Imperial College London

Henry Rzepa

The chemical bond zoo is [relatively
small](https://en.wikipedia.org/wiki/Chemical_bond) (the bond being a
somewhat fuzzy concept, I am not sure there is an actual count of
occupants). So when two new candidates come along, it is worth taking
notice. I have previously noted the [Chemical Bonds at the 21st
Century-2017:
CB2017](http://cb2017.rwth-aachen.de/index.html){target="talkmain"} Aachen
conference, where both were discussed.

1.  The first now has a name, the
    *[**exo-bond**]{style="color: #ff0000;"}*, one example of which is
    the C~2~ diatomic. The hint that a quadruple bond could be
    formulated between the two carbon atoms goes back a little
    while\[cite\]10.1103/PhysRev.56.778\[/cite\] (see Table 1), but
    revived interest really took off after \~2010, around the time [my
    blog](https://doi.org/10.14469/hpc/2853) on the topic also appeared.
    You can see the abundance of post 2010 articles in the bibliography
    at the Aachen
    [bond-slam](http://dipc.ehu.es/bondslam/index.php/Controversial_Bond_Orders).
    At the conference, four speakers all agreed using rather different
    methods that there was indeed "something" additional to a C≡C triple
    bond and that this "something" might be worth \~15-30 kcal/mol of
    stabilization.^†^ The debate centered around whether this term
    deserved to be called a bond, or whether it should be downgraded to
    merely that of *biradicaloid* stabilizations.^‡^ The more
    conventional population of a σ^\*^-antibond it was argued would not
    result in such stabilizations. Since many kinds of bonds have
    stabilization energies of similar magnitude, not least the weaker
    hydrogen bonds, agostic bonds, halogen bonds etc, let us for the
    sake of argument call it a bond here. Because four electrons might
    occupy the same space along the σ-symmetric C-C axis, they
    experience significant so-called static correlation^∞^ which results
    in partition into one electron pair occupying the central region
    (the *endo-bond*) and the other pair in the outer region (the
    *exo-bond). * This separation decreases the Pauli electron
    repulsions along the entire C-C axis region.  [An
    example](http://www.ch.imperial.ac.uk/rzepa/blog/?p=2251) of an
    *exo-bond* is found in [\[1.1.1\]
    propellane](http://www.ch.imperial.ac.uk/rzepa/blog/?p=2251), where
    the notional central C-C bond is thought to actually occupy the
    region outside the central C-C bond axis, but largely in this
    example because of angular strains. In this case however, the
    propellane bond is not competing with an *endo-bond* along the same
    axis. We might conclude therefore that the convention of
    characterising a bond using the separation between the two nuclei
    (the *bond-length*) is rather stressed when one has two different
    bonds along the axis of the nuclei, one of which is obviously
    "*longer*" than the other.

    Which brings us to representations; e*.g.* Chemdraw now allows
    drawing of quadruple bonds and so it can be drawn thus quite
    simply.  
    ![](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2017/09/CC-1.jpeg){.aligncenter
    .size-full .wp-image-18773 decoding="async" width="133"}  
    The second form breaks the century-old convention that all bonds
    along a diatomic axis are drawn in the same manner, by isolating the
    *exo-bond* to make the point clear. Perhaps we should stick to the
    first, but be prepared to explain the underlying complexity of the
    quantum mechanical symmetries as we do to students with σ/π/δ/φ
    bonds, which are another mechanism for avoiding having bonds in
    exactly the same regions. I know the story has not yet ended; but is
    it time to at least speculate when the text-books will start to
    reflect/discuss the *exo-bond*?

2.  The second I dub the ***[hyper-bond]{style="color: #ff0000;"}***.
    This goes back to G. N. Lewis and his famous octet rule for main
    group elements, the expansion of which was subsequently described by
    the term hypervalent. That term has become rather confused with
    hypercoordinate, since hypervalent is [often
    used](https://en.wikipedia.org/wiki/Hypervalent_molecule) to
    describe hypercoordinate species such as PCl~5~, SF~6~ or
    [I.I~7~](http://www.ch.imperial.ac.uk/rzepa/blog/?p=2687). But this
    does rather break the original definition, since few if indeed any
    of these hypercoordinate molecules have a significantly expanded
    octet shell. At the Aachen meeting, a molecule fitting the original
    definition was
    [presented](http://dipc.ehu.es/bondslam/index.php/Hypervalence),
    appearing first in early form [on this
    blog](http://www.ch.imperial.ac.uk/rzepa/blog/?p=15823). Put simply,
    a wavefunction for CH~3~F^2-^ can be calculated
    (ωB97XD/Def2-QZVPPD/SCRF=water, DOI: [cb3n ](https://doi.org/cb3n))
    for which the two additional electrons populate a molecular orbital
    with significant contributions from the 3s/3p valence shell AOs
    (atomic orbitals) for both carbon and fluorine. The alternative
    would have been to populate the anti-bonding C-H or C-F orbitals
    composed of 2s/2p valence shell AOs. The former results in a total
    population of these higher valence shells of 1.55e and makes the C-F
    (Wiberg) bond order \>1 (1.14) and the total Wiberg bond indices \>4
    for carbon (4.162) and \>1 for F (1.275). The resulting HOMO
    (highest occupied molecular orbital) or NBO (they are very similar)
    looks as below. It takes the approximate form of a torus or cylinder
    wrapping the inner C-F bond, a second layer to the C-F bond if you
    wish.   

    <table data-border="0">
    <colgroup>
    <col style="width: 50%" />
    <col style="width: 50%" />
    </colgroup>
    <tbody>
    <tr class="odd">
    <td><div id="attachment_18783" class="wp-caption aligncenter"
    style="width: 150px">
    <img
    src="http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2017/09/295.jpg"
    class="size-full wp-image-18783" decoding="async"
    aria-describedby="caption-attachment-18783"
    srcset="https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2017/09/295.jpg 344w, https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2017/09/295-300x216.jpg 300w"
    sizes="(max-width: 344px) 100vw, 344px" width="140" />
    <p>Normal valence shell F-C σ-orbital defining the regular C-F bond.</p>
    </div></td>
    <td><div id="attachment_18784" class="wp-caption aligncenter"
    style="width: 230px">
    <img
    src="http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2017/09/294.jpg"
    class="size-full wp-image-18784" decoding="async"
    aria-describedby="caption-attachment-18784"
    srcset="https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2017/09/294.jpg 552w, https://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2017/09/294-288x300.jpg 288w"
    sizes="(max-width: 552px) 100vw, 552px" width="220" />
    <p>Higher valence shell F-C σ-orbital defining the C-F hyper-bond.</p>
    </div></td>
    </tr>
    </tbody>
    </table>

    Rather than the entire molecule being defined as hypervalent, only
    one (in this case localized) orbital is given the term and the other
    orbitals are conventional.

In both cases the molecules are either very reactive (C~2~) or with such
a low barrier to fragmentation (into CH~3~^--^ and F^--^ for CH~3~F^2-^)
that detection of the latter is unlikely. But these are interesting
*Gedanken experiments* in quantum mechanics, which in turn catalyse the
development of new techniques and in some cases might even lead to the
design and isolation of new types of molecules.

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

^†^The known thermochemistry of the two reactions; HC≡CH → HC≡C + H•;
HC≡C• → CC + H• is \~17 kcal/mol less endothermic for the second step,
suggesting some factor is needed to account for the additional
stabilization when CC is formed.

^‡^The singlet to triplet excitation energy for C~2~ is \~+30 kcal/mol,
so the *biradicaloid* electrons are certainly spin-coupled.

^∞^Other "difficult" correlated molecules include Be~2~ and B~2~.

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The chemical bond zoo is relatively small (the bond being a somewhat fuzzy concept, I am not sure there is an actual count of occupants). So when two new candidates come along, it is worth taking notice. I have previously noted the Chemical Bonds at the 21st Century-2017: CB2017 Aachen conference, where both were discussed.

Publicaciones de Rogue Scholar

Two new types in the chemical bonding zoo: exo-bonds and hyper-bonds?