Molecular orbital mixing in second period elements

Why do the $\pi\_u(2p)$ and $\sigma\_g(2p)$ diatomic MO mix within the second period elements as it's shown in the image below?


[![](https://i.stack.imgur.com/XN6Z9.png)](https://i.stack.imgur.com/XN6Z9.png)




If we consider the OM from both 2s and 2p AO, we have the following diagram, which is only valid when the 2s and 2p are far in energy (O2 and F2). This is because as they have a higher Zeff, the 2s orbitals are more stabilized.
For lighter homo-diatomic molecules the AO are very near so they mix


[![](https://i.stack.imgur.com/WrK8l.png)](https://i.stack.imgur.com/WrK8l.png)


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This is a zero order answer but hope it is helpful.


The model that is commonly used to describe the MO is based on the results of expressing the MO as a linear combination of atomic orbitals (LCAO), thus obtaining the MOs and their energies. The contribution of each AO to a particular MO depends on its shape and energy. In general, the LCAO coefficients are optimised to minimise the energy of the molecule and its occupied MO.


Since the atoms of different elements have different nuclear charges and number of electrons, the magnitudes of the attractive nucleus-electron and repulsive electron-electron forces are different and, in consecuence, the energies of AOs of the same type for different elements differ. Thus, when the LCAO method is applied to calculate the MO of a homonuclear diatomic molécule, differences in the energies of the MO are observed.


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