# 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?

Sep 3, 2016

The molecular orbitals of diatomic elements in the second period have orbital mixing effects, and from nitrogen to oxygen, the ${\sigma}_{2 {p}_{z}}$ becomes lower in energy than the ${\pi}_{2 {p}_{x}}$ and ${\pi}_{2 {p}_{y}}$ 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 ${\sigma}_{g} \left(2 s\right)$ (the ${\sigma}_{2 s}$), the ${\sigma}_{g} \left(2 p\right)$ (the ${\sigma}_{2 {p}_{z}}$), and the ${\pi}_{u} \left(2 p\right)$ (the ${\pi}_{2 {p}_{x}}$ and ${\pi}_{2 {p}_{y}}$).

Due to orbital mixing effects, which are most prevalent in ${\text{Li}}_{2}$ and least prevalent in ${\text{Ne}}_{2}$:

• the ${\sigma}_{g} \left(2 s\right)$ orbital is lower in energy than it would be without these effects.
• the ${\sigma}_{g} \left(2 p\right)$ 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 ${\sigma}_{g} \left(2 s\right)$ orbital increases in energy (or decreases by less) as we move from left to right on the periodic table.
• the ${\sigma}_{g} \left(2 p\right)$ 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 ${\sigma}_{g} \left(2 p\right)$ orbital is slightly higher in energy than the ${\pi}_{u} \left(2 p\right)$ orbitals, but for oxygen, the ordering switches.

It's because the orbital energy of the ${\sigma}_{g} \left(2 p\right)$ 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 ${\sigma}_{g} \left(2 p\right)$ orbitals are overtaken by the ${\pi}_{u} \left(2 p\right)$ 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.