Can a bond form between two atoms that don't have 8 electrons?

Question

Generally, atoms like to have 8 valence electrons. But, I'm wondering if it's possible for two types of atoms to form a bond where neither of them gains 8 electrons. Take Carbon, which has 4 valence electrons; and Hydrogen, which has 1. We know that 4 Hydrogen atoms + 1 carbon atom makes a molecule of CH4. But can carbon make a molecule with just one hydrogen atom?

Answer 1

Absolutely! Perhaps the conceptually simplest example to consider is when the prototypical valence-deficient atom, boron, binds to itself.

There are a large number of known, stable diboron compounds containing boron-boron covalent bonds. In the simplest case of a diboron compound with a single covalent bond between boron atoms, we have a diboron(4) compound (the 4 suffix establishes there are four other non-boron atoms bound directly to the boron atoms, implicitly specifying there is a single covalent B-B bond). These are not to be confused with diborane, which is actually an example of a diboron(6) compound and has no boron-boron bond.

There's actually a great open-access review article on the rich chemistry of diboron(4) compounds, which I recommend at least for browsing the chemical structures. Unsurprisingly these compounds often react as you would expect electron-deficient compounds to, readily accepting electron pairs from Lewis bases, for example.

Not all representatives are very stable; alkyl- and hydrogen-substituted diborons are sensitive to water and air and can combust readily. However, they can be stabilised when atoms containing lone electron pairs are next to the boron atoms, as the lone pairs can be partially donated into the empty boron orbital. In these cases it not as clear-cut to say the boron atoms have an unfilled octet.

Diboron(4) compounds are hardly just laboratory curiosities. In particular, tetrahydroxydiboron esters such as bis(pinacolato)diboron are widely used in Miyaura borylation and other borylation reactions, setting things up for Suzuki-Miyaura cross-coupling, one of the most important and widely used C-C bond-forming reactions today.

Also interestingly, it is possible to create double and even triple covalent boron-boron bonds in diborenes and diborynes, though it is certainly rarer. A nice review on this subject can be found here.

Regarding your specific query using carbon, it's rather more difficult to construct something similar. Dicarbon ($\ce{C2}$) is known, though it is very reactive and is found only at high temperatures, such as in flames. It could be said that both atoms in dicarbon have incomplete octets, though pinning down the exact nature of the bonding in this situation can be a delicate matter. I can't think of any simple way to get two valence-deficient carbons to bond.