Which of the following cannot exist on the basis of MO theory?
To find out about the existence of a molecule, we have to check the bond order. If the bond order is 0 or negative, then the molecule does not exist.
So, to check the bond order,
Let's draw their MO diagrams.
Now,
For H2+→ We have 1 less electron in energy level diagram
For He2+→ We have 1 less electron in energy level diagram (Because of the + sign, i.e., it means one less electron)
Now,
Bond Order = 12 [Bonding electrons - Anti Bonding electrons]
(BE) - (ABE)
For H2+
Bond order = 12 [1 - 0] = 1/2 [Possible]
For He2+
Bond order = 12 [2 - 1] = 1/2 [Possible]
For He2
Bond order = 12 [2 - 2] = 0 [Not possible]
For O2
Bond order =12 [10 - 6] = 2 [Possible]
So, only He2 has bond order 0, therefore not possible.