# Bonding in diatomic C2, a carbon-carbon quadruple bond?

Carbon is well known to form single, double, and triple $\ce{C-C}$ bonds in compounds. There is a recent report (2012) that carbon forms a quadruple bond in diatomic carbon, $\ce{C2}$. The excerpt below is taken from that report. The fourth bond seems pretty odd to me.

$\ce{C2}$ and its isoelectronic molecules $\ce{CN+}$, BN and $\ce{CB-}$ (each having eight valence electrons) are bound by a quadruple bond. The bonding comprises not only one σ- and two π-bonds, but also one weak ‘inverted’ bond, which can be characterized by the interaction of electrons in two outwardly pointing sp hybrid orbitals.

According to Shaik, the existence of the fourth bond in $\ce{C2}$ suggests that it is not really diradical...
If $\ce{C2}$ were a diradical it would immediately form higher clusters. I think the fact that you can isolate $\ce{C2}$ tells you it has a barrier, small as it may be, to prevent that.

Molecular orbital theory for dicarbon, on the other hand, predicts a C-C double bond in $\ce{C2}$ with 2 pairs of electrons in $\pi$ bonding orbitals and a bond order of two. "The bond dissociation energies (BDE) of $\ce{B2, C2}$, and $\ce{N2}$ show increasing BDE consistent with single, double, and triple bonds." (Ref) So this model of the $\ce{C2}$ molecule seems quite reasonable.

My questions, since this is most definitely not my area of expertise:

• Is dicarbon found naturally in any quantity and how stable is it? Is it easy to make in the lab? (The Wikipedia article reports it in stellar atmospheres, electric arcs, etc.)
• Is there good evidence for the presence of a quadruple bond in $\ce{C2}$ that wouldn't be equally well explained by double bonding?
• You may be interested in this blog post by Rzepa on the $\ce{CN+}$ cation, which putatively contains a $\ce{CN}$ quadruple bond and is isoelectronic with $\ce{C2}$ – Richard Terrett Jun 5 '12 at 2:56
• @Richard Terrett Thanks for the reference...it's one I hadn't found. So, the quadruple bond is plausible from a calculation stand point (if I'm reading that right). Is there experimental evidence that could/would support one view or the other? As I said, I'm "a bit" out of my field here. – Janice DelMar Jun 5 '12 at 5:39
• @JaniceDelMar There is no evidence, and there never will be. The C2 molecule looks like any other homodiatomic: two fluffy balls of electron density pushed together. Where are the four ropes in that picture? – Eric Brown May 4 '13 at 6:31
• It would not necessarily form higher clusters, because maybe 2 C-C -> C-C-C-C is an endothermic reaction. The product, too, is a diradical! It's a non-explanation. – Eric Brown May 4 '13 at 6:37

Okay, this is not so much of an answer as it is a summary of my own progress on this topic after giving it some thought. I don't think it's a settled debate in the community yet, so I don't feel so much ashamed about it :)

A few of the things worthy of note are:

• The bond energy found by the authors for this fourth bond is 13.2 kcal/mol, i.e. about 55 kJ/mol. This is very weak for a covalent bond. You can compare it to other values here, or to the energies of the first three bonds in triple-bonded carbon, which are respectively 348, 266 and 225 kJ/mol. This fourth bond is actually even weaker than the strongest of hydrogen bonds ($\ce{F\bond{...}H–F}$, at 160 kJ/mol). Another point of view on this article could thus be: “valence bond necessarily predicts a quadruple bond, and it was now precisely calculated and found to be quite weak”.

• The findings of this article are consistent with earlier calculations using other quantum chemistry methods (e.g. the DFT calculations in ref. 48 of the Nature Chemistry paper) which have found a bond order between 3 and 4 for molecular dicarbon.

• However, the existence of this quadruple bonds is somewhat at odds with the cohesive energy of gas-phase dicarbon, which according to Wikipedia is 6.32 eV, i.e. 609 kJ/mol. This latter value is much more in line with typical double bonds, reported at an average of 614 kJ/mol. This is still a bit of a mistery to me…

The real issue is that no one has ever taken a picture (i.e. electron density) of genuine, unambigious, cases of a single, double, triple, quadruple??? bonds. And they never will, because these concepts are not based on quantum mechanics.

Two atoms reside next to each other, and if they have a favorable electrostatic interaction, then a certain type of topology arises in their electron density. (q.v. Quantum Theory of Atoms in Molecules)

You might as well say that every "bond" is a single-bond, or, equivalently, and infinity-bond.

These types of articles are bogus, as they can not be confirmed experimentally. They got lucky with the reviewers, and/or an editor who knows their readership is just dying to hear news of a quadruple bond, having heard for so many years that triple is the highest you can go.

I mean, what are people looking for? Four "ropes" that link between the two carbon atoms? Where is the unambiguous, unbiased dividing line between bond energies of a single/double/triple/quadruple bond?

• 1) Electron density can be observed. 2) Quadruple bonds are pretty obvious in metals complexes 3) Even hextuple bonds are theoretically possible in certain molecules... – Mithoron Aug 21 '17 at 14:33
• 1) Yes, that's why I cited electron density as an example of an observable which might be used to confirm. 2) citation needed 3) example needed. Hexatuple bonds? – Eric Brown Aug 22 '17 at 12:13