physical chemistry - Explaining valence with quantum mechanics

Can anyone give me a quantum mechanical explanation of the theory of valence? (i.e. why atoms bond just enough to have a complete orbital)

EDIT: To clarify, I already have an idea of why atoms bond, and the molecular orbit makes sense to me. The problem is that the valence bond theory provides a simple and fairly accurate description for when a molecule is stable. To make this more concrete: why is CH_4 more stable than CH_3 or CH_5. Looking up the former on wikipedia, I see a better way of phrasing the question might be: why are free radicals reactive? (Should I change the title?)