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

Actually, diatomic carbon, or `C_2`, does exist, but only as a gas and at extremely high temperatures.

This article from the literature discusses it:
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.

![http://www.reddit.com/r/askscience/comments/2o2emd/is_there_such_a_thing_as_a_quadruple_bond/]()

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_(2s)^(2)`, `pi_(2px)^(2)`, and `pi_(2py)^(2)`, and only 2 occupy an antibonding orbital - `sigma_(2s)^(star 2)`.

The diatomic carbon molecule has a bond order equal to

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

`"B.O." = 1/2(6-2) = 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:

`:"C"="C":`

Those lone pairs of electrons are highly reactive, which is why diatomic carbon can only exist at temperatures close to `4000^@"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 `(E_(""^3 Pi_g) > E_(""^1 Sigma_g))`, 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"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)