect is manifest in crystal structures.

A periodic table for anomeric centres, this time with quantified interactions.

[Hypervalency](https://en.wikipedia.org/wiki/Hypervalent_molecule){target="_blank"}
is defined as a molecule that contains one or more main group elements
formally bearing more than eight  electrons in their  valence shell. One
example of a molecule so characterised was
CLi~6~\[cite\]10.1038/355432a0\[/cite\] where the description \""*carbon
can expand its octet of electrons to form this relatively stable
molecule*" was used. Yet, in this latter case, the octet expansion is
[in fact an
illusion,](http://www.ch.imperial.ac.uk/rzepa/blog/?p=10801){target="_blank"}
as indeed are many examples that are cited. The octet shell remains
resolutely un-expanded. Here I will explore the tiny molecule CH~3~F^2-^
where two extra electrons have been added to fluoromethane.

Two such electrons added to *e.g.* such a methane derivative can be in
principle accommodated in two ways:

1. The electrons on carbon could expand the octet shell by populating
 molecular orbitals constructed using 3s or 3p atomic orbitals (AOs)
 as well as the normal 2s and 2p shells. This is also the normal
 \"explanation\" for expanded octets, the assumption being that as
 one moves down the rows of the periodic table (e.g. P, S, Cl, etc)
 these shells become energetically more accessible (*e.g.* the 3d or
 4s shell for P, S, Cl etc). In fact, for *e.g.* PF~5~, the occupancy
 of
 such  \"[Rydberg](https://en.wikipedia.org/wiki/Rydberg_atom){target="_blank"}\"
 shells is only \~0.2 electrons, not a significant octet expansion.
2. The electrons can instead or as well as populate the antibonding
 molecular orbitals (MOs) formed from just the 2s/2p AOs. For a
 methane derivative, there are four bonding MOs (into which the octet
 of electrons are placed) and four anti-bonding MOs all constructed
 from the total of eight AOs. Well known examples of populating
 antibonding MOs are the series N≡N, O=O (singlet), F-F, Ne...Ne
 where the additional electrons are added to anti-bonding MOs and
 have the effect of reducing the bond orders from 3 to 2 to 1 to 0.
 And of course all core shells contain populated bonding and
 antibonding pairs.

Here are some ωB97XD/Def2-TZVPPD/scrf=water calculations. All these
species are molecules with all-real vibrations, being stable toward
dissociation to *e.g.* CH~3~^--^ + H^--^ or CH~3~^--^ + F^--^.  A
transition state for this latter dissocation with
IRC\[cite\]10042/196173\[/cite\] can be characterised. In all cases the
energy of the highest occupied MO or NBO is -ve, meaning that the
electrons are bound, at least in part due to the solvent field applied.

