Why do the PE of atoms decrease when they form bonds

[abcd8989]

In fact, why do the PE of atoms decrease when they form bonds, in terms of molecular interpretation, i.e. what actually happened in the atoms making they have lower energies?

 

[alxm]

PE = Potential energy? Anyway.. When two atoms bond, it's the total electronic energy that gets lower.
That includes both kinetic and potential energy. Answering 'what happens' is difficult, because chemical bonding is a fundamentally quantum-mechanical phenomenon (and even if it was classical it'd be difficult to explain). There are different ways of looking at it, which amount to different ways of interpreting the math. The ones most taught are valence-bond theory (orbital hybridization) and molecular orbital theory.

To try to explain the latter one, very briefly: Electrons in atoms can only occupy particular states; orbitals. The Pauli Principle states that you can only have two electrons (with opposite spin) in each orbital. When two atoms get close to each other, the states change. Atomic orbitals 'combine' to become molecular orbitals. There are two ways this can happen: 'Constructively' or 'destructively'; this is analogous to wave interference in classical mechanics (and an example of electrons behaving in a 'wave-like' fashion in quantum mechanics). When the two orbitals interfere constructively, they reinforce each other and you have electronic density between the two atoms. That's what's termed a bonding molecular orbital. When they interfere destructively, they 'cancel out', and you lose electronic density between the atoms. That's called an 'anti-bonding' orbital. Depending on which atomic orbitals combine, you have different kinds of molecular orbitals, each one with a bonding and anti-bonding version. The bonding orbitals always have lower energy, because they're spatially more spread out (which in quantum mechanics means the electrons have less kinetic energy).

So when two hydrogen atoms get close, their 1s atomic orbitals combine to form two σ orbitals, one bonding and one anti-bonding. The bonding orbital, being lowest in energy, gets filled with the two electrons, and so you have a chemical bond. When two helium atoms get close, their 1s atomic orbitals combine in the same way. But since helium has two electrons in its 1s orbital, you have four electrons in total. So both the bonding and anti-bonding σ orbital get filled. The anti-bonding orbital counteracts the bonding orbital, and the result is that they don't bond.

So there are several factors here. The electrons can't move any which way but only occupy certain states. The energy of those states depends on how the kinetic and potential energy of the electrons, which is very complicated in itself, but the states that constitute bond formation are lower in energy than their corresponding anti-bonding ones. However, the Pauli Principle means you can't have more than two in any single state. So the former explains why they bond at all, and the latter is needed to understand why they don't always bond.