Question

Why is the energy ordering of the `pi` and `sigma` orbitals made from the `2p` atomic orbitals switched going from `"N"_2` to `"O"_2`?

Answer 1

The molecular orbitals of diatomic elements in the second period have orbital mixing effects, and from nitrogen to oxygen, the `sigma_(2p_z)` becomes lower in energy than the `pi_(2p_x)` and `pi_(2p_y)` orbitals since these effects have been decreasing across the period from left to right, and for nitrogen it is borderline.

The relevant orbitals are the `sigma_(g)(2s)` (the `sigma_(2s)`), the `sigma_(g)(2p)` (the `sigma_(2p_z)`), and the `pi_(u)(2p)` (the `pi_(2p_x)` and `pi_(2p_y)`).

Due to orbital mixing effects, which are most prevalent in `"Li"_2` and least prevalent in `"Ne"_2`:

• the `sigma_(g)(2s)` orbital is lower in energy than it would be without these effects.
• the `sigma_(g)(2p)` orbital is higher in energy than it would be without these effects.

These orbital mixing effects have a lesser and lesser effect as we go from left to right on the periodic table, so:

• the `sigma_(g)(2s)` orbital increases in energy (or decreases by less) as we move from left to right on the periodic table.
• the `sigma_(g)(2p)` orbital decreases in energy (or increases by less) as we move from left to right on the periodic table.

You can see that at nitrogen, the `sigma_(g)(2p)` orbital is slightly higher in energy than the `pi_(u)(2p)` orbitals, but for oxygen, the ordering switches.

It's because the orbital energy of the `sigma_(g)(2p)` as been increasing by less and less relative to without the orbital mixing effects, and going from nitrogen to oxygen, the effects are small enough that the `sigma_(g)(2p)` orbitals are overtaken by the `pi_(u)(2p)` orbitals in energy.

As for why the orbitals "mix", the quick reason is because they have the same "symmetry". It's a quantum mechanical phenomenon.