# Does "C"_2 exist, and if so, describe its electron distribution?

Jun 7, 2015

Actually, diatomic carbon, or ${C}_{2}$, does exist, but only as a gas and at extremely high temperatures.

http://pubs.acs.org/doi/abs/10.1021/ja00194a042

(You can view that in full if you have an ACS subscription.)

You can also prove this by constructing carbon's molecular orbital diagram.

The ${C}_{2}$ molecule has a total of 8 valence electrons, 4 from each carbon atom. As you can see, 6 valence electrons occupy bonding orbitals - ${\sigma}_{2 s}^{2}$, ${\pi}_{2 p x}^{2}$, and ${\pi}_{2 p y}^{2}$, and only 2 occupy an antibonding orbital - ${\sigma}_{2 s}^{\star 2}$.

The diatomic carbon molecule has a bond order equal to

"B.O." = 1/2("bonding electrons"-"antibonding electrons")

$\text{B.O.} = \frac{1}{2} \left(6 - 2\right) = 2$

This suggests that the two carbon atoms are bonded via a double bond. However, as you can see, it's not a "classical double bond", meaning that it is not comprised of a sigma and a pi bond

If you go by this explanation, the Lewis structure of diatomic carbon looks like:

$: \text{C"="C} :$

Those lone pairs of electrons are highly reactive, which is why diatomic carbon can only exist at temperatures close to ${4000}^{\circ} \text{C}$.

The literature article above describes how computational chemistry was able to predict the structure of ${C}_{2}$, which would be a mixture of the ""^1 Sigma_g and ""^3 Pi_g states. These energy states are similar in energy $\left({E}_{{\text{^3 Pi_g) > E_(}}^{1} {\Sigma}_{g}}\right)$, so thermal excitation would allow both to exist more-or-less at the same time.

The ground-state singlet would look like a diradical ${C}_{2}$ with a triple bond:

$\cdot \text{C"-="C} \cdot$

And the ground-state triplet would have two electrons in carbon 1's bonding $p$-orbital lobe and one electron each in carbon 2's bonding and antibonding $p$-orbital lobes.

(the Lewis structure of the standard prediction of diatomic carbon above IS this structure, but doesn't indicate which lobes are being occupied)