Why are the pi bonding molecular orbitals (pi_(2p_x), pi_(2p_y)) lower in energy than sigma bonding molecular orbital (sigma_(2p_z)) in the MO diagram of the "N"_2 molecule?

1 Answer
Feb 11, 2016

Because from right to left, the orbital mixing interaction between two compatible orbitals of similar energies decreases the energy of the lower-energy orbital (relative to what it would be without mixing) and increases the energy of the higher-energy orbital (relative to what it would be without mixing).

This effect is still barely present on N_2, so its sigma bonding MO is still higher in energy than its pi bonding MOs.


In "N"_2, the sigma_g(2s) and sigma_g(2p_z) molecular orbitals are compatible (they are both symmetric with respect to infinite rotation and inversion), AND they are close enough in energy (generally within pm "12 eV"), so they mix.

Not surprisingly, this effect is called orbital mixing, and the result of it enhances the bonding with additional electron stabilization. This is often shown for the second-period elements.

Inorganic Chemistry, Miessler et al., Ch. 5.2.3Inorganic Chemistry, Miessler et al., Ch. 5.2.3

From "Li"_2 to "N"_2, we would actually see a trend of the sigma_g(2s) decreasing in energy (faster than) the sigma_g(2p_z) decreases in energy; the effect of orbital mixing decreases as the sigma_g(2s) and sigma_g(2p_z) get farther and farther apart in energy.

Therefore, the effects of the mixing become less and less significant from left to right.

Nitrogen is the last element in the second period for which the diminishing effects of the orbital mixing are still significant enough for the energies of the sigma_g(2p_z) to still be higher than the pi_(u(2p_x)) and pi_(u(2p_y)) in energy.

From "O"_2 through "Ne"_2, the sigma_g(2s) and sigma_g(2p_z) are too far apart in energy to interact, so the orbital mixing effects are no longer as significant.

At that point, the sigma_g(2p_z) has crossed the pi_(u(2p_x)) and pi_(u(2p_y)) orbitals in energy, so the orbital ordering "switches" and these diatomics have a sigma_g(2p_z) MO lower in energy than the pi_(u(2p_x)) and pi_(u(2p_y)) MOs.