Draw the molecular orbital diagrams of : O_2 ; O_2^+ ; O_2^- ?

To draw a molecular orbital (MO) diagram you need to consider which atomic orbitals (AOs) the molecule has.
ATOMIC ORBITAL DIAGRAM FOR OXYGEN ATOM
Oxygen atom is on period 2 so it has access to its ##1s## ##2s## and ##2p## AOs. Their relative energies are ##mathbf(2p > 2s)## ##mathbf(>>)## ##mathbf(1s)##.
(The ##1s## is much much lower in energy than the ##2s## and usually is not even on the MO diagram if done to-scale).
Then note that oxygen atom has ##8## total electrons (including core) so you fill the AOs with ##8## electrons according to:
If you are unsure about any of these rules or principles you should ask for further clarification as I assume you already are familiar with these.
At this point we have the AO diagram as follows for both oxygen atoms:
DETERMINING ATOMIC ORBITAL INTERACTIONS
Next consider which orbitals can interact with each other. That means which ones can overlap to create an effective bond.
For a homonuclear diatomic molecule like ##O_2## this is simple; just choose the orbitals that are alike in look and energy. So the ##2s## interacts with the ##2s## and the ##2p## interacts with the ##2p## etc.
These interactions generate what are called molecular orbitals and they will conserve the number of orbitals. That means with ##mathbf(10)## AOs in you get ##mathbf(10)## MOs out—##5## per oxygen. So we will be drawing ##10## MOs soon.
TYPES OF MOS TO DRAW
Next recall that there exist (##sigma## ##pi## etc) and antibonding (##sigma^*## ##pi^*## etc) orbitals. The former is stabilized (lower in energy) relative to the AOs and the latter is destabilized (higher in energy) relative to the AOs.
When we consider these interactions we’ll see the ##ns## (sigma head-on) interactions:
and the slightly more complicated ##np## (pi sidelong and sigma head-on) interactions:
With ##O_2## the orbital ordering is normal (with ##N_2## it is weirder and you should ask your teacher about an orbital mixing effect if you want to know why). Normal means it is just like what I’m showing you here.
So when we combine what we see here into the full diagram we first get:
And then when we fill the MOs with the ##16## total electrons contributed from both oxygens according to the same three rules and principles defined for the AO diagram we get:
Remember that that was for ##O_2##!
If you have any questions still and if this is still confusing just ask.