<table style="width:100%;" data-border="1">
<colgroup>
<col style="width: 16%" />
<col style="width: 16%" />
<col style="width: 16%" />
<col style="width: 16%" />
<col style="width: 16%" />
<col style="width: 16%" />
</colgroup>
<tbody>
<tr class="header">
<th>Molecule</th>
<th>Wiberg CH order</th>
<th>Wiberg CF order</th>
<th>Natural Populations</th>
<th>E HONBO, au</th>
<th>dataDOI</th>
</tr>
&#10;<tr class="odd">
<td>CH42-</td>
<td>0.773</td>
<td>–</td>
<td>C:[core]2S(1.98)2p(3.82)3S( 0.15)4d( 0.01)
H:1S( 1.00)</td>
<td>-0.144<img
src="http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2016/02/CH4.jpg"
class="aligncenter size-full wp-image-15846" loading="lazy"
decoding="async"
srcset="https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2016/02/CH4.jpg 280w, https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2016/02/CH4-150x150.jpg 150w, https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2016/02/CH4-144x144.jpg 144w"
sizes="(max-width: 100px) 100vw, 100px" width="100" height="100"
alt="CH4" /></td>
<td>[cite]10.14469/ch/191837[/cite]</td>
</tr>
<tr class="even">
<td>CH3F2-</td>
<td>0.980</td>
<td>1.213</td>
<td>C:[core]2S(1.05)2p( 3.20)3S(1.26)4p( 0.01)4d( 0.01)
H:1S( 0.84)2S( 0.01)2p( 0.02)
F:[core]2S(1.88)2p( 5.61)3S( 0.30)3p( 0.04)3d( 0.01)4p(
0.01)</td>
<td>-0.068
<div id="attachment_15843" class="wp-caption aligncenter"
style="width: 110px">
<img
src="http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2016/02/CH3F.jpg"
class="size-full wp-image-15843" loading="lazy" decoding="async"
aria-describedby="caption-attachment-15843"
onclick="jmolInitialize(&#39;../Jmol/&#39;,&#39;JmolAppletSigned.jar&#39;);jmolSetAppletColor(&#39;white&#39;);jmolApplet([450,450],&#39;load wp-content/uploads/2016/02/CH3F_mo10.cub.xyz;isosurface colour red blue wp-content/uploads/2016/02/CH3F_mo10.cub.jvxl translucent;&#39;);"
srcset="https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2016/02/CH3F-150x150.jpg 150w, https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2016/02/CH3F-144x144.jpg 144w"
sizes="(max-width: 100px) 100vw, 100px" width="100" height="100"
alt="Click for 3D" />
Click for 3D
</div></td>
<td>[cite]10.14469/ch/191919[/cite]</td>
</tr>
<tr class="odd">
<td>CH2F22-</td>
<td>0.871</td>
<td>0.897</td>
<td>C:[core]2S(1.60)2p( 2.64)3S(0.39)3p( 0.01)4d( 0.01)
H:1S(1.19)2S( 0.06)
F:[core]2S(1.86)2p( 5.52)3S( 0.01)3p( 0.01)4p( 0.01)</td>
<td>-0.281
<div id="attachment_15844" class="wp-caption aligncenter"
style="width: 110px">
<img
src="http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2016/02/CH2F2.jpg"
class="size-full wp-image-15844" loading="lazy" decoding="async"
aria-describedby="caption-attachment-15844"
onclick="jmolInitialize(&#39;../Jmol/&#39;,&#39;JmolAppletSigned.jar&#39;);jmolSetAppletColor(&#39;white&#39;);jmolApplet([450,450],&#39;load wp-content/uploads/2016/02/CH2CF2_mo14.cub.xyz;isosurface colour red blue wp-content/uploads/2016/02/CH2CF2_mo14.cub.jvxl translucent;&#39;);"
srcset="https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2016/02/CH2F2-150x150.jpg 150w, https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2016/02/CH2F2-144x144.jpg 144w"
sizes="(max-width: 100px) 100vw, 100px" width="100" height="100"
alt="Click for 3D" />
Click for 3D
</div></td>
<td>[cite]10.14469/ch/191918[/cite]</td>
</tr>
<tr class="even">
<td>CF42-</td>
<td>–</td>
<td>0.801</td>
<td>C:[core]2S(1.94)2p( 1.96)3S( 0.19)3p( 0.04)5d( 0.01)
F:[core]2S(1.89)2p( 5.54)3p( 0.01)3d( 0.02)
 </td>
<td>-0.148<img
src="http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2016/02/CF4.jpg"
class="aligncenter size-full wp-image-15845" loading="lazy"
decoding="async"
srcset="https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2016/02/CF4.jpg 376w, https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2016/02/CF4-150x150.jpg 150w, https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2016/02/CF4-300x300.jpg 300w, https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2016/02/CF4-144x144.jpg 144w"
sizes="(max-width: 100px) 100vw, 100px" width="100" height="100"
alt="CF4" /></td>
<td>[cite]10.14469/ch/191916[/cite]</td>
</tr>
</tbody>
</table>

1. CH~4~^2- ^shows only small Rydberg occupancy (\< 0.2e), but a
 significantly reduced bond order for the four C-H bonds (each
 C-H bonding NBO also has some antibonding character for the other
 three CHs) and hence the molecule is not truly hypervalent.
2. CH~3~F^2-^ in contrast shows quite different behavour. The C-H bond
 order is almost 1 and the C-F bond order is actually \>1. Of the two
 extra electrons, \~1.28 now occupy carbon Rydberg AOs and the
 fluorine also has significant Rydberg population (\~0.36e). So this
 is a real hypervalent system, in which the total valencies exceed
 that expected from an octet.
3. CH~2~F~2~^2-^ is somewhere inbetween the previous two systems. The
 carbon has modest Rydberg occupancy (\~0.4e) but there is also
 significant occupation of the antibonding MOs. Both the C-H and C-F
 bond orders are \<1.
4. CF~4~^2-^ shows a further reduction in the C Rydberg occpancy
 (\<0.2) and the C-F bond order is also reduced. This reduction in
 bond order is also seen in other so-called hypervalent systems such
 as PF~5~.

So of these systems, CH~3~F^2-^ can be reasonably called hypervalent,
whilst the others have much less such character. It does appear that
there is a fine balance between placing extra electrons into Rydberg
orbitals to expand the \"octet\" and hence valencies, and placing them
in anti-bonding orbitals where the individual valencies are actually
reduced. It seems that substituting methane with just one fluorine
encourages population of the Rydberg orbitals, but that more fluorines
encourage instead population of the antibonding orbitals. What is
remarkable is that CH~3~F^2-^ actually has a (small) barrier to
dissociation. The challenge now is to try to design a system which has a
significant Rydberg population, a low antibonding population AND is
stable to dissociation; this will require some inspiration. So do not
hold your breaths!

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rel="author"}
:::

Hypervalency is defined as a molecule that contains one or more main group elements formally bearing more than eight  electrons in their  valence shell. One example of a molecule so characterised was CLi

 6

[cite]10.1038/355432a0[/cite] where the description "“

 carbon can expand its octet of electrons to form this relatively stable molecule

” was used.

Messaggi di Rogue Scholar

A periodic table for anomeric centres, this time with quantified interactions.

Real hypervalency in a small molecule.