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Τhe electrons in the antibonding MO are the unpaired electrons of the molecule? E.g. $\ce{O2}$, by writing down the diagram for the MO we notice that there are only 2 electrons in the top antibonding orbitals thus 2 unpaired electrons, yet by writing down the Lewis structure, the molecule turns out to have 0 unpaired electrons.. So, what do the electrons in the anti bonding orbitals do if they don't represent the unpaired electrons of the molecule?

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    $\begingroup$ Refrain from merging multiple questions into one. $\endgroup$ – Zenix Dec 25 '19 at 17:30
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    $\begingroup$ For second part, how did you get two $\sigma$ bonds? $\endgroup$ – Zenix Dec 25 '19 at 17:46
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The antibonding orbital doesn't necessarily tell you the number of unpaired electrons - it's coincidental that for O$_2$, the HOMO (highest occupied molecular orbital) is a (1$\pi_g)^2 $ orbital - or, if you prefer to write it like you have for N$_2$, ($\pi ^1 _{2px} = \pi ^1 _{2py}$). $\pi$ orbitals are doubly degenerate, so the lowest energy configuration is for the 2 electrons to occupy different orbitals (one in each of the 2 $\pi$ orbitals). This means they're both unpaired, as shown in this MO diagram of O$_2$ from Wikipedia. For an example of an MO diagram where there are unpaired electrons in an orbital which is not antibonding, try drawing the B$_2$ MO diagram (remember that s-p mixing occurs).

[MO Diagram of dioxygen

In terms of what they do, antibonding electrons destabilise the bond, "cancelling out" the energetically favourable effect of bonding electrons - try drawing an MO diagram for He$_2$ or Ne$_2$. It should be apparent why they don't form stable molecules.

As far as N$_2$ goes, I think you may have neglected to take into account the effect of the $\sigma ^* _{2s} $ electrons. Remember that antibonding electrons cancel out bonding electrons.

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The Lewis model has weaknesses. O2 is a good example of the failure of the Lewis model. It does not give the good structure for the O2 molecule. The Lewis structure of O2 has no unpaired electrons. But the experiment shows that a jet of O2 is deflected in a magnetic field, which can only be explained by the presence of at least one free electron.

The molecule N2 has one sigma bonds (and not two) and two pi bonds. Why do you think that there is two sigma bonds ?

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    $\begingroup$ Free electron is not the best term $\endgroup$ – Alchimista Dec 27 '19 at 8:19

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