Imperial College London

Henry Rzepa

This is another of those posts that has morphed from an earlier one
noting the death of the great chemist [George
Olah](http://www.ch.imperial.ac.uk/rzepa/blog/?p=17633). The discussion
about the norbornyl cation concentrated on whether this species existed
in a single minimum symmetric energy well (the non-classical
Winstein/Olah proposal) or a double minimum well connected by a
symmetric transition state (the classical Brown proposal). In a comment
on the post, I added other examples in chemistry of single/double
minima, mapped here to non-classical/classical structures. I now expand
on [the examples related to small aromatic or anti-aromatic
rings]{style="color: #ff00ff;"}.

|                                                                  |                                                                                                                                                    |                                                                                                                                                                                                                                                                                             |
|------------------------------------------------------------------|----------------------------------------------------------------------------------------------------------------------------------------------------|---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|
| Examples of symmetric energy potentials                          |                                                                                                                                                    |                                                                                                                                                                                                                                                                                             |
| System                                                           | Classical with 1 imaginary normal mode                                                                                                             | Non-classical with 0 imaginary modes                                                                                                                                                                                                                                                        |
| Norbornyl cation                                                 | TS for \[1,2\] sigmatropic                                                                                                                         | Minimum, this post                                                                                                                                                                                                                                                                          |
| [Singlet \[6\], \[10\]; 4n+2 annulenes]{style="color: #ff00ff;"} | [--]{style="color: #ff00ff;"}                                                                                                                      | [[Minimum with](http://www.ch.imperial.ac.uk/rzepa/blog/?p=485){style="color: #ff00ff;"} [Kekulé](http://www.ch.imperial.ac.uk/rzepa/blog/?p=12560){style="color: #ff00ff;"}[ vibration](http://www.ch.imperial.ac.uk/rzepa/blog/?p=485){style="color: #ff00ff;"}]{style="color: #ff00ff;"} |
| [Singlet \[4\], \[8\]; 4n annulenes]{style="color: #ff00ff;"}    | [[TS for bond shift, 1 imaginary normal mode](http://www.ch.imperial.ac.uk/rzepa/blog/?p=17543){style="color: #ff00ff;"}]{style="color: #ff00ff;"} | [--]{style="color: #ff00ff;"}                                                                                                                                                                                                                                                               |
| [Triplet \[4\], \[8\]; 4n annulenes]{style="color: #ff00ff;"}    | [--]{style="color: #ff00ff;"}                                                                                                                      | [Minimum, with [Kekulé](http://www.ch.imperial.ac.uk/rzepa/blog/?p=12560){style="color: #ff00ff;"} vibration (**?**)]{style="color: #ff00ff;"}                                                                                                                                              |
| Semibullvalenes                                                  | TS for \[3,3\] sigmatropic                                                                                                                         | [Minimum](http://www.ch.imperial.ac.uk/rzepa/blog/?p=17041)                                                                                                                                                                                                                                 |
| Strong Hydrogen bonds                                            | TS for proton transfer                                                                                                                             | [Minimum](http://www.ch.imperial.ac.uk/rzepa/blog/?p=13252)                                                                                                                                                                                                                                 |
| S~N~2 substitutions                                              | TS for substitution (C)                                                                                                                            | [Minimum (Si)](http://www.ch.imperial.ac.uk/rzepa/blog/?p=783)                                                                                                                                                                                                                              |
| Jahn-Teller distortions                                          | [Dynamic Jahn-Teller effects](http://www.ch.imperial.ac.uk/rzepa/blog/?p=14043)                                                                    | No Jahn-Teller distortions                                                                                                                                                                                                                                                                  |

In the table above, you might notice a
(**[?]{style="color: #ff0000;"}**) associated with the entry for
(aromatic) triplet state **4n **annulenes. Here I expand the
**[?]{style="color: #ff0000;"}** by considering triplet cyclobutadiene
and triplet cyclo-octatetraene (ωB97XD/Def2-TZVPP,
[10.14469/hpc/2241](https://doi.org/10.14469/hpc/2241)
and [10.14469/hpc/2242](https://doi.org/10.14469/hpc/2242)
respectively). Each has a normal vibrational mode shown animated below,
which oscillates between the two
[Kekulé](http://www.ch.imperial.ac.uk/rzepa/blog/?p=12560) representations
of the molecule with wavenumbers of 1397 and 1744 cm^-1^ respectively.
These [Kekulé](http://www.ch.imperial.ac.uk/rzepa/blog/?p=12560) modes
are both real, which indicates that the symmetric species (D~4h~ and
D~8h ~symmetry) is in each case the equilibrium minimum energy position
(r~CC~ 1.431 and 1.395Å). For comparison the aromatic singlet state 4n+2
annulene benzene (r~CC~ 1.387Å) has the value 1339 cm^-1^. Notice that
both the triplet state wavenumbers are elevated compared to singlet
benzene, because in each case the triplet ring π-bond orders are lower,
thus decreasing the natural tendency of the π-system to [desymmetrise
the
ring.](http://www.ch.imperial.ac.uk/rzepa/blog/?p=485)\[cite\]10.1021/cr990363l\[/cite\]

![](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2017/03/4-1397.gif){.aligncenter
.size-full .wp-image-17672 decoding="async" width="450"}

![](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2017/03/C8-1744.gif){.aligncenter
.size-full .wp-image-17671 decoding="async" width="450"}

To complete the theme, I will look at singlet cyclobutadiene. According
to the table above, the symmetric form should be a transition state (TS)
for bond shifting, with one imaginary normal mode. To calculate this
mode, one has to use a method that correctly reflects the symmetry, in
this case a CASSCF(4,4)/6-311G(d,p) wavefunction (DOI:
[10.14469/hpc/2244](harp://doi.org/10.14469/hpc/2244)). The mode
(r~CC~ 1.444Å) shown below has a wavenumber of 1477*i* cm^-1^;^ ^its
vectors of course resemble those of the triplet mode, but its force
constant is now negative rather than positive!

![](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2017/03/c4-s.gif){.aligncenter
.size-full .wp-image-17690 decoding="async" width="450"}

At first sight any connection between the property of the norbornyl
cation at the core of the controversies all those decades ago and
aromatic/antiaromatic rings might seem tenuous. But in the end many
aspects of chemistry boil down to symmetries and from there to [Évariste
Galois](https://en.wikipedia.org/wiki/Évariste_Galois), who started the
ball rolling.

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[https://orcid.org/0000-0002-8635-8390](https://orcid.org/0000-0002-8635-8390){target="_blank"
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This is another of those posts that has morphed from an earlier one noting the death of the great chemist George Olah.

Messaggi di Rogue Scholar

Expanding on the curious connection between the norbornyl cation and small-ring aromatics.