Why Do Atoms (generally) Follow The Octet Rule?

Astrum

I understand that there are a lot of exceptions to the octet rule, but why do atoms generally WANT to be filled up with electrons?

I asked my chemistry friend about this, he didn't have an answer, so I'm assuming that there is a fundamental answer somewhere in QM.

mfb

There are more exceptions than atoms following this rule.
Those atoms have (apart from filled shells) 8 low-energy states for electrons, so they "like" to fill them with electrons. That number of 8 comes from the solution of the Schroedinger equation for hydrogen-like atoms, with some modifications to account for other electrons.

mes314159

Actually, if I understand correctly, the standard Schrodinger equation does not account for the octet rule, since the filling of shells requires the Pauli Exclusion principle (PEP) as well. The PEP is usually treated as an ad hoc extra assumption in basic chemistry QM, whereas in fact it falls directly out of a relativistic treatment, something Schrodinger himself did not do (or did he?). In my opinion this should be treated as more important in basic QM than it typically is, since without the PEP there would be no atoms as we know them, hence no matter and no chemistry (or very different chemistry). The fact that the math of the relativistic solution is hard should not preclude at least an introductory presentation in intro physchem.

mfb

Those are the modifications to account for other electrons - you have to fill other orbitals, and their energy gets modified (in particular, s-orbitals are below p-orbitals and those are below d-orbitals with the same principal quantum number).

Astrum

So, you're saying that the reason that 8 is sometimes favored by hydrogen like atoms, is answered by Schrödingers equations?

mfb

Depends on the interpretation of "answered".
If you look for total antisymmetric solutions for n electrons around a nucleus (satisfying the Schrödinger equation), you get energy levels where you can see that number of 8 with the correct interpretation. This is a messy way to calculate energy levels, however.