Reason for repulsion of neutral atoms

Question

One thing that sometimes confuses me is why electrically neutral atoms repel each other at close distances.

Everywhere I try to find an answer says that it’s because of Pauli repulsion at close distances.

The problem I have with that is that Pauli’s exclusion principle is, well, a principle. What would the Pauli force look like even?

Imagine two hydrogen atoms coming close to each other. At some point, the two electrons would begin to repel each other, and although the nuclei would attract each other’s electron, it would not be enough to overcome the repulsion because the Coulomb force scales with the inverse square of distance. Although that seems reasonable, it doesn't really make sense because atoms are neutral and shouldn't repel.

What am I missing here?

Answer 1

Well, first, when two hydrogen atoms approach each other, they attract. Given a way to get rid if the excess energy, they form a molecule. The electrons in the molecule have opposite spin, so the exclusion principle does not prevent them occupying the same phase space.

A better example would be two helium atoms. Each one has a pair of electrons in the lowest energy state. But now, if you bring them together, you're trying to put pairs of electrons into the same state, not allowed by the exclusion principle. The way nature escapes this is by raising the electron momentum, thus the energy, which gives the electrons more room in phase space.

But, to raise the electron energy requires work. Mechanical work is force times distance. So, a repulsive force is required between the atoms in this model.

"What would the Pauli force look like even?" To the extent that anything in the microworld conforms to classical intuition, between helium atoms it resembles the force between two elastic balls. The electron energy is analogous to the elastic energy of a solid. Indeed, much of the elastic energy of solids comes from this process happening at the microscopic level.

Most atoms are not as symmetrical as helium. That makes the Pauli repulsion dependent on direction, and leaves a way for Coulomb attraction to prevail in some directions at some distances. Thus, we get chemistry